ETH Price: $2,076.78 (-4.92%)

Transaction Decoder

Block:
24684706 at Mar-18-2026 01:35:59 PM +UTC
Transaction Fee:
0.00003652178884302 ETH $0.08
Gas Used:
155,571 Gas / 0.23475962 Gwei

Emitted Events:

747 PoolManager.Swap( id=2287A9620ADCBF6250DC71BE9EE9B2D3A1EC85A464FC6F5C06669E8D07B61BBA, sender=0x80C554fbe15940fC3ce305cd56A108993c178dbd, amount0=216467628422722344, amount1=-484821468, sqrtPriceX96=3749818820734974022385664, liquidity=38368543467117534, tick=-199178, fee=100 )
748 WETH9.Deposit( dst=0x80C554fbe15940fC3ce305cd56A108993c178dbd, wad=216467628422722344 )
749 WETH9.Transfer( src=0x80C554fbe15940fC3ce305cd56A108993c178dbd, dst=[Receiver] 0xbdb3ba9ffe392549e1f8658dd2630c141fdf47b6, wad=216467628422722344 )
750 TetherToken.Transfer( from=[Receiver] 0xbdb3ba9ffe392549e1f8658dd2630c141fdf47b6, to=0x80C554fbe15940fC3ce305cd56A108993c178dbd, value=484821468 )
751 TetherToken.Transfer( from=0x80C554fbe15940fC3ce305cd56A108993c178dbd, to=PoolManager, value=484821468 )

Account State Difference:

  Address   Before After State Difference Code
0x00000000...e3dE08A90
(Uniswap V4: Pool Manager)
38,739.705601548882850777 Eth38,739.489133920460128433 Eth0.216467628422722344
(Titan Builder)
16.801061739197717756 Eth16.801076035634213432 Eth0.000014296436495676
0x6A5ac574...2578c81F7
2.617980328193232192 Eth
Nonce: 82977
2.617943806379704466 Eth
Nonce: 82978
0.000036521813527726
0xBdb3ba9f...41fDF47B6
(MEV Bot: 0xBdb...7B6)
37.113125392456707518 Eth37.113111096044896548 Eth0.00001429641181097
0xC02aaA39...83C756Cc2 2,227,983.237219050262029787 Eth2,227,983.453686678684752131 Eth0.216467628422722344
0xdAC17F95...13D831ec7

Execution Trace

ETH 0.000000000024684706 MEV Bot: 0xBdb...7B6.70000000( )
  • 0x80c554fbe15940fc3ce305cd56a108993c178dbd.128acb08( )
    • PoolManager.unlock( data=0x000000000000000000000000DAC17F958D2EE523A2206206994597C13D831EC70000000000000000000000000000000000000000000000000000000000000000 ) => ( result=0x000000000000000003010C294181F328FFFFFFFFFFFFFFFFFFFFFFFFE31A3624 )
      • 0x80c554fbe15940fc3ce305cd56a108993c178dbd.91dd7346( )
        • PoolManager.swap( key=[{name:currency0, type:address, order:1, indexed:false, value:0x0000000000000000000000000000000000000000, valueString:0x0000000000000000000000000000000000000000}, {name:currency1, type:address, order:2, indexed:false, value:0xdAC17F958D2ee523a2206206994597C13D831ec7, valueString:0xdAC17F958D2ee523a2206206994597C13D831ec7}, {name:fee, type:uint24, order:3, indexed:false, value:100, valueString:100}, {name:tickSpacing, type:int24, order:4, indexed:false, value:1, valueString:1}, {name:hooks, type:address, order:5, indexed:false, value:0x0000000000000000000000000000000000000000, valueString:0x0000000000000000000000000000000000000000}], params=[{name:zeroForOne, type:bool, order:1, indexed:false, value:false, valueString:False}, {name:amountSpecified, type:int256, order:2, indexed:false, value:-50000000000, valueString:-50000000000}, {name:sqrtPriceLimitX96, type:uint160, order:3, indexed:false, value:3749818820734974022385664, valueString:3749818820734974022385664}], hookData=0x ) => ( swapDelta=73660116961446172826850903022120572246694232210651362852 )
        • PoolManager.take( currency=0x0000000000000000000000000000000000000000, to=0x80C554fbe15940fC3ce305cd56A108993c178dbd, amount=216467628422722344 )
          • ETH 0.216467628422722344 0x80c554fbe15940fc3ce305cd56a108993c178dbd.CALL( )
          • ETH 0.216467628422722344 WETH9.CALL( )
          • WETH9.transfer( dst=0xBdb3ba9ffe392549E1f8658DD2630c141fDF47B6, wad=216467628422722344 ) => ( True )
          • PoolManager.sync( currency=0xdAC17F958D2ee523a2206206994597C13D831ec7 )
            • TetherToken.balanceOf( who=0x000000000004444c5dc75cB358380D2e3dE08A90 ) => ( 36268746904792 )
            • MEV Bot: 0xBdb...7B6.fa461e33( )
              • TetherToken.transfer( _to=0x80C554fbe15940fC3ce305cd56A108993c178dbd, _value=484821468 )
              • TetherToken.transfer( _to=0x000000000004444c5dc75cB358380D2e3dE08A90, _value=484821468 )
              • PoolManager.CALL( )
                • TetherToken.balanceOf( who=0x000000000004444c5dc75cB358380D2e3dE08A90 ) => ( 36269231726260 )
                • ETH 0.000014296436495676 Titan Builder.CALL( )
                  File 1 of 3: PoolManager
                  // SPDX-License-Identifier: BUSL-1.1
                  pragma solidity 0.8.26;
                  import {Hooks} from "./libraries/Hooks.sol";
                  import {Pool} from "./libraries/Pool.sol";
                  import {SafeCast} from "./libraries/SafeCast.sol";
                  import {Position} from "./libraries/Position.sol";
                  import {LPFeeLibrary} from "./libraries/LPFeeLibrary.sol";
                  import {Currency, CurrencyLibrary} from "./types/Currency.sol";
                  import {PoolKey} from "./types/PoolKey.sol";
                  import {TickMath} from "./libraries/TickMath.sol";
                  import {NoDelegateCall} from "./NoDelegateCall.sol";
                  import {IHooks} from "./interfaces/IHooks.sol";
                  import {IPoolManager} from "./interfaces/IPoolManager.sol";
                  import {IUnlockCallback} from "./interfaces/callback/IUnlockCallback.sol";
                  import {ProtocolFees} from "./ProtocolFees.sol";
                  import {ERC6909Claims} from "./ERC6909Claims.sol";
                  import {PoolId} from "./types/PoolId.sol";
                  import {BalanceDelta, BalanceDeltaLibrary} from "./types/BalanceDelta.sol";
                  import {BeforeSwapDelta} from "./types/BeforeSwapDelta.sol";
                  import {Lock} from "./libraries/Lock.sol";
                  import {CurrencyDelta} from "./libraries/CurrencyDelta.sol";
                  import {NonzeroDeltaCount} from "./libraries/NonzeroDeltaCount.sol";
                  import {CurrencyReserves} from "./libraries/CurrencyReserves.sol";
                  import {Extsload} from "./Extsload.sol";
                  import {Exttload} from "./Exttload.sol";
                  import {CustomRevert} from "./libraries/CustomRevert.sol";
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                  /// @title PoolManager
                  /// @notice Holds the state for all pools
                  contract PoolManager is IPoolManager, ProtocolFees, NoDelegateCall, ERC6909Claims, Extsload, Exttload {
                      using SafeCast for *;
                      using Pool for *;
                      using Hooks for IHooks;
                      using CurrencyDelta for Currency;
                      using LPFeeLibrary for uint24;
                      using CurrencyReserves for Currency;
                      using CustomRevert for bytes4;
                      int24 private constant MAX_TICK_SPACING = TickMath.MAX_TICK_SPACING;
                      int24 private constant MIN_TICK_SPACING = TickMath.MIN_TICK_SPACING;
                      mapping(PoolId id => Pool.State) internal _pools;
                      /// @notice This will revert if the contract is locked
                      modifier onlyWhenUnlocked() {
                          if (!Lock.isUnlocked()) ManagerLocked.selector.revertWith();
                          _;
                      }
                      constructor(address initialOwner) ProtocolFees(initialOwner) {}
                      /// @inheritdoc IPoolManager
                      function unlock(bytes calldata data) external override returns (bytes memory result) {
                          if (Lock.isUnlocked()) AlreadyUnlocked.selector.revertWith();
                          Lock.unlock();
                          // the caller does everything in this callback, including paying what they owe via calls to settle
                          result = IUnlockCallback(msg.sender).unlockCallback(data);
                          if (NonzeroDeltaCount.read() != 0) CurrencyNotSettled.selector.revertWith();
                          Lock.lock();
                      }
                      /// @inheritdoc IPoolManager
                      function initialize(PoolKey memory key, uint160 sqrtPriceX96) external noDelegateCall returns (int24 tick) {
                          // see TickBitmap.sol for overflow conditions that can arise from tick spacing being too large
                          if (key.tickSpacing > MAX_TICK_SPACING) TickSpacingTooLarge.selector.revertWith(key.tickSpacing);
                          if (key.tickSpacing < MIN_TICK_SPACING) TickSpacingTooSmall.selector.revertWith(key.tickSpacing);
                          if (key.currency0 >= key.currency1) {
                              CurrenciesOutOfOrderOrEqual.selector.revertWith(
                                  Currency.unwrap(key.currency0), Currency.unwrap(key.currency1)
                              );
                          }
                          if (!key.hooks.isValidHookAddress(key.fee)) Hooks.HookAddressNotValid.selector.revertWith(address(key.hooks));
                          uint24 lpFee = key.fee.getInitialLPFee();
                          key.hooks.beforeInitialize(key, sqrtPriceX96);
                          PoolId id = key.toId();
                          tick = _pools[id].initialize(sqrtPriceX96, lpFee);
                          // event is emitted before the afterInitialize call to ensure events are always emitted in order
                          // emit all details of a pool key. poolkeys are not saved in storage and must always be provided by the caller
                          // the key's fee may be a static fee or a sentinel to denote a dynamic fee.
                          emit Initialize(id, key.currency0, key.currency1, key.fee, key.tickSpacing, key.hooks, sqrtPriceX96, tick);
                          key.hooks.afterInitialize(key, sqrtPriceX96, tick);
                      }
                      /// @inheritdoc IPoolManager
                      function modifyLiquidity(
                          PoolKey memory key,
                          IPoolManager.ModifyLiquidityParams memory params,
                          bytes calldata hookData
                      ) external onlyWhenUnlocked noDelegateCall returns (BalanceDelta callerDelta, BalanceDelta feesAccrued) {
                          PoolId id = key.toId();
                          {
                              Pool.State storage pool = _getPool(id);
                              pool.checkPoolInitialized();
                              key.hooks.beforeModifyLiquidity(key, params, hookData);
                              BalanceDelta principalDelta;
                              (principalDelta, feesAccrued) = pool.modifyLiquidity(
                                  Pool.ModifyLiquidityParams({
                                      owner: msg.sender,
                                      tickLower: params.tickLower,
                                      tickUpper: params.tickUpper,
                                      liquidityDelta: params.liquidityDelta.toInt128(),
                                      tickSpacing: key.tickSpacing,
                                      salt: params.salt
                                  })
                              );
                              // fee delta and principal delta are both accrued to the caller
                              callerDelta = principalDelta + feesAccrued;
                          }
                          // event is emitted before the afterModifyLiquidity call to ensure events are always emitted in order
                          emit ModifyLiquidity(id, msg.sender, params.tickLower, params.tickUpper, params.liquidityDelta, params.salt);
                          BalanceDelta hookDelta;
                          (callerDelta, hookDelta) = key.hooks.afterModifyLiquidity(key, params, callerDelta, feesAccrued, hookData);
                          // if the hook doesn't have the flag to be able to return deltas, hookDelta will always be 0
                          if (hookDelta != BalanceDeltaLibrary.ZERO_DELTA) _accountPoolBalanceDelta(key, hookDelta, address(key.hooks));
                          _accountPoolBalanceDelta(key, callerDelta, msg.sender);
                      }
                      /// @inheritdoc IPoolManager
                      function swap(PoolKey memory key, IPoolManager.SwapParams memory params, bytes calldata hookData)
                          external
                          onlyWhenUnlocked
                          noDelegateCall
                          returns (BalanceDelta swapDelta)
                      {
                          if (params.amountSpecified == 0) SwapAmountCannotBeZero.selector.revertWith();
                          PoolId id = key.toId();
                          Pool.State storage pool = _getPool(id);
                          pool.checkPoolInitialized();
                          BeforeSwapDelta beforeSwapDelta;
                          {
                              int256 amountToSwap;
                              uint24 lpFeeOverride;
                              (amountToSwap, beforeSwapDelta, lpFeeOverride) = key.hooks.beforeSwap(key, params, hookData);
                              // execute swap, account protocol fees, and emit swap event
                              // _swap is needed to avoid stack too deep error
                              swapDelta = _swap(
                                  pool,
                                  id,
                                  Pool.SwapParams({
                                      tickSpacing: key.tickSpacing,
                                      zeroForOne: params.zeroForOne,
                                      amountSpecified: amountToSwap,
                                      sqrtPriceLimitX96: params.sqrtPriceLimitX96,
                                      lpFeeOverride: lpFeeOverride
                                  }),
                                  params.zeroForOne ? key.currency0 : key.currency1 // input token
                              );
                          }
                          BalanceDelta hookDelta;
                          (swapDelta, hookDelta) = key.hooks.afterSwap(key, params, swapDelta, hookData, beforeSwapDelta);
                          // if the hook doesn't have the flag to be able to return deltas, hookDelta will always be 0
                          if (hookDelta != BalanceDeltaLibrary.ZERO_DELTA) _accountPoolBalanceDelta(key, hookDelta, address(key.hooks));
                          _accountPoolBalanceDelta(key, swapDelta, msg.sender);
                      }
                      /// @notice Internal swap function to execute a swap, take protocol fees on input token, and emit the swap event
                      function _swap(Pool.State storage pool, PoolId id, Pool.SwapParams memory params, Currency inputCurrency)
                          internal
                          returns (BalanceDelta)
                      {
                          (BalanceDelta delta, uint256 amountToProtocol, uint24 swapFee, Pool.SwapResult memory result) =
                              pool.swap(params);
                          // the fee is on the input currency
                          if (amountToProtocol > 0) _updateProtocolFees(inputCurrency, amountToProtocol);
                          // event is emitted before the afterSwap call to ensure events are always emitted in order
                          emit Swap(
                              id,
                              msg.sender,
                              delta.amount0(),
                              delta.amount1(),
                              result.sqrtPriceX96,
                              result.liquidity,
                              result.tick,
                              swapFee
                          );
                          return delta;
                      }
                      /// @inheritdoc IPoolManager
                      function donate(PoolKey memory key, uint256 amount0, uint256 amount1, bytes calldata hookData)
                          external
                          onlyWhenUnlocked
                          noDelegateCall
                          returns (BalanceDelta delta)
                      {
                          PoolId poolId = key.toId();
                          Pool.State storage pool = _getPool(poolId);
                          pool.checkPoolInitialized();
                          key.hooks.beforeDonate(key, amount0, amount1, hookData);
                          delta = pool.donate(amount0, amount1);
                          _accountPoolBalanceDelta(key, delta, msg.sender);
                          // event is emitted before the afterDonate call to ensure events are always emitted in order
                          emit Donate(poolId, msg.sender, amount0, amount1);
                          key.hooks.afterDonate(key, amount0, amount1, hookData);
                      }
                      /// @inheritdoc IPoolManager
                      function sync(Currency currency) external {
                          // address(0) is used for the native currency
                          if (currency.isAddressZero()) {
                              // The reserves balance is not used for native settling, so we only need to reset the currency.
                              CurrencyReserves.resetCurrency();
                          } else {
                              uint256 balance = currency.balanceOfSelf();
                              CurrencyReserves.syncCurrencyAndReserves(currency, balance);
                          }
                      }
                      /// @inheritdoc IPoolManager
                      function take(Currency currency, address to, uint256 amount) external onlyWhenUnlocked {
                          unchecked {
                              // negation must be safe as amount is not negative
                              _accountDelta(currency, -(amount.toInt128()), msg.sender);
                              currency.transfer(to, amount);
                          }
                      }
                      /// @inheritdoc IPoolManager
                      function settle() external payable onlyWhenUnlocked returns (uint256) {
                          return _settle(msg.sender);
                      }
                      /// @inheritdoc IPoolManager
                      function settleFor(address recipient) external payable onlyWhenUnlocked returns (uint256) {
                          return _settle(recipient);
                      }
                      /// @inheritdoc IPoolManager
                      function clear(Currency currency, uint256 amount) external onlyWhenUnlocked {
                          int256 current = currency.getDelta(msg.sender);
                          // Because input is `uint256`, only positive amounts can be cleared.
                          int128 amountDelta = amount.toInt128();
                          if (amountDelta != current) MustClearExactPositiveDelta.selector.revertWith();
                          // negation must be safe as amountDelta is positive
                          unchecked {
                              _accountDelta(currency, -(amountDelta), msg.sender);
                          }
                      }
                      /// @inheritdoc IPoolManager
                      function mint(address to, uint256 id, uint256 amount) external onlyWhenUnlocked {
                          unchecked {
                              Currency currency = CurrencyLibrary.fromId(id);
                              // negation must be safe as amount is not negative
                              _accountDelta(currency, -(amount.toInt128()), msg.sender);
                              _mint(to, currency.toId(), amount);
                          }
                      }
                      /// @inheritdoc IPoolManager
                      function burn(address from, uint256 id, uint256 amount) external onlyWhenUnlocked {
                          Currency currency = CurrencyLibrary.fromId(id);
                          _accountDelta(currency, amount.toInt128(), msg.sender);
                          _burnFrom(from, currency.toId(), amount);
                      }
                      /// @inheritdoc IPoolManager
                      function updateDynamicLPFee(PoolKey memory key, uint24 newDynamicLPFee) external {
                          if (!key.fee.isDynamicFee() || msg.sender != address(key.hooks)) {
                              UnauthorizedDynamicLPFeeUpdate.selector.revertWith();
                          }
                          newDynamicLPFee.validate();
                          PoolId id = key.toId();
                          _pools[id].setLPFee(newDynamicLPFee);
                      }
                      // if settling native, integrators should still call `sync` first to avoid DoS attack vectors
                      function _settle(address recipient) internal returns (uint256 paid) {
                          Currency currency = CurrencyReserves.getSyncedCurrency();
                          // if not previously synced, or the syncedCurrency slot has been reset, expects native currency to be settled
                          if (currency.isAddressZero()) {
                              paid = msg.value;
                          } else {
                              if (msg.value > 0) NonzeroNativeValue.selector.revertWith();
                              // Reserves are guaranteed to be set because currency and reserves are always set together
                              uint256 reservesBefore = CurrencyReserves.getSyncedReserves();
                              uint256 reservesNow = currency.balanceOfSelf();
                              paid = reservesNow - reservesBefore;
                              CurrencyReserves.resetCurrency();
                          }
                          _accountDelta(currency, paid.toInt128(), recipient);
                      }
                      /// @notice Adds a balance delta in a currency for a target address
                      function _accountDelta(Currency currency, int128 delta, address target) internal {
                          if (delta == 0) return;
                          (int256 previous, int256 next) = currency.applyDelta(target, delta);
                          if (next == 0) {
                              NonzeroDeltaCount.decrement();
                          } else if (previous == 0) {
                              NonzeroDeltaCount.increment();
                          }
                      }
                      /// @notice Accounts the deltas of 2 currencies to a target address
                      function _accountPoolBalanceDelta(PoolKey memory key, BalanceDelta delta, address target) internal {
                          _accountDelta(key.currency0, delta.amount0(), target);
                          _accountDelta(key.currency1, delta.amount1(), target);
                      }
                      /// @notice Implementation of the _getPool function defined in ProtocolFees
                      function _getPool(PoolId id) internal view override returns (Pool.State storage) {
                          return _pools[id];
                      }
                      /// @notice Implementation of the _isUnlocked function defined in ProtocolFees
                      function _isUnlocked() internal view override returns (bool) {
                          return Lock.isUnlocked();
                      }
                  }
                  // SPDX-License-Identifier: MIT
                  pragma solidity ^0.8.0;
                  import {PoolKey} from "../types/PoolKey.sol";
                  import {IHooks} from "../interfaces/IHooks.sol";
                  import {SafeCast} from "./SafeCast.sol";
                  import {LPFeeLibrary} from "./LPFeeLibrary.sol";
                  import {BalanceDelta, toBalanceDelta, BalanceDeltaLibrary} from "../types/BalanceDelta.sol";
                  import {BeforeSwapDelta, BeforeSwapDeltaLibrary} from "../types/BeforeSwapDelta.sol";
                  import {IPoolManager} from "../interfaces/IPoolManager.sol";
                  import {ParseBytes} from "./ParseBytes.sol";
                  import {CustomRevert} from "./CustomRevert.sol";
                  /// @notice V4 decides whether to invoke specific hooks by inspecting the least significant bits
                  /// of the address that the hooks contract is deployed to.
                  /// For example, a hooks contract deployed to address: 0x0000000000000000000000000000000000002400
                  /// has the lowest bits '10 0100 0000 0000' which would cause the 'before initialize' and 'after add liquidity' hooks to be used.
                  library Hooks {
                      using LPFeeLibrary for uint24;
                      using Hooks for IHooks;
                      using SafeCast for int256;
                      using BeforeSwapDeltaLibrary for BeforeSwapDelta;
                      using ParseBytes for bytes;
                      using CustomRevert for bytes4;
                      uint160 internal constant ALL_HOOK_MASK = uint160((1 << 14) - 1);
                      uint160 internal constant BEFORE_INITIALIZE_FLAG = 1 << 13;
                      uint160 internal constant AFTER_INITIALIZE_FLAG = 1 << 12;
                      uint160 internal constant BEFORE_ADD_LIQUIDITY_FLAG = 1 << 11;
                      uint160 internal constant AFTER_ADD_LIQUIDITY_FLAG = 1 << 10;
                      uint160 internal constant BEFORE_REMOVE_LIQUIDITY_FLAG = 1 << 9;
                      uint160 internal constant AFTER_REMOVE_LIQUIDITY_FLAG = 1 << 8;
                      uint160 internal constant BEFORE_SWAP_FLAG = 1 << 7;
                      uint160 internal constant AFTER_SWAP_FLAG = 1 << 6;
                      uint160 internal constant BEFORE_DONATE_FLAG = 1 << 5;
                      uint160 internal constant AFTER_DONATE_FLAG = 1 << 4;
                      uint160 internal constant BEFORE_SWAP_RETURNS_DELTA_FLAG = 1 << 3;
                      uint160 internal constant AFTER_SWAP_RETURNS_DELTA_FLAG = 1 << 2;
                      uint160 internal constant AFTER_ADD_LIQUIDITY_RETURNS_DELTA_FLAG = 1 << 1;
                      uint160 internal constant AFTER_REMOVE_LIQUIDITY_RETURNS_DELTA_FLAG = 1 << 0;
                      struct Permissions {
                          bool beforeInitialize;
                          bool afterInitialize;
                          bool beforeAddLiquidity;
                          bool afterAddLiquidity;
                          bool beforeRemoveLiquidity;
                          bool afterRemoveLiquidity;
                          bool beforeSwap;
                          bool afterSwap;
                          bool beforeDonate;
                          bool afterDonate;
                          bool beforeSwapReturnDelta;
                          bool afterSwapReturnDelta;
                          bool afterAddLiquidityReturnDelta;
                          bool afterRemoveLiquidityReturnDelta;
                      }
                      /// @notice Thrown if the address will not lead to the specified hook calls being called
                      /// @param hooks The address of the hooks contract
                      error HookAddressNotValid(address hooks);
                      /// @notice Hook did not return its selector
                      error InvalidHookResponse();
                      /// @notice Additional context for ERC-7751 wrapped error when a hook call fails
                      error HookCallFailed();
                      /// @notice The hook's delta changed the swap from exactIn to exactOut or vice versa
                      error HookDeltaExceedsSwapAmount();
                      /// @notice Utility function intended to be used in hook constructors to ensure
                      /// the deployed hooks address causes the intended hooks to be called
                      /// @param permissions The hooks that are intended to be called
                      /// @dev permissions param is memory as the function will be called from constructors
                      function validateHookPermissions(IHooks self, Permissions memory permissions) internal pure {
                          if (
                              permissions.beforeInitialize != self.hasPermission(BEFORE_INITIALIZE_FLAG)
                                  || permissions.afterInitialize != self.hasPermission(AFTER_INITIALIZE_FLAG)
                                  || permissions.beforeAddLiquidity != self.hasPermission(BEFORE_ADD_LIQUIDITY_FLAG)
                                  || permissions.afterAddLiquidity != self.hasPermission(AFTER_ADD_LIQUIDITY_FLAG)
                                  || permissions.beforeRemoveLiquidity != self.hasPermission(BEFORE_REMOVE_LIQUIDITY_FLAG)
                                  || permissions.afterRemoveLiquidity != self.hasPermission(AFTER_REMOVE_LIQUIDITY_FLAG)
                                  || permissions.beforeSwap != self.hasPermission(BEFORE_SWAP_FLAG)
                                  || permissions.afterSwap != self.hasPermission(AFTER_SWAP_FLAG)
                                  || permissions.beforeDonate != self.hasPermission(BEFORE_DONATE_FLAG)
                                  || permissions.afterDonate != self.hasPermission(AFTER_DONATE_FLAG)
                                  || permissions.beforeSwapReturnDelta != self.hasPermission(BEFORE_SWAP_RETURNS_DELTA_FLAG)
                                  || permissions.afterSwapReturnDelta != self.hasPermission(AFTER_SWAP_RETURNS_DELTA_FLAG)
                                  || permissions.afterAddLiquidityReturnDelta != self.hasPermission(AFTER_ADD_LIQUIDITY_RETURNS_DELTA_FLAG)
                                  || permissions.afterRemoveLiquidityReturnDelta
                                      != self.hasPermission(AFTER_REMOVE_LIQUIDITY_RETURNS_DELTA_FLAG)
                          ) {
                              HookAddressNotValid.selector.revertWith(address(self));
                          }
                      }
                      /// @notice Ensures that the hook address includes at least one hook flag or dynamic fees, or is the 0 address
                      /// @param self The hook to verify
                      /// @param fee The fee of the pool the hook is used with
                      /// @return bool True if the hook address is valid
                      function isValidHookAddress(IHooks self, uint24 fee) internal pure returns (bool) {
                          // The hook can only have a flag to return a hook delta on an action if it also has the corresponding action flag
                          if (!self.hasPermission(BEFORE_SWAP_FLAG) && self.hasPermission(BEFORE_SWAP_RETURNS_DELTA_FLAG)) return false;
                          if (!self.hasPermission(AFTER_SWAP_FLAG) && self.hasPermission(AFTER_SWAP_RETURNS_DELTA_FLAG)) return false;
                          if (!self.hasPermission(AFTER_ADD_LIQUIDITY_FLAG) && self.hasPermission(AFTER_ADD_LIQUIDITY_RETURNS_DELTA_FLAG))
                          {
                              return false;
                          }
                          if (
                              !self.hasPermission(AFTER_REMOVE_LIQUIDITY_FLAG)
                                  && self.hasPermission(AFTER_REMOVE_LIQUIDITY_RETURNS_DELTA_FLAG)
                          ) return false;
                          // If there is no hook contract set, then fee cannot be dynamic
                          // If a hook contract is set, it must have at least 1 flag set, or have a dynamic fee
                          return address(self) == address(0)
                              ? !fee.isDynamicFee()
                              : (uint160(address(self)) & ALL_HOOK_MASK > 0 || fee.isDynamicFee());
                      }
                      /// @notice performs a hook call using the given calldata on the given hook that doesn't return a delta
                      /// @return result The complete data returned by the hook
                      function callHook(IHooks self, bytes memory data) internal returns (bytes memory result) {
                          bool success;
                          assembly ("memory-safe") {
                              success := call(gas(), self, 0, add(data, 0x20), mload(data), 0, 0)
                          }
                          // Revert with FailedHookCall, containing any error message to bubble up
                          if (!success) CustomRevert.bubbleUpAndRevertWith(address(self), bytes4(data), HookCallFailed.selector);
                          // The call was successful, fetch the returned data
                          assembly ("memory-safe") {
                              // allocate result byte array from the free memory pointer
                              result := mload(0x40)
                              // store new free memory pointer at the end of the array padded to 32 bytes
                              mstore(0x40, add(result, and(add(returndatasize(), 0x3f), not(0x1f))))
                              // store length in memory
                              mstore(result, returndatasize())
                              // copy return data to result
                              returndatacopy(add(result, 0x20), 0, returndatasize())
                          }
                          // Length must be at least 32 to contain the selector. Check expected selector and returned selector match.
                          if (result.length < 32 || result.parseSelector() != data.parseSelector()) {
                              InvalidHookResponse.selector.revertWith();
                          }
                      }
                      /// @notice performs a hook call using the given calldata on the given hook
                      /// @return int256 The delta returned by the hook
                      function callHookWithReturnDelta(IHooks self, bytes memory data, bool parseReturn) internal returns (int256) {
                          bytes memory result = callHook(self, data);
                          // If this hook wasn't meant to return something, default to 0 delta
                          if (!parseReturn) return 0;
                          // A length of 64 bytes is required to return a bytes4, and a 32 byte delta
                          if (result.length != 64) InvalidHookResponse.selector.revertWith();
                          return result.parseReturnDelta();
                      }
                      /// @notice modifier to prevent calling a hook if they initiated the action
                      modifier noSelfCall(IHooks self) {
                          if (msg.sender != address(self)) {
                              _;
                          }
                      }
                      /// @notice calls beforeInitialize hook if permissioned and validates return value
                      function beforeInitialize(IHooks self, PoolKey memory key, uint160 sqrtPriceX96) internal noSelfCall(self) {
                          if (self.hasPermission(BEFORE_INITIALIZE_FLAG)) {
                              self.callHook(abi.encodeCall(IHooks.beforeInitialize, (msg.sender, key, sqrtPriceX96)));
                          }
                      }
                      /// @notice calls afterInitialize hook if permissioned and validates return value
                      function afterInitialize(IHooks self, PoolKey memory key, uint160 sqrtPriceX96, int24 tick)
                          internal
                          noSelfCall(self)
                      {
                          if (self.hasPermission(AFTER_INITIALIZE_FLAG)) {
                              self.callHook(abi.encodeCall(IHooks.afterInitialize, (msg.sender, key, sqrtPriceX96, tick)));
                          }
                      }
                      /// @notice calls beforeModifyLiquidity hook if permissioned and validates return value
                      function beforeModifyLiquidity(
                          IHooks self,
                          PoolKey memory key,
                          IPoolManager.ModifyLiquidityParams memory params,
                          bytes calldata hookData
                      ) internal noSelfCall(self) {
                          if (params.liquidityDelta > 0 && self.hasPermission(BEFORE_ADD_LIQUIDITY_FLAG)) {
                              self.callHook(abi.encodeCall(IHooks.beforeAddLiquidity, (msg.sender, key, params, hookData)));
                          } else if (params.liquidityDelta <= 0 && self.hasPermission(BEFORE_REMOVE_LIQUIDITY_FLAG)) {
                              self.callHook(abi.encodeCall(IHooks.beforeRemoveLiquidity, (msg.sender, key, params, hookData)));
                          }
                      }
                      /// @notice calls afterModifyLiquidity hook if permissioned and validates return value
                      function afterModifyLiquidity(
                          IHooks self,
                          PoolKey memory key,
                          IPoolManager.ModifyLiquidityParams memory params,
                          BalanceDelta delta,
                          BalanceDelta feesAccrued,
                          bytes calldata hookData
                      ) internal returns (BalanceDelta callerDelta, BalanceDelta hookDelta) {
                          if (msg.sender == address(self)) return (delta, BalanceDeltaLibrary.ZERO_DELTA);
                          callerDelta = delta;
                          if (params.liquidityDelta > 0) {
                              if (self.hasPermission(AFTER_ADD_LIQUIDITY_FLAG)) {
                                  hookDelta = BalanceDelta.wrap(
                                      self.callHookWithReturnDelta(
                                          abi.encodeCall(
                                              IHooks.afterAddLiquidity, (msg.sender, key, params, delta, feesAccrued, hookData)
                                          ),
                                          self.hasPermission(AFTER_ADD_LIQUIDITY_RETURNS_DELTA_FLAG)
                                      )
                                  );
                                  callerDelta = callerDelta - hookDelta;
                              }
                          } else {
                              if (self.hasPermission(AFTER_REMOVE_LIQUIDITY_FLAG)) {
                                  hookDelta = BalanceDelta.wrap(
                                      self.callHookWithReturnDelta(
                                          abi.encodeCall(
                                              IHooks.afterRemoveLiquidity, (msg.sender, key, params, delta, feesAccrued, hookData)
                                          ),
                                          self.hasPermission(AFTER_REMOVE_LIQUIDITY_RETURNS_DELTA_FLAG)
                                      )
                                  );
                                  callerDelta = callerDelta - hookDelta;
                              }
                          }
                      }
                      /// @notice calls beforeSwap hook if permissioned and validates return value
                      function beforeSwap(IHooks self, PoolKey memory key, IPoolManager.SwapParams memory params, bytes calldata hookData)
                          internal
                          returns (int256 amountToSwap, BeforeSwapDelta hookReturn, uint24 lpFeeOverride)
                      {
                          amountToSwap = params.amountSpecified;
                          if (msg.sender == address(self)) return (amountToSwap, BeforeSwapDeltaLibrary.ZERO_DELTA, lpFeeOverride);
                          if (self.hasPermission(BEFORE_SWAP_FLAG)) {
                              bytes memory result = callHook(self, abi.encodeCall(IHooks.beforeSwap, (msg.sender, key, params, hookData)));
                              // A length of 96 bytes is required to return a bytes4, a 32 byte delta, and an LP fee
                              if (result.length != 96) InvalidHookResponse.selector.revertWith();
                              // dynamic fee pools that want to override the cache fee, return a valid fee with the override flag. If override flag
                              // is set but an invalid fee is returned, the transaction will revert. Otherwise the current LP fee will be used
                              if (key.fee.isDynamicFee()) lpFeeOverride = result.parseFee();
                              // skip this logic for the case where the hook return is 0
                              if (self.hasPermission(BEFORE_SWAP_RETURNS_DELTA_FLAG)) {
                                  hookReturn = BeforeSwapDelta.wrap(result.parseReturnDelta());
                                  // any return in unspecified is passed to the afterSwap hook for handling
                                  int128 hookDeltaSpecified = hookReturn.getSpecifiedDelta();
                                  // Update the swap amount according to the hook's return, and check that the swap type doesn't change (exact input/output)
                                  if (hookDeltaSpecified != 0) {
                                      bool exactInput = amountToSwap < 0;
                                      amountToSwap += hookDeltaSpecified;
                                      if (exactInput ? amountToSwap > 0 : amountToSwap < 0) {
                                          HookDeltaExceedsSwapAmount.selector.revertWith();
                                      }
                                  }
                              }
                          }
                      }
                      /// @notice calls afterSwap hook if permissioned and validates return value
                      function afterSwap(
                          IHooks self,
                          PoolKey memory key,
                          IPoolManager.SwapParams memory params,
                          BalanceDelta swapDelta,
                          bytes calldata hookData,
                          BeforeSwapDelta beforeSwapHookReturn
                      ) internal returns (BalanceDelta, BalanceDelta) {
                          if (msg.sender == address(self)) return (swapDelta, BalanceDeltaLibrary.ZERO_DELTA);
                          int128 hookDeltaSpecified = beforeSwapHookReturn.getSpecifiedDelta();
                          int128 hookDeltaUnspecified = beforeSwapHookReturn.getUnspecifiedDelta();
                          if (self.hasPermission(AFTER_SWAP_FLAG)) {
                              hookDeltaUnspecified += self.callHookWithReturnDelta(
                                  abi.encodeCall(IHooks.afterSwap, (msg.sender, key, params, swapDelta, hookData)),
                                  self.hasPermission(AFTER_SWAP_RETURNS_DELTA_FLAG)
                              ).toInt128();
                          }
                          BalanceDelta hookDelta;
                          if (hookDeltaUnspecified != 0 || hookDeltaSpecified != 0) {
                              hookDelta = (params.amountSpecified < 0 == params.zeroForOne)
                                  ? toBalanceDelta(hookDeltaSpecified, hookDeltaUnspecified)
                                  : toBalanceDelta(hookDeltaUnspecified, hookDeltaSpecified);
                              // the caller has to pay for (or receive) the hook's delta
                              swapDelta = swapDelta - hookDelta;
                          }
                          return (swapDelta, hookDelta);
                      }
                      /// @notice calls beforeDonate hook if permissioned and validates return value
                      function beforeDonate(IHooks self, PoolKey memory key, uint256 amount0, uint256 amount1, bytes calldata hookData)
                          internal
                          noSelfCall(self)
                      {
                          if (self.hasPermission(BEFORE_DONATE_FLAG)) {
                              self.callHook(abi.encodeCall(IHooks.beforeDonate, (msg.sender, key, amount0, amount1, hookData)));
                          }
                      }
                      /// @notice calls afterDonate hook if permissioned and validates return value
                      function afterDonate(IHooks self, PoolKey memory key, uint256 amount0, uint256 amount1, bytes calldata hookData)
                          internal
                          noSelfCall(self)
                      {
                          if (self.hasPermission(AFTER_DONATE_FLAG)) {
                              self.callHook(abi.encodeCall(IHooks.afterDonate, (msg.sender, key, amount0, amount1, hookData)));
                          }
                      }
                      function hasPermission(IHooks self, uint160 flag) internal pure returns (bool) {
                          return uint160(address(self)) & flag != 0;
                      }
                  }
                  // SPDX-License-Identifier: BUSL-1.1
                  pragma solidity ^0.8.0;
                  import {SafeCast} from "./SafeCast.sol";
                  import {TickBitmap} from "./TickBitmap.sol";
                  import {Position} from "./Position.sol";
                  import {UnsafeMath} from "./UnsafeMath.sol";
                  import {FixedPoint128} from "./FixedPoint128.sol";
                  import {TickMath} from "./TickMath.sol";
                  import {SqrtPriceMath} from "./SqrtPriceMath.sol";
                  import {SwapMath} from "./SwapMath.sol";
                  import {BalanceDelta, toBalanceDelta, BalanceDeltaLibrary} from "../types/BalanceDelta.sol";
                  import {Slot0} from "../types/Slot0.sol";
                  import {ProtocolFeeLibrary} from "./ProtocolFeeLibrary.sol";
                  import {LiquidityMath} from "./LiquidityMath.sol";
                  import {LPFeeLibrary} from "./LPFeeLibrary.sol";
                  import {CustomRevert} from "./CustomRevert.sol";
                  /// @notice a library with all actions that can be performed on a pool
                  library Pool {
                      using SafeCast for *;
                      using TickBitmap for mapping(int16 => uint256);
                      using Position for mapping(bytes32 => Position.State);
                      using Position for Position.State;
                      using Pool for State;
                      using ProtocolFeeLibrary for *;
                      using LPFeeLibrary for uint24;
                      using CustomRevert for bytes4;
                      /// @notice Thrown when tickLower is not below tickUpper
                      /// @param tickLower The invalid tickLower
                      /// @param tickUpper The invalid tickUpper
                      error TicksMisordered(int24 tickLower, int24 tickUpper);
                      /// @notice Thrown when tickLower is less than min tick
                      /// @param tickLower The invalid tickLower
                      error TickLowerOutOfBounds(int24 tickLower);
                      /// @notice Thrown when tickUpper exceeds max tick
                      /// @param tickUpper The invalid tickUpper
                      error TickUpperOutOfBounds(int24 tickUpper);
                      /// @notice For the tick spacing, the tick has too much liquidity
                      error TickLiquidityOverflow(int24 tick);
                      /// @notice Thrown when trying to initialize an already initialized pool
                      error PoolAlreadyInitialized();
                      /// @notice Thrown when trying to interact with a non-initialized pool
                      error PoolNotInitialized();
                      /// @notice Thrown when sqrtPriceLimitX96 on a swap has already exceeded its limit
                      /// @param sqrtPriceCurrentX96 The invalid, already surpassed sqrtPriceLimitX96
                      /// @param sqrtPriceLimitX96 The surpassed price limit
                      error PriceLimitAlreadyExceeded(uint160 sqrtPriceCurrentX96, uint160 sqrtPriceLimitX96);
                      /// @notice Thrown when sqrtPriceLimitX96 lies outside of valid tick/price range
                      /// @param sqrtPriceLimitX96 The invalid, out-of-bounds sqrtPriceLimitX96
                      error PriceLimitOutOfBounds(uint160 sqrtPriceLimitX96);
                      /// @notice Thrown by donate if there is currently 0 liquidity, since the fees will not go to any liquidity providers
                      error NoLiquidityToReceiveFees();
                      /// @notice Thrown when trying to swap with max lp fee and specifying an output amount
                      error InvalidFeeForExactOut();
                      // info stored for each initialized individual tick
                      struct TickInfo {
                          // the total position liquidity that references this tick
                          uint128 liquidityGross;
                          // amount of net liquidity added (subtracted) when tick is crossed from left to right (right to left),
                          int128 liquidityNet;
                          // fee growth per unit of liquidity on the _other_ side of this tick (relative to the current tick)
                          // only has relative meaning, not absolute — the value depends on when the tick is initialized
                          uint256 feeGrowthOutside0X128;
                          uint256 feeGrowthOutside1X128;
                      }
                      /// @notice The state of a pool
                      /// @dev Note that feeGrowthGlobal can be artificially inflated
                      /// For pools with a single liquidity position, actors can donate to themselves to freely inflate feeGrowthGlobal
                      /// atomically donating and collecting fees in the same unlockCallback may make the inflated value more extreme
                      struct State {
                          Slot0 slot0;
                          uint256 feeGrowthGlobal0X128;
                          uint256 feeGrowthGlobal1X128;
                          uint128 liquidity;
                          mapping(int24 tick => TickInfo) ticks;
                          mapping(int16 wordPos => uint256) tickBitmap;
                          mapping(bytes32 positionKey => Position.State) positions;
                      }
                      /// @dev Common checks for valid tick inputs.
                      function checkTicks(int24 tickLower, int24 tickUpper) private pure {
                          if (tickLower >= tickUpper) TicksMisordered.selector.revertWith(tickLower, tickUpper);
                          if (tickLower < TickMath.MIN_TICK) TickLowerOutOfBounds.selector.revertWith(tickLower);
                          if (tickUpper > TickMath.MAX_TICK) TickUpperOutOfBounds.selector.revertWith(tickUpper);
                      }
                      function initialize(State storage self, uint160 sqrtPriceX96, uint24 lpFee) internal returns (int24 tick) {
                          if (self.slot0.sqrtPriceX96() != 0) PoolAlreadyInitialized.selector.revertWith();
                          tick = TickMath.getTickAtSqrtPrice(sqrtPriceX96);
                          // the initial protocolFee is 0 so doesn't need to be set
                          self.slot0 = Slot0.wrap(bytes32(0)).setSqrtPriceX96(sqrtPriceX96).setTick(tick).setLpFee(lpFee);
                      }
                      function setProtocolFee(State storage self, uint24 protocolFee) internal {
                          self.checkPoolInitialized();
                          self.slot0 = self.slot0.setProtocolFee(protocolFee);
                      }
                      /// @notice Only dynamic fee pools may update the lp fee.
                      function setLPFee(State storage self, uint24 lpFee) internal {
                          self.checkPoolInitialized();
                          self.slot0 = self.slot0.setLpFee(lpFee);
                      }
                      struct ModifyLiquidityParams {
                          // the address that owns the position
                          address owner;
                          // the lower and upper tick of the position
                          int24 tickLower;
                          int24 tickUpper;
                          // any change in liquidity
                          int128 liquidityDelta;
                          // the spacing between ticks
                          int24 tickSpacing;
                          // used to distinguish positions of the same owner, at the same tick range
                          bytes32 salt;
                      }
                      struct ModifyLiquidityState {
                          bool flippedLower;
                          uint128 liquidityGrossAfterLower;
                          bool flippedUpper;
                          uint128 liquidityGrossAfterUpper;
                      }
                      /// @notice Effect changes to a position in a pool
                      /// @dev PoolManager checks that the pool is initialized before calling
                      /// @param params the position details and the change to the position's liquidity to effect
                      /// @return delta the deltas of the token balances of the pool, from the liquidity change
                      /// @return feeDelta the fees generated by the liquidity range
                      function modifyLiquidity(State storage self, ModifyLiquidityParams memory params)
                          internal
                          returns (BalanceDelta delta, BalanceDelta feeDelta)
                      {
                          int128 liquidityDelta = params.liquidityDelta;
                          int24 tickLower = params.tickLower;
                          int24 tickUpper = params.tickUpper;
                          checkTicks(tickLower, tickUpper);
                          {
                              ModifyLiquidityState memory state;
                              // if we need to update the ticks, do it
                              if (liquidityDelta != 0) {
                                  (state.flippedLower, state.liquidityGrossAfterLower) =
                                      updateTick(self, tickLower, liquidityDelta, false);
                                  (state.flippedUpper, state.liquidityGrossAfterUpper) = updateTick(self, tickUpper, liquidityDelta, true);
                                  // `>` and `>=` are logically equivalent here but `>=` is cheaper
                                  if (liquidityDelta >= 0) {
                                      uint128 maxLiquidityPerTick = tickSpacingToMaxLiquidityPerTick(params.tickSpacing);
                                      if (state.liquidityGrossAfterLower > maxLiquidityPerTick) {
                                          TickLiquidityOverflow.selector.revertWith(tickLower);
                                      }
                                      if (state.liquidityGrossAfterUpper > maxLiquidityPerTick) {
                                          TickLiquidityOverflow.selector.revertWith(tickUpper);
                                      }
                                  }
                                  if (state.flippedLower) {
                                      self.tickBitmap.flipTick(tickLower, params.tickSpacing);
                                  }
                                  if (state.flippedUpper) {
                                      self.tickBitmap.flipTick(tickUpper, params.tickSpacing);
                                  }
                              }
                              {
                                  (uint256 feeGrowthInside0X128, uint256 feeGrowthInside1X128) =
                                      getFeeGrowthInside(self, tickLower, tickUpper);
                                  Position.State storage position = self.positions.get(params.owner, tickLower, tickUpper, params.salt);
                                  (uint256 feesOwed0, uint256 feesOwed1) =
                                      position.update(liquidityDelta, feeGrowthInside0X128, feeGrowthInside1X128);
                                  // Fees earned from LPing are calculated, and returned
                                  feeDelta = toBalanceDelta(feesOwed0.toInt128(), feesOwed1.toInt128());
                              }
                              // clear any tick data that is no longer needed
                              if (liquidityDelta < 0) {
                                  if (state.flippedLower) {
                                      clearTick(self, tickLower);
                                  }
                                  if (state.flippedUpper) {
                                      clearTick(self, tickUpper);
                                  }
                              }
                          }
                          if (liquidityDelta != 0) {
                              Slot0 _slot0 = self.slot0;
                              (int24 tick, uint160 sqrtPriceX96) = (_slot0.tick(), _slot0.sqrtPriceX96());
                              if (tick < tickLower) {
                                  // current tick is below the passed range; liquidity can only become in range by crossing from left to
                                  // right, when we'll need _more_ currency0 (it's becoming more valuable) so user must provide it
                                  delta = toBalanceDelta(
                                      SqrtPriceMath.getAmount0Delta(
                                          TickMath.getSqrtPriceAtTick(tickLower), TickMath.getSqrtPriceAtTick(tickUpper), liquidityDelta
                                      ).toInt128(),
                                      0
                                  );
                              } else if (tick < tickUpper) {
                                  delta = toBalanceDelta(
                                      SqrtPriceMath.getAmount0Delta(sqrtPriceX96, TickMath.getSqrtPriceAtTick(tickUpper), liquidityDelta)
                                          .toInt128(),
                                      SqrtPriceMath.getAmount1Delta(TickMath.getSqrtPriceAtTick(tickLower), sqrtPriceX96, liquidityDelta)
                                          .toInt128()
                                  );
                                  self.liquidity = LiquidityMath.addDelta(self.liquidity, liquidityDelta);
                              } else {
                                  // current tick is above the passed range; liquidity can only become in range by crossing from right to
                                  // left, when we'll need _more_ currency1 (it's becoming more valuable) so user must provide it
                                  delta = toBalanceDelta(
                                      0,
                                      SqrtPriceMath.getAmount1Delta(
                                          TickMath.getSqrtPriceAtTick(tickLower), TickMath.getSqrtPriceAtTick(tickUpper), liquidityDelta
                                      ).toInt128()
                                  );
                              }
                          }
                      }
                      // Tracks the state of a pool throughout a swap, and returns these values at the end of the swap
                      struct SwapResult {
                          // the current sqrt(price)
                          uint160 sqrtPriceX96;
                          // the tick associated with the current price
                          int24 tick;
                          // the current liquidity in range
                          uint128 liquidity;
                      }
                      struct StepComputations {
                          // the price at the beginning of the step
                          uint160 sqrtPriceStartX96;
                          // the next tick to swap to from the current tick in the swap direction
                          int24 tickNext;
                          // whether tickNext is initialized or not
                          bool initialized;
                          // sqrt(price) for the next tick (1/0)
                          uint160 sqrtPriceNextX96;
                          // how much is being swapped in in this step
                          uint256 amountIn;
                          // how much is being swapped out
                          uint256 amountOut;
                          // how much fee is being paid in
                          uint256 feeAmount;
                          // the global fee growth of the input token. updated in storage at the end of swap
                          uint256 feeGrowthGlobalX128;
                      }
                      struct SwapParams {
                          int256 amountSpecified;
                          int24 tickSpacing;
                          bool zeroForOne;
                          uint160 sqrtPriceLimitX96;
                          uint24 lpFeeOverride;
                      }
                      /// @notice Executes a swap against the state, and returns the amount deltas of the pool
                      /// @dev PoolManager checks that the pool is initialized before calling
                      function swap(State storage self, SwapParams memory params)
                          internal
                          returns (BalanceDelta swapDelta, uint256 amountToProtocol, uint24 swapFee, SwapResult memory result)
                      {
                          Slot0 slot0Start = self.slot0;
                          bool zeroForOne = params.zeroForOne;
                          uint256 protocolFee =
                              zeroForOne ? slot0Start.protocolFee().getZeroForOneFee() : slot0Start.protocolFee().getOneForZeroFee();
                          // the amount remaining to be swapped in/out of the input/output asset. initially set to the amountSpecified
                          int256 amountSpecifiedRemaining = params.amountSpecified;
                          // the amount swapped out/in of the output/input asset. initially set to 0
                          int256 amountCalculated = 0;
                          // initialize to the current sqrt(price)
                          result.sqrtPriceX96 = slot0Start.sqrtPriceX96();
                          // initialize to the current tick
                          result.tick = slot0Start.tick();
                          // initialize to the current liquidity
                          result.liquidity = self.liquidity;
                          // if the beforeSwap hook returned a valid fee override, use that as the LP fee, otherwise load from storage
                          // lpFee, swapFee, and protocolFee are all in pips
                          {
                              uint24 lpFee = params.lpFeeOverride.isOverride()
                                  ? params.lpFeeOverride.removeOverrideFlagAndValidate()
                                  : slot0Start.lpFee();
                              swapFee = protocolFee == 0 ? lpFee : uint16(protocolFee).calculateSwapFee(lpFee);
                          }
                          // a swap fee totaling MAX_SWAP_FEE (100%) makes exact output swaps impossible since the input is entirely consumed by the fee
                          if (swapFee >= SwapMath.MAX_SWAP_FEE) {
                              // if exactOutput
                              if (params.amountSpecified > 0) {
                                  InvalidFeeForExactOut.selector.revertWith();
                              }
                          }
                          // swapFee is the pool's fee in pips (LP fee + protocol fee)
                          // when the amount swapped is 0, there is no protocolFee applied and the fee amount paid to the protocol is set to 0
                          if (params.amountSpecified == 0) return (BalanceDeltaLibrary.ZERO_DELTA, 0, swapFee, result);
                          if (zeroForOne) {
                              if (params.sqrtPriceLimitX96 >= slot0Start.sqrtPriceX96()) {
                                  PriceLimitAlreadyExceeded.selector.revertWith(slot0Start.sqrtPriceX96(), params.sqrtPriceLimitX96);
                              }
                              // Swaps can never occur at MIN_TICK, only at MIN_TICK + 1, except at initialization of a pool
                              // Under certain circumstances outlined below, the tick will preemptively reach MIN_TICK without swapping there
                              if (params.sqrtPriceLimitX96 <= TickMath.MIN_SQRT_PRICE) {
                                  PriceLimitOutOfBounds.selector.revertWith(params.sqrtPriceLimitX96);
                              }
                          } else {
                              if (params.sqrtPriceLimitX96 <= slot0Start.sqrtPriceX96()) {
                                  PriceLimitAlreadyExceeded.selector.revertWith(slot0Start.sqrtPriceX96(), params.sqrtPriceLimitX96);
                              }
                              if (params.sqrtPriceLimitX96 >= TickMath.MAX_SQRT_PRICE) {
                                  PriceLimitOutOfBounds.selector.revertWith(params.sqrtPriceLimitX96);
                              }
                          }
                          StepComputations memory step;
                          step.feeGrowthGlobalX128 = zeroForOne ? self.feeGrowthGlobal0X128 : self.feeGrowthGlobal1X128;
                          // continue swapping as long as we haven't used the entire input/output and haven't reached the price limit
                          while (!(amountSpecifiedRemaining == 0 || result.sqrtPriceX96 == params.sqrtPriceLimitX96)) {
                              step.sqrtPriceStartX96 = result.sqrtPriceX96;
                              (step.tickNext, step.initialized) =
                                  self.tickBitmap.nextInitializedTickWithinOneWord(result.tick, params.tickSpacing, zeroForOne);
                              // ensure that we do not overshoot the min/max tick, as the tick bitmap is not aware of these bounds
                              if (step.tickNext <= TickMath.MIN_TICK) {
                                  step.tickNext = TickMath.MIN_TICK;
                              }
                              if (step.tickNext >= TickMath.MAX_TICK) {
                                  step.tickNext = TickMath.MAX_TICK;
                              }
                              // get the price for the next tick
                              step.sqrtPriceNextX96 = TickMath.getSqrtPriceAtTick(step.tickNext);
                              // compute values to swap to the target tick, price limit, or point where input/output amount is exhausted
                              (result.sqrtPriceX96, step.amountIn, step.amountOut, step.feeAmount) = SwapMath.computeSwapStep(
                                  result.sqrtPriceX96,
                                  SwapMath.getSqrtPriceTarget(zeroForOne, step.sqrtPriceNextX96, params.sqrtPriceLimitX96),
                                  result.liquidity,
                                  amountSpecifiedRemaining,
                                  swapFee
                              );
                              // if exactOutput
                              if (params.amountSpecified > 0) {
                                  unchecked {
                                      amountSpecifiedRemaining -= step.amountOut.toInt256();
                                  }
                                  amountCalculated -= (step.amountIn + step.feeAmount).toInt256();
                              } else {
                                  // safe because we test that amountSpecified > amountIn + feeAmount in SwapMath
                                  unchecked {
                                      amountSpecifiedRemaining += (step.amountIn + step.feeAmount).toInt256();
                                  }
                                  amountCalculated += step.amountOut.toInt256();
                              }
                              // if the protocol fee is on, calculate how much is owed, decrement feeAmount, and increment protocolFee
                              if (protocolFee > 0) {
                                  unchecked {
                                      // step.amountIn does not include the swap fee, as it's already been taken from it,
                                      // so add it back to get the total amountIn and use that to calculate the amount of fees owed to the protocol
                                      // cannot overflow due to limits on the size of protocolFee and params.amountSpecified
                                      // this rounds down to favor LPs over the protocol
                                      uint256 delta = (swapFee == protocolFee)
                                          ? step.feeAmount // lp fee is 0, so the entire fee is owed to the protocol instead
                                          : (step.amountIn + step.feeAmount) * protocolFee / ProtocolFeeLibrary.PIPS_DENOMINATOR;
                                      // subtract it from the total fee and add it to the protocol fee
                                      step.feeAmount -= delta;
                                      amountToProtocol += delta;
                                  }
                              }
                              // update global fee tracker
                              if (result.liquidity > 0) {
                                  unchecked {
                                      // FullMath.mulDiv isn't needed as the numerator can't overflow uint256 since tokens have a max supply of type(uint128).max
                                      step.feeGrowthGlobalX128 +=
                                          UnsafeMath.simpleMulDiv(step.feeAmount, FixedPoint128.Q128, result.liquidity);
                                  }
                              }
                              // Shift tick if we reached the next price, and preemptively decrement for zeroForOne swaps to tickNext - 1.
                              // If the swap doesn't continue (if amountRemaining == 0 or sqrtPriceLimit is met), slot0.tick will be 1 less
                              // than getTickAtSqrtPrice(slot0.sqrtPrice). This doesn't affect swaps, but donation calls should verify both
                              // price and tick to reward the correct LPs.
                              if (result.sqrtPriceX96 == step.sqrtPriceNextX96) {
                                  // if the tick is initialized, run the tick transition
                                  if (step.initialized) {
                                      (uint256 feeGrowthGlobal0X128, uint256 feeGrowthGlobal1X128) = zeroForOne
                                          ? (step.feeGrowthGlobalX128, self.feeGrowthGlobal1X128)
                                          : (self.feeGrowthGlobal0X128, step.feeGrowthGlobalX128);
                                      int128 liquidityNet =
                                          Pool.crossTick(self, step.tickNext, feeGrowthGlobal0X128, feeGrowthGlobal1X128);
                                      // if we're moving leftward, we interpret liquidityNet as the opposite sign
                                      // safe because liquidityNet cannot be type(int128).min
                                      unchecked {
                                          if (zeroForOne) liquidityNet = -liquidityNet;
                                      }
                                      result.liquidity = LiquidityMath.addDelta(result.liquidity, liquidityNet);
                                  }
                                  unchecked {
                                      result.tick = zeroForOne ? step.tickNext - 1 : step.tickNext;
                                  }
                              } else if (result.sqrtPriceX96 != step.sqrtPriceStartX96) {
                                  // recompute unless we're on a lower tick boundary (i.e. already transitioned ticks), and haven't moved
                                  result.tick = TickMath.getTickAtSqrtPrice(result.sqrtPriceX96);
                              }
                          }
                          self.slot0 = slot0Start.setTick(result.tick).setSqrtPriceX96(result.sqrtPriceX96);
                          // update liquidity if it changed
                          if (self.liquidity != result.liquidity) self.liquidity = result.liquidity;
                          // update fee growth global
                          if (!zeroForOne) {
                              self.feeGrowthGlobal1X128 = step.feeGrowthGlobalX128;
                          } else {
                              self.feeGrowthGlobal0X128 = step.feeGrowthGlobalX128;
                          }
                          unchecked {
                              // "if currency1 is specified"
                              if (zeroForOne != (params.amountSpecified < 0)) {
                                  swapDelta = toBalanceDelta(
                                      amountCalculated.toInt128(), (params.amountSpecified - amountSpecifiedRemaining).toInt128()
                                  );
                              } else {
                                  swapDelta = toBalanceDelta(
                                      (params.amountSpecified - amountSpecifiedRemaining).toInt128(), amountCalculated.toInt128()
                                  );
                              }
                          }
                      }
                      /// @notice Donates the given amount of currency0 and currency1 to the pool
                      function donate(State storage state, uint256 amount0, uint256 amount1) internal returns (BalanceDelta delta) {
                          uint128 liquidity = state.liquidity;
                          if (liquidity == 0) NoLiquidityToReceiveFees.selector.revertWith();
                          unchecked {
                              // negation safe as amount0 and amount1 are always positive
                              delta = toBalanceDelta(-(amount0.toInt128()), -(amount1.toInt128()));
                              // FullMath.mulDiv is unnecessary because the numerator is bounded by type(int128).max * Q128, which is less than type(uint256).max
                              if (amount0 > 0) {
                                  state.feeGrowthGlobal0X128 += UnsafeMath.simpleMulDiv(amount0, FixedPoint128.Q128, liquidity);
                              }
                              if (amount1 > 0) {
                                  state.feeGrowthGlobal1X128 += UnsafeMath.simpleMulDiv(amount1, FixedPoint128.Q128, liquidity);
                              }
                          }
                      }
                      /// @notice Retrieves fee growth data
                      /// @param self The Pool state struct
                      /// @param tickLower The lower tick boundary of the position
                      /// @param tickUpper The upper tick boundary of the position
                      /// @return feeGrowthInside0X128 The all-time fee growth in token0, per unit of liquidity, inside the position's tick boundaries
                      /// @return feeGrowthInside1X128 The all-time fee growth in token1, per unit of liquidity, inside the position's tick boundaries
                      function getFeeGrowthInside(State storage self, int24 tickLower, int24 tickUpper)
                          internal
                          view
                          returns (uint256 feeGrowthInside0X128, uint256 feeGrowthInside1X128)
                      {
                          TickInfo storage lower = self.ticks[tickLower];
                          TickInfo storage upper = self.ticks[tickUpper];
                          int24 tickCurrent = self.slot0.tick();
                          unchecked {
                              if (tickCurrent < tickLower) {
                                  feeGrowthInside0X128 = lower.feeGrowthOutside0X128 - upper.feeGrowthOutside0X128;
                                  feeGrowthInside1X128 = lower.feeGrowthOutside1X128 - upper.feeGrowthOutside1X128;
                              } else if (tickCurrent >= tickUpper) {
                                  feeGrowthInside0X128 = upper.feeGrowthOutside0X128 - lower.feeGrowthOutside0X128;
                                  feeGrowthInside1X128 = upper.feeGrowthOutside1X128 - lower.feeGrowthOutside1X128;
                              } else {
                                  feeGrowthInside0X128 =
                                      self.feeGrowthGlobal0X128 - lower.feeGrowthOutside0X128 - upper.feeGrowthOutside0X128;
                                  feeGrowthInside1X128 =
                                      self.feeGrowthGlobal1X128 - lower.feeGrowthOutside1X128 - upper.feeGrowthOutside1X128;
                              }
                          }
                      }
                      /// @notice Updates a tick and returns true if the tick was flipped from initialized to uninitialized, or vice versa
                      /// @param self The mapping containing all tick information for initialized ticks
                      /// @param tick The tick that will be updated
                      /// @param liquidityDelta A new amount of liquidity to be added (subtracted) when tick is crossed from left to right (right to left)
                      /// @param upper true for updating a position's upper tick, or false for updating a position's lower tick
                      /// @return flipped Whether the tick was flipped from initialized to uninitialized, or vice versa
                      /// @return liquidityGrossAfter The total amount of liquidity for all positions that references the tick after the update
                      function updateTick(State storage self, int24 tick, int128 liquidityDelta, bool upper)
                          internal
                          returns (bool flipped, uint128 liquidityGrossAfter)
                      {
                          TickInfo storage info = self.ticks[tick];
                          uint128 liquidityGrossBefore = info.liquidityGross;
                          int128 liquidityNetBefore = info.liquidityNet;
                          liquidityGrossAfter = LiquidityMath.addDelta(liquidityGrossBefore, liquidityDelta);
                          flipped = (liquidityGrossAfter == 0) != (liquidityGrossBefore == 0);
                          if (liquidityGrossBefore == 0) {
                              // by convention, we assume that all growth before a tick was initialized happened _below_ the tick
                              if (tick <= self.slot0.tick()) {
                                  info.feeGrowthOutside0X128 = self.feeGrowthGlobal0X128;
                                  info.feeGrowthOutside1X128 = self.feeGrowthGlobal1X128;
                              }
                          }
                          // when the lower (upper) tick is crossed left to right, liquidity must be added (removed)
                          // when the lower (upper) tick is crossed right to left, liquidity must be removed (added)
                          int128 liquidityNet = upper ? liquidityNetBefore - liquidityDelta : liquidityNetBefore + liquidityDelta;
                          assembly ("memory-safe") {
                              // liquidityGrossAfter and liquidityNet are packed in the first slot of `info`
                              // So we can store them with a single sstore by packing them ourselves first
                              sstore(
                                  info.slot,
                                  // bitwise OR to pack liquidityGrossAfter and liquidityNet
                                  or(
                                      // Put liquidityGrossAfter in the lower bits, clearing out the upper bits
                                      and(liquidityGrossAfter, 0xffffffffffffffffffffffffffffffff),
                                      // Shift liquidityNet to put it in the upper bits (no need for signextend since we're shifting left)
                                      shl(128, liquidityNet)
                                  )
                              )
                          }
                      }
                      /// @notice Derives max liquidity per tick from given tick spacing
                      /// @dev Executed when adding liquidity
                      /// @param tickSpacing The amount of required tick separation, realized in multiples of `tickSpacing`
                      ///     e.g., a tickSpacing of 3 requires ticks to be initialized every 3rd tick i.e., ..., -6, -3, 0, 3, 6, ...
                      /// @return result The max liquidity per tick
                      function tickSpacingToMaxLiquidityPerTick(int24 tickSpacing) internal pure returns (uint128 result) {
                          // Equivalent to:
                          // int24 minTick = (TickMath.MIN_TICK / tickSpacing);
                          // if (TickMath.MIN_TICK  % tickSpacing != 0) minTick--;
                          // int24 maxTick = (TickMath.MAX_TICK / tickSpacing);
                          // uint24 numTicks = maxTick - minTick + 1;
                          // return type(uint128).max / numTicks;
                          int24 MAX_TICK = TickMath.MAX_TICK;
                          int24 MIN_TICK = TickMath.MIN_TICK;
                          // tick spacing will never be 0 since TickMath.MIN_TICK_SPACING is 1
                          assembly ("memory-safe") {
                              tickSpacing := signextend(2, tickSpacing)
                              let minTick := sub(sdiv(MIN_TICK, tickSpacing), slt(smod(MIN_TICK, tickSpacing), 0))
                              let maxTick := sdiv(MAX_TICK, tickSpacing)
                              let numTicks := add(sub(maxTick, minTick), 1)
                              result := div(sub(shl(128, 1), 1), numTicks)
                          }
                      }
                      /// @notice Reverts if the given pool has not been initialized
                      function checkPoolInitialized(State storage self) internal view {
                          if (self.slot0.sqrtPriceX96() == 0) PoolNotInitialized.selector.revertWith();
                      }
                      /// @notice Clears tick data
                      /// @param self The mapping containing all initialized tick information for initialized ticks
                      /// @param tick The tick that will be cleared
                      function clearTick(State storage self, int24 tick) internal {
                          delete self.ticks[tick];
                      }
                      /// @notice Transitions to next tick as needed by price movement
                      /// @param self The Pool state struct
                      /// @param tick The destination tick of the transition
                      /// @param feeGrowthGlobal0X128 The all-time global fee growth, per unit of liquidity, in token0
                      /// @param feeGrowthGlobal1X128 The all-time global fee growth, per unit of liquidity, in token1
                      /// @return liquidityNet The amount of liquidity added (subtracted) when tick is crossed from left to right (right to left)
                      function crossTick(State storage self, int24 tick, uint256 feeGrowthGlobal0X128, uint256 feeGrowthGlobal1X128)
                          internal
                          returns (int128 liquidityNet)
                      {
                          unchecked {
                              TickInfo storage info = self.ticks[tick];
                              info.feeGrowthOutside0X128 = feeGrowthGlobal0X128 - info.feeGrowthOutside0X128;
                              info.feeGrowthOutside1X128 = feeGrowthGlobal1X128 - info.feeGrowthOutside1X128;
                              liquidityNet = info.liquidityNet;
                          }
                      }
                  }
                  // SPDX-License-Identifier: MIT
                  pragma solidity ^0.8.0;
                  import {CustomRevert} from "./CustomRevert.sol";
                  /// @title Safe casting methods
                  /// @notice Contains methods for safely casting between types
                  library SafeCast {
                      using CustomRevert for bytes4;
                      error SafeCastOverflow();
                      /// @notice Cast a uint256 to a uint160, revert on overflow
                      /// @param x The uint256 to be downcasted
                      /// @return y The downcasted integer, now type uint160
                      function toUint160(uint256 x) internal pure returns (uint160 y) {
                          y = uint160(x);
                          if (y != x) SafeCastOverflow.selector.revertWith();
                      }
                      /// @notice Cast a uint256 to a uint128, revert on overflow
                      /// @param x The uint256 to be downcasted
                      /// @return y The downcasted integer, now type uint128
                      function toUint128(uint256 x) internal pure returns (uint128 y) {
                          y = uint128(x);
                          if (x != y) SafeCastOverflow.selector.revertWith();
                      }
                      /// @notice Cast a int128 to a uint128, revert on overflow or underflow
                      /// @param x The int128 to be casted
                      /// @return y The casted integer, now type uint128
                      function toUint128(int128 x) internal pure returns (uint128 y) {
                          if (x < 0) SafeCastOverflow.selector.revertWith();
                          y = uint128(x);
                      }
                      /// @notice Cast a int256 to a int128, revert on overflow or underflow
                      /// @param x The int256 to be downcasted
                      /// @return y The downcasted integer, now type int128
                      function toInt128(int256 x) internal pure returns (int128 y) {
                          y = int128(x);
                          if (y != x) SafeCastOverflow.selector.revertWith();
                      }
                      /// @notice Cast a uint256 to a int256, revert on overflow
                      /// @param x The uint256 to be casted
                      /// @return y The casted integer, now type int256
                      function toInt256(uint256 x) internal pure returns (int256 y) {
                          y = int256(x);
                          if (y < 0) SafeCastOverflow.selector.revertWith();
                      }
                      /// @notice Cast a uint256 to a int128, revert on overflow
                      /// @param x The uint256 to be downcasted
                      /// @return The downcasted integer, now type int128
                      function toInt128(uint256 x) internal pure returns (int128) {
                          if (x >= 1 << 127) SafeCastOverflow.selector.revertWith();
                          return int128(int256(x));
                      }
                  }
                  // SPDX-License-Identifier: BUSL-1.1
                  pragma solidity ^0.8.0;
                  import {FullMath} from "./FullMath.sol";
                  import {FixedPoint128} from "./FixedPoint128.sol";
                  import {LiquidityMath} from "./LiquidityMath.sol";
                  import {CustomRevert} from "./CustomRevert.sol";
                  /// @title Position
                  /// @notice Positions represent an owner address' liquidity between a lower and upper tick boundary
                  /// @dev Positions store additional state for tracking fees owed to the position
                  library Position {
                      using CustomRevert for bytes4;
                      /// @notice Cannot update a position with no liquidity
                      error CannotUpdateEmptyPosition();
                      // info stored for each user's position
                      struct State {
                          // the amount of liquidity owned by this position
                          uint128 liquidity;
                          // fee growth per unit of liquidity as of the last update to liquidity or fees owed
                          uint256 feeGrowthInside0LastX128;
                          uint256 feeGrowthInside1LastX128;
                      }
                      /// @notice Returns the State struct of a position, given an owner and position boundaries
                      /// @param self The mapping containing all user positions
                      /// @param owner The address of the position owner
                      /// @param tickLower The lower tick boundary of the position
                      /// @param tickUpper The upper tick boundary of the position
                      /// @param salt A unique value to differentiate between multiple positions in the same range
                      /// @return position The position info struct of the given owners' position
                      function get(mapping(bytes32 => State) storage self, address owner, int24 tickLower, int24 tickUpper, bytes32 salt)
                          internal
                          view
                          returns (State storage position)
                      {
                          bytes32 positionKey = calculatePositionKey(owner, tickLower, tickUpper, salt);
                          position = self[positionKey];
                      }
                      /// @notice A helper function to calculate the position key
                      /// @param owner The address of the position owner
                      /// @param tickLower the lower tick boundary of the position
                      /// @param tickUpper the upper tick boundary of the position
                      /// @param salt A unique value to differentiate between multiple positions in the same range, by the same owner. Passed in by the caller.
                      function calculatePositionKey(address owner, int24 tickLower, int24 tickUpper, bytes32 salt)
                          internal
                          pure
                          returns (bytes32 positionKey)
                      {
                          // positionKey = keccak256(abi.encodePacked(owner, tickLower, tickUpper, salt))
                          assembly ("memory-safe") {
                              let fmp := mload(0x40)
                              mstore(add(fmp, 0x26), salt) // [0x26, 0x46)
                              mstore(add(fmp, 0x06), tickUpper) // [0x23, 0x26)
                              mstore(add(fmp, 0x03), tickLower) // [0x20, 0x23)
                              mstore(fmp, owner) // [0x0c, 0x20)
                              positionKey := keccak256(add(fmp, 0x0c), 0x3a) // len is 58 bytes
                              // now clean the memory we used
                              mstore(add(fmp, 0x40), 0) // fmp+0x40 held salt
                              mstore(add(fmp, 0x20), 0) // fmp+0x20 held tickLower, tickUpper, salt
                              mstore(fmp, 0) // fmp held owner
                          }
                      }
                      /// @notice Credits accumulated fees to a user's position
                      /// @param self The individual position to update
                      /// @param liquidityDelta The change in pool liquidity as a result of the position update
                      /// @param feeGrowthInside0X128 The all-time fee growth in currency0, per unit of liquidity, inside the position's tick boundaries
                      /// @param feeGrowthInside1X128 The all-time fee growth in currency1, per unit of liquidity, inside the position's tick boundaries
                      /// @return feesOwed0 The amount of currency0 owed to the position owner
                      /// @return feesOwed1 The amount of currency1 owed to the position owner
                      function update(
                          State storage self,
                          int128 liquidityDelta,
                          uint256 feeGrowthInside0X128,
                          uint256 feeGrowthInside1X128
                      ) internal returns (uint256 feesOwed0, uint256 feesOwed1) {
                          uint128 liquidity = self.liquidity;
                          if (liquidityDelta == 0) {
                              // disallow pokes for 0 liquidity positions
                              if (liquidity == 0) CannotUpdateEmptyPosition.selector.revertWith();
                          } else {
                              self.liquidity = LiquidityMath.addDelta(liquidity, liquidityDelta);
                          }
                          // calculate accumulated fees. overflow in the subtraction of fee growth is expected
                          unchecked {
                              feesOwed0 =
                                  FullMath.mulDiv(feeGrowthInside0X128 - self.feeGrowthInside0LastX128, liquidity, FixedPoint128.Q128);
                              feesOwed1 =
                                  FullMath.mulDiv(feeGrowthInside1X128 - self.feeGrowthInside1LastX128, liquidity, FixedPoint128.Q128);
                          }
                          // update the position
                          self.feeGrowthInside0LastX128 = feeGrowthInside0X128;
                          self.feeGrowthInside1LastX128 = feeGrowthInside1X128;
                      }
                  }
                  // SPDX-License-Identifier: MIT
                  pragma solidity ^0.8.0;
                  import {CustomRevert} from "./CustomRevert.sol";
                  /// @notice Library of helper functions for a pools LP fee
                  library LPFeeLibrary {
                      using LPFeeLibrary for uint24;
                      using CustomRevert for bytes4;
                      /// @notice Thrown when the static or dynamic fee on a pool exceeds 100%.
                      error LPFeeTooLarge(uint24 fee);
                      /// @notice An lp fee of exactly 0b1000000... signals a dynamic fee pool. This isn't a valid static fee as it is > MAX_LP_FEE
                      uint24 public constant DYNAMIC_FEE_FLAG = 0x800000;
                      /// @notice the second bit of the fee returned by beforeSwap is used to signal if the stored LP fee should be overridden in this swap
                      // only dynamic-fee pools can return a fee via the beforeSwap hook
                      uint24 public constant OVERRIDE_FEE_FLAG = 0x400000;
                      /// @notice mask to remove the override fee flag from a fee returned by the beforeSwaphook
                      uint24 public constant REMOVE_OVERRIDE_MASK = 0xBFFFFF;
                      /// @notice the lp fee is represented in hundredths of a bip, so the max is 100%
                      uint24 public constant MAX_LP_FEE = 1000000;
                      /// @notice returns true if a pool's LP fee signals that the pool has a dynamic fee
                      /// @param self The fee to check
                      /// @return bool True of the fee is dynamic
                      function isDynamicFee(uint24 self) internal pure returns (bool) {
                          return self == DYNAMIC_FEE_FLAG;
                      }
                      /// @notice returns true if an LP fee is valid, aka not above the maximum permitted fee
                      /// @param self The fee to check
                      /// @return bool True of the fee is valid
                      function isValid(uint24 self) internal pure returns (bool) {
                          return self <= MAX_LP_FEE;
                      }
                      /// @notice validates whether an LP fee is larger than the maximum, and reverts if invalid
                      /// @param self The fee to validate
                      function validate(uint24 self) internal pure {
                          if (!self.isValid()) LPFeeTooLarge.selector.revertWith(self);
                      }
                      /// @notice gets and validates the initial LP fee for a pool. Dynamic fee pools have an initial fee of 0.
                      /// @dev if a dynamic fee pool wants a non-0 initial fee, it should call `updateDynamicLPFee` in the afterInitialize hook
                      /// @param self The fee to get the initial LP from
                      /// @return initialFee 0 if the fee is dynamic, otherwise the fee (if valid)
                      function getInitialLPFee(uint24 self) internal pure returns (uint24) {
                          // the initial fee for a dynamic fee pool is 0
                          if (self.isDynamicFee()) return 0;
                          self.validate();
                          return self;
                      }
                      /// @notice returns true if the fee has the override flag set (2nd highest bit of the uint24)
                      /// @param self The fee to check
                      /// @return bool True of the fee has the override flag set
                      function isOverride(uint24 self) internal pure returns (bool) {
                          return self & OVERRIDE_FEE_FLAG != 0;
                      }
                      /// @notice returns a fee with the override flag removed
                      /// @param self The fee to remove the override flag from
                      /// @return fee The fee without the override flag set
                      function removeOverrideFlag(uint24 self) internal pure returns (uint24) {
                          return self & REMOVE_OVERRIDE_MASK;
                      }
                      /// @notice Removes the override flag and validates the fee (reverts if the fee is too large)
                      /// @param self The fee to remove the override flag from, and then validate
                      /// @return fee The fee without the override flag set (if valid)
                      function removeOverrideFlagAndValidate(uint24 self) internal pure returns (uint24 fee) {
                          fee = self.removeOverrideFlag();
                          fee.validate();
                      }
                  }
                  // SPDX-License-Identifier: MIT
                  pragma solidity ^0.8.0;
                  import {IERC20Minimal} from "../interfaces/external/IERC20Minimal.sol";
                  import {CustomRevert} from "../libraries/CustomRevert.sol";
                  type Currency is address;
                  using {greaterThan as >, lessThan as <, greaterThanOrEqualTo as >=, equals as ==} for Currency global;
                  using CurrencyLibrary for Currency global;
                  function equals(Currency currency, Currency other) pure returns (bool) {
                      return Currency.unwrap(currency) == Currency.unwrap(other);
                  }
                  function greaterThan(Currency currency, Currency other) pure returns (bool) {
                      return Currency.unwrap(currency) > Currency.unwrap(other);
                  }
                  function lessThan(Currency currency, Currency other) pure returns (bool) {
                      return Currency.unwrap(currency) < Currency.unwrap(other);
                  }
                  function greaterThanOrEqualTo(Currency currency, Currency other) pure returns (bool) {
                      return Currency.unwrap(currency) >= Currency.unwrap(other);
                  }
                  /// @title CurrencyLibrary
                  /// @dev This library allows for transferring and holding native tokens and ERC20 tokens
                  library CurrencyLibrary {
                      /// @notice Additional context for ERC-7751 wrapped error when a native transfer fails
                      error NativeTransferFailed();
                      /// @notice Additional context for ERC-7751 wrapped error when an ERC20 transfer fails
                      error ERC20TransferFailed();
                      /// @notice A constant to represent the native currency
                      Currency public constant ADDRESS_ZERO = Currency.wrap(address(0));
                      function transfer(Currency currency, address to, uint256 amount) internal {
                          // altered from https://github.com/transmissions11/solmate/blob/44a9963d4c78111f77caa0e65d677b8b46d6f2e6/src/utils/SafeTransferLib.sol
                          // modified custom error selectors
                          bool success;
                          if (currency.isAddressZero()) {
                              assembly ("memory-safe") {
                                  // Transfer the ETH and revert if it fails.
                                  success := call(gas(), to, amount, 0, 0, 0, 0)
                              }
                              // revert with NativeTransferFailed, containing the bubbled up error as an argument
                              if (!success) {
                                  CustomRevert.bubbleUpAndRevertWith(to, bytes4(0), NativeTransferFailed.selector);
                              }
                          } else {
                              assembly ("memory-safe") {
                                  // Get a pointer to some free memory.
                                  let fmp := mload(0x40)
                                  // Write the abi-encoded calldata into memory, beginning with the function selector.
                                  mstore(fmp, 0xa9059cbb00000000000000000000000000000000000000000000000000000000)
                                  mstore(add(fmp, 4), and(to, 0xffffffffffffffffffffffffffffffffffffffff)) // Append and mask the "to" argument.
                                  mstore(add(fmp, 36), amount) // Append the "amount" argument. Masking not required as it's a full 32 byte type.
                                  success :=
                                      and(
                                          // Set success to whether the call reverted, if not we check it either
                                          // returned exactly 1 (can't just be non-zero data), or had no return data.
                                          or(and(eq(mload(0), 1), gt(returndatasize(), 31)), iszero(returndatasize())),
                                          // We use 68 because the length of our calldata totals up like so: 4 + 32 * 2.
                                          // We use 0 and 32 to copy up to 32 bytes of return data into the scratch space.
                                          // Counterintuitively, this call must be positioned second to the or() call in the
                                          // surrounding and() call or else returndatasize() will be zero during the computation.
                                          call(gas(), currency, 0, fmp, 68, 0, 32)
                                      )
                                  // Now clean the memory we used
                                  mstore(fmp, 0) // 4 byte `selector` and 28 bytes of `to` were stored here
                                  mstore(add(fmp, 0x20), 0) // 4 bytes of `to` and 28 bytes of `amount` were stored here
                                  mstore(add(fmp, 0x40), 0) // 4 bytes of `amount` were stored here
                              }
                              // revert with ERC20TransferFailed, containing the bubbled up error as an argument
                              if (!success) {
                                  CustomRevert.bubbleUpAndRevertWith(
                                      Currency.unwrap(currency), IERC20Minimal.transfer.selector, ERC20TransferFailed.selector
                                  );
                              }
                          }
                      }
                      function balanceOfSelf(Currency currency) internal view returns (uint256) {
                          if (currency.isAddressZero()) {
                              return address(this).balance;
                          } else {
                              return IERC20Minimal(Currency.unwrap(currency)).balanceOf(address(this));
                          }
                      }
                      function balanceOf(Currency currency, address owner) internal view returns (uint256) {
                          if (currency.isAddressZero()) {
                              return owner.balance;
                          } else {
                              return IERC20Minimal(Currency.unwrap(currency)).balanceOf(owner);
                          }
                      }
                      function isAddressZero(Currency currency) internal pure returns (bool) {
                          return Currency.unwrap(currency) == Currency.unwrap(ADDRESS_ZERO);
                      }
                      function toId(Currency currency) internal pure returns (uint256) {
                          return uint160(Currency.unwrap(currency));
                      }
                      // If the upper 12 bytes are non-zero, they will be zero-ed out
                      // Therefore, fromId() and toId() are not inverses of each other
                      function fromId(uint256 id) internal pure returns (Currency) {
                          return Currency.wrap(address(uint160(id)));
                      }
                  }
                  // SPDX-License-Identifier: MIT
                  pragma solidity ^0.8.0;
                  import {Currency} from "./Currency.sol";
                  import {IHooks} from "../interfaces/IHooks.sol";
                  import {PoolIdLibrary} from "./PoolId.sol";
                  using PoolIdLibrary for PoolKey global;
                  /// @notice Returns the key for identifying a pool
                  struct PoolKey {
                      /// @notice The lower currency of the pool, sorted numerically
                      Currency currency0;
                      /// @notice The higher currency of the pool, sorted numerically
                      Currency currency1;
                      /// @notice The pool LP fee, capped at 1_000_000. If the highest bit is 1, the pool has a dynamic fee and must be exactly equal to 0x800000
                      uint24 fee;
                      /// @notice Ticks that involve positions must be a multiple of tick spacing
                      int24 tickSpacing;
                      /// @notice The hooks of the pool
                      IHooks hooks;
                  }
                  // SPDX-License-Identifier: MIT
                  pragma solidity ^0.8.0;
                  import {BitMath} from "./BitMath.sol";
                  import {CustomRevert} from "./CustomRevert.sol";
                  /// @title Math library for computing sqrt prices from ticks and vice versa
                  /// @notice Computes sqrt price for ticks of size 1.0001, i.e. sqrt(1.0001^tick) as fixed point Q64.96 numbers. Supports
                  /// prices between 2**-128 and 2**128
                  library TickMath {
                      using CustomRevert for bytes4;
                      /// @notice Thrown when the tick passed to #getSqrtPriceAtTick is not between MIN_TICK and MAX_TICK
                      error InvalidTick(int24 tick);
                      /// @notice Thrown when the price passed to #getTickAtSqrtPrice does not correspond to a price between MIN_TICK and MAX_TICK
                      error InvalidSqrtPrice(uint160 sqrtPriceX96);
                      /// @dev The minimum tick that may be passed to #getSqrtPriceAtTick computed from log base 1.0001 of 2**-128
                      /// @dev If ever MIN_TICK and MAX_TICK are not centered around 0, the absTick logic in getSqrtPriceAtTick cannot be used
                      int24 internal constant MIN_TICK = -887272;
                      /// @dev The maximum tick that may be passed to #getSqrtPriceAtTick computed from log base 1.0001 of 2**128
                      /// @dev If ever MIN_TICK and MAX_TICK are not centered around 0, the absTick logic in getSqrtPriceAtTick cannot be used
                      int24 internal constant MAX_TICK = 887272;
                      /// @dev The minimum tick spacing value drawn from the range of type int16 that is greater than 0, i.e. min from the range [1, 32767]
                      int24 internal constant MIN_TICK_SPACING = 1;
                      /// @dev The maximum tick spacing value drawn from the range of type int16, i.e. max from the range [1, 32767]
                      int24 internal constant MAX_TICK_SPACING = type(int16).max;
                      /// @dev The minimum value that can be returned from #getSqrtPriceAtTick. Equivalent to getSqrtPriceAtTick(MIN_TICK)
                      uint160 internal constant MIN_SQRT_PRICE = 4295128739;
                      /// @dev The maximum value that can be returned from #getSqrtPriceAtTick. Equivalent to getSqrtPriceAtTick(MAX_TICK)
                      uint160 internal constant MAX_SQRT_PRICE = 1461446703485210103287273052203988822378723970342;
                      /// @dev A threshold used for optimized bounds check, equals `MAX_SQRT_PRICE - MIN_SQRT_PRICE - 1`
                      uint160 internal constant MAX_SQRT_PRICE_MINUS_MIN_SQRT_PRICE_MINUS_ONE =
                          1461446703485210103287273052203988822378723970342 - 4295128739 - 1;
                      /// @notice Given a tickSpacing, compute the maximum usable tick
                      function maxUsableTick(int24 tickSpacing) internal pure returns (int24) {
                          unchecked {
                              return (MAX_TICK / tickSpacing) * tickSpacing;
                          }
                      }
                      /// @notice Given a tickSpacing, compute the minimum usable tick
                      function minUsableTick(int24 tickSpacing) internal pure returns (int24) {
                          unchecked {
                              return (MIN_TICK / tickSpacing) * tickSpacing;
                          }
                      }
                      /// @notice Calculates sqrt(1.0001^tick) * 2^96
                      /// @dev Throws if |tick| > max tick
                      /// @param tick The input tick for the above formula
                      /// @return sqrtPriceX96 A Fixed point Q64.96 number representing the sqrt of the price of the two assets (currency1/currency0)
                      /// at the given tick
                      function getSqrtPriceAtTick(int24 tick) internal pure returns (uint160 sqrtPriceX96) {
                          unchecked {
                              uint256 absTick;
                              assembly ("memory-safe") {
                                  tick := signextend(2, tick)
                                  // mask = 0 if tick >= 0 else -1 (all 1s)
                                  let mask := sar(255, tick)
                                  // if tick >= 0, |tick| = tick = 0 ^ tick
                                  // if tick < 0, |tick| = ~~|tick| = ~(-|tick| - 1) = ~(tick - 1) = (-1) ^ (tick - 1)
                                  // either way, |tick| = mask ^ (tick + mask)
                                  absTick := xor(mask, add(mask, tick))
                              }
                              if (absTick > uint256(int256(MAX_TICK))) InvalidTick.selector.revertWith(tick);
                              // The tick is decomposed into bits, and for each bit with index i that is set, the product of 1/sqrt(1.0001^(2^i))
                              // is calculated (using Q128.128). The constants used for this calculation are rounded to the nearest integer
                              // Equivalent to:
                              //     price = absTick & 0x1 != 0 ? 0xfffcb933bd6fad37aa2d162d1a594001 : 0x100000000000000000000000000000000;
                              //     or price = int(2**128 / sqrt(1.0001)) if (absTick & 0x1) else 1 << 128
                              uint256 price;
                              assembly ("memory-safe") {
                                  price := xor(shl(128, 1), mul(xor(shl(128, 1), 0xfffcb933bd6fad37aa2d162d1a594001), and(absTick, 0x1)))
                              }
                              if (absTick & 0x2 != 0) price = (price * 0xfff97272373d413259a46990580e213a) >> 128;
                              if (absTick & 0x4 != 0) price = (price * 0xfff2e50f5f656932ef12357cf3c7fdcc) >> 128;
                              if (absTick & 0x8 != 0) price = (price * 0xffe5caca7e10e4e61c3624eaa0941cd0) >> 128;
                              if (absTick & 0x10 != 0) price = (price * 0xffcb9843d60f6159c9db58835c926644) >> 128;
                              if (absTick & 0x20 != 0) price = (price * 0xff973b41fa98c081472e6896dfb254c0) >> 128;
                              if (absTick & 0x40 != 0) price = (price * 0xff2ea16466c96a3843ec78b326b52861) >> 128;
                              if (absTick & 0x80 != 0) price = (price * 0xfe5dee046a99a2a811c461f1969c3053) >> 128;
                              if (absTick & 0x100 != 0) price = (price * 0xfcbe86c7900a88aedcffc83b479aa3a4) >> 128;
                              if (absTick & 0x200 != 0) price = (price * 0xf987a7253ac413176f2b074cf7815e54) >> 128;
                              if (absTick & 0x400 != 0) price = (price * 0xf3392b0822b70005940c7a398e4b70f3) >> 128;
                              if (absTick & 0x800 != 0) price = (price * 0xe7159475a2c29b7443b29c7fa6e889d9) >> 128;
                              if (absTick & 0x1000 != 0) price = (price * 0xd097f3bdfd2022b8845ad8f792aa5825) >> 128;
                              if (absTick & 0x2000 != 0) price = (price * 0xa9f746462d870fdf8a65dc1f90e061e5) >> 128;
                              if (absTick & 0x4000 != 0) price = (price * 0x70d869a156d2a1b890bb3df62baf32f7) >> 128;
                              if (absTick & 0x8000 != 0) price = (price * 0x31be135f97d08fd981231505542fcfa6) >> 128;
                              if (absTick & 0x10000 != 0) price = (price * 0x9aa508b5b7a84e1c677de54f3e99bc9) >> 128;
                              if (absTick & 0x20000 != 0) price = (price * 0x5d6af8dedb81196699c329225ee604) >> 128;
                              if (absTick & 0x40000 != 0) price = (price * 0x2216e584f5fa1ea926041bedfe98) >> 128;
                              if (absTick & 0x80000 != 0) price = (price * 0x48a170391f7dc42444e8fa2) >> 128;
                              assembly ("memory-safe") {
                                  // if (tick > 0) price = type(uint256).max / price;
                                  if sgt(tick, 0) { price := div(not(0), price) }
                                  // this divides by 1<<32 rounding up to go from a Q128.128 to a Q128.96.
                                  // we then downcast because we know the result always fits within 160 bits due to our tick input constraint
                                  // we round up in the division so getTickAtSqrtPrice of the output price is always consistent
                                  // `sub(shl(32, 1), 1)` is `type(uint32).max`
                                  // `price + type(uint32).max` will not overflow because `price` fits in 192 bits
                                  sqrtPriceX96 := shr(32, add(price, sub(shl(32, 1), 1)))
                              }
                          }
                      }
                      /// @notice Calculates the greatest tick value such that getSqrtPriceAtTick(tick) <= sqrtPriceX96
                      /// @dev Throws in case sqrtPriceX96 < MIN_SQRT_PRICE, as MIN_SQRT_PRICE is the lowest value getSqrtPriceAtTick may
                      /// ever return.
                      /// @param sqrtPriceX96 The sqrt price for which to compute the tick as a Q64.96
                      /// @return tick The greatest tick for which the getSqrtPriceAtTick(tick) is less than or equal to the input sqrtPriceX96
                      function getTickAtSqrtPrice(uint160 sqrtPriceX96) internal pure returns (int24 tick) {
                          unchecked {
                              // Equivalent: if (sqrtPriceX96 < MIN_SQRT_PRICE || sqrtPriceX96 >= MAX_SQRT_PRICE) revert InvalidSqrtPrice();
                              // second inequality must be >= because the price can never reach the price at the max tick
                              // if sqrtPriceX96 < MIN_SQRT_PRICE, the `sub` underflows and `gt` is true
                              // if sqrtPriceX96 >= MAX_SQRT_PRICE, sqrtPriceX96 - MIN_SQRT_PRICE > MAX_SQRT_PRICE - MIN_SQRT_PRICE - 1
                              if ((sqrtPriceX96 - MIN_SQRT_PRICE) > MAX_SQRT_PRICE_MINUS_MIN_SQRT_PRICE_MINUS_ONE) {
                                  InvalidSqrtPrice.selector.revertWith(sqrtPriceX96);
                              }
                              uint256 price = uint256(sqrtPriceX96) << 32;
                              uint256 r = price;
                              uint256 msb = BitMath.mostSignificantBit(r);
                              if (msb >= 128) r = price >> (msb - 127);
                              else r = price << (127 - msb);
                              int256 log_2 = (int256(msb) - 128) << 64;
                              assembly ("memory-safe") {
                                  r := shr(127, mul(r, r))
                                  let f := shr(128, r)
                                  log_2 := or(log_2, shl(63, f))
                                  r := shr(f, r)
                              }
                              assembly ("memory-safe") {
                                  r := shr(127, mul(r, r))
                                  let f := shr(128, r)
                                  log_2 := or(log_2, shl(62, f))
                                  r := shr(f, r)
                              }
                              assembly ("memory-safe") {
                                  r := shr(127, mul(r, r))
                                  let f := shr(128, r)
                                  log_2 := or(log_2, shl(61, f))
                                  r := shr(f, r)
                              }
                              assembly ("memory-safe") {
                                  r := shr(127, mul(r, r))
                                  let f := shr(128, r)
                                  log_2 := or(log_2, shl(60, f))
                                  r := shr(f, r)
                              }
                              assembly ("memory-safe") {
                                  r := shr(127, mul(r, r))
                                  let f := shr(128, r)
                                  log_2 := or(log_2, shl(59, f))
                                  r := shr(f, r)
                              }
                              assembly ("memory-safe") {
                                  r := shr(127, mul(r, r))
                                  let f := shr(128, r)
                                  log_2 := or(log_2, shl(58, f))
                                  r := shr(f, r)
                              }
                              assembly ("memory-safe") {
                                  r := shr(127, mul(r, r))
                                  let f := shr(128, r)
                                  log_2 := or(log_2, shl(57, f))
                                  r := shr(f, r)
                              }
                              assembly ("memory-safe") {
                                  r := shr(127, mul(r, r))
                                  let f := shr(128, r)
                                  log_2 := or(log_2, shl(56, f))
                                  r := shr(f, r)
                              }
                              assembly ("memory-safe") {
                                  r := shr(127, mul(r, r))
                                  let f := shr(128, r)
                                  log_2 := or(log_2, shl(55, f))
                                  r := shr(f, r)
                              }
                              assembly ("memory-safe") {
                                  r := shr(127, mul(r, r))
                                  let f := shr(128, r)
                                  log_2 := or(log_2, shl(54, f))
                                  r := shr(f, r)
                              }
                              assembly ("memory-safe") {
                                  r := shr(127, mul(r, r))
                                  let f := shr(128, r)
                                  log_2 := or(log_2, shl(53, f))
                                  r := shr(f, r)
                              }
                              assembly ("memory-safe") {
                                  r := shr(127, mul(r, r))
                                  let f := shr(128, r)
                                  log_2 := or(log_2, shl(52, f))
                                  r := shr(f, r)
                              }
                              assembly ("memory-safe") {
                                  r := shr(127, mul(r, r))
                                  let f := shr(128, r)
                                  log_2 := or(log_2, shl(51, f))
                                  r := shr(f, r)
                              }
                              assembly ("memory-safe") {
                                  r := shr(127, mul(r, r))
                                  let f := shr(128, r)
                                  log_2 := or(log_2, shl(50, f))
                              }
                              int256 log_sqrt10001 = log_2 * 255738958999603826347141; // Q22.128 number
                              // Magic number represents the ceiling of the maximum value of the error when approximating log_sqrt10001(x)
                              int24 tickLow = int24((log_sqrt10001 - 3402992956809132418596140100660247210) >> 128);
                              // Magic number represents the minimum value of the error when approximating log_sqrt10001(x), when
                              // sqrtPrice is from the range (2^-64, 2^64). This is safe as MIN_SQRT_PRICE is more than 2^-64. If MIN_SQRT_PRICE
                              // is changed, this may need to be changed too
                              int24 tickHi = int24((log_sqrt10001 + 291339464771989622907027621153398088495) >> 128);
                              tick = tickLow == tickHi ? tickLow : getSqrtPriceAtTick(tickHi) <= sqrtPriceX96 ? tickHi : tickLow;
                          }
                      }
                  }
                  // SPDX-License-Identifier: MIT
                  pragma solidity ^0.8.0;
                  import {CustomRevert} from "./libraries/CustomRevert.sol";
                  /// @title Prevents delegatecall to a contract
                  /// @notice Base contract that provides a modifier for preventing delegatecall to methods in a child contract
                  abstract contract NoDelegateCall {
                      using CustomRevert for bytes4;
                      error DelegateCallNotAllowed();
                      /// @dev The original address of this contract
                      address private immutable original;
                      constructor() {
                          // Immutables are computed in the init code of the contract, and then inlined into the deployed bytecode.
                          // In other words, this variable won't change when it's checked at runtime.
                          original = address(this);
                      }
                      /// @dev Private method is used instead of inlining into modifier because modifiers are copied into each method,
                      ///     and the use of immutable means the address bytes are copied in every place the modifier is used.
                      function checkNotDelegateCall() private view {
                          if (address(this) != original) DelegateCallNotAllowed.selector.revertWith();
                      }
                      /// @notice Prevents delegatecall into the modified method
                      modifier noDelegateCall() {
                          checkNotDelegateCall();
                          _;
                      }
                  }
                  // SPDX-License-Identifier: MIT
                  pragma solidity ^0.8.0;
                  import {PoolKey} from "../types/PoolKey.sol";
                  import {BalanceDelta} from "../types/BalanceDelta.sol";
                  import {IPoolManager} from "./IPoolManager.sol";
                  import {BeforeSwapDelta} from "../types/BeforeSwapDelta.sol";
                  /// @notice V4 decides whether to invoke specific hooks by inspecting the least significant bits
                  /// of the address that the hooks contract is deployed to.
                  /// For example, a hooks contract deployed to address: 0x0000000000000000000000000000000000002400
                  /// has the lowest bits '10 0100 0000 0000' which would cause the 'before initialize' and 'after add liquidity' hooks to be used.
                  /// See the Hooks library for the full spec.
                  /// @dev Should only be callable by the v4 PoolManager.
                  interface IHooks {
                      /// @notice The hook called before the state of a pool is initialized
                      /// @param sender The initial msg.sender for the initialize call
                      /// @param key The key for the pool being initialized
                      /// @param sqrtPriceX96 The sqrt(price) of the pool as a Q64.96
                      /// @return bytes4 The function selector for the hook
                      function beforeInitialize(address sender, PoolKey calldata key, uint160 sqrtPriceX96) external returns (bytes4);
                      /// @notice The hook called after the state of a pool is initialized
                      /// @param sender The initial msg.sender for the initialize call
                      /// @param key The key for the pool being initialized
                      /// @param sqrtPriceX96 The sqrt(price) of the pool as a Q64.96
                      /// @param tick The current tick after the state of a pool is initialized
                      /// @return bytes4 The function selector for the hook
                      function afterInitialize(address sender, PoolKey calldata key, uint160 sqrtPriceX96, int24 tick)
                          external
                          returns (bytes4);
                      /// @notice The hook called before liquidity is added
                      /// @param sender The initial msg.sender for the add liquidity call
                      /// @param key The key for the pool
                      /// @param params The parameters for adding liquidity
                      /// @param hookData Arbitrary data handed into the PoolManager by the liquidity provider to be passed on to the hook
                      /// @return bytes4 The function selector for the hook
                      function beforeAddLiquidity(
                          address sender,
                          PoolKey calldata key,
                          IPoolManager.ModifyLiquidityParams calldata params,
                          bytes calldata hookData
                      ) external returns (bytes4);
                      /// @notice The hook called after liquidity is added
                      /// @param sender The initial msg.sender for the add liquidity call
                      /// @param key The key for the pool
                      /// @param params The parameters for adding liquidity
                      /// @param delta The caller's balance delta after adding liquidity; the sum of principal delta, fees accrued, and hook delta
                      /// @param feesAccrued The fees accrued since the last time fees were collected from this position
                      /// @param hookData Arbitrary data handed into the PoolManager by the liquidity provider to be passed on to the hook
                      /// @return bytes4 The function selector for the hook
                      /// @return BalanceDelta The hook's delta in token0 and token1. Positive: the hook is owed/took currency, negative: the hook owes/sent currency
                      function afterAddLiquidity(
                          address sender,
                          PoolKey calldata key,
                          IPoolManager.ModifyLiquidityParams calldata params,
                          BalanceDelta delta,
                          BalanceDelta feesAccrued,
                          bytes calldata hookData
                      ) external returns (bytes4, BalanceDelta);
                      /// @notice The hook called before liquidity is removed
                      /// @param sender The initial msg.sender for the remove liquidity call
                      /// @param key The key for the pool
                      /// @param params The parameters for removing liquidity
                      /// @param hookData Arbitrary data handed into the PoolManager by the liquidity provider to be be passed on to the hook
                      /// @return bytes4 The function selector for the hook
                      function beforeRemoveLiquidity(
                          address sender,
                          PoolKey calldata key,
                          IPoolManager.ModifyLiquidityParams calldata params,
                          bytes calldata hookData
                      ) external returns (bytes4);
                      /// @notice The hook called after liquidity is removed
                      /// @param sender The initial msg.sender for the remove liquidity call
                      /// @param key The key for the pool
                      /// @param params The parameters for removing liquidity
                      /// @param delta The caller's balance delta after removing liquidity; the sum of principal delta, fees accrued, and hook delta
                      /// @param feesAccrued The fees accrued since the last time fees were collected from this position
                      /// @param hookData Arbitrary data handed into the PoolManager by the liquidity provider to be be passed on to the hook
                      /// @return bytes4 The function selector for the hook
                      /// @return BalanceDelta The hook's delta in token0 and token1. Positive: the hook is owed/took currency, negative: the hook owes/sent currency
                      function afterRemoveLiquidity(
                          address sender,
                          PoolKey calldata key,
                          IPoolManager.ModifyLiquidityParams calldata params,
                          BalanceDelta delta,
                          BalanceDelta feesAccrued,
                          bytes calldata hookData
                      ) external returns (bytes4, BalanceDelta);
                      /// @notice The hook called before a swap
                      /// @param sender The initial msg.sender for the swap call
                      /// @param key The key for the pool
                      /// @param params The parameters for the swap
                      /// @param hookData Arbitrary data handed into the PoolManager by the swapper to be be passed on to the hook
                      /// @return bytes4 The function selector for the hook
                      /// @return BeforeSwapDelta The hook's delta in specified and unspecified currencies. Positive: the hook is owed/took currency, negative: the hook owes/sent currency
                      /// @return uint24 Optionally override the lp fee, only used if three conditions are met: 1. the Pool has a dynamic fee, 2. the value's 2nd highest bit is set (23rd bit, 0x400000), and 3. the value is less than or equal to the maximum fee (1 million)
                      function beforeSwap(
                          address sender,
                          PoolKey calldata key,
                          IPoolManager.SwapParams calldata params,
                          bytes calldata hookData
                      ) external returns (bytes4, BeforeSwapDelta, uint24);
                      /// @notice The hook called after a swap
                      /// @param sender The initial msg.sender for the swap call
                      /// @param key The key for the pool
                      /// @param params The parameters for the swap
                      /// @param delta The amount owed to the caller (positive) or owed to the pool (negative)
                      /// @param hookData Arbitrary data handed into the PoolManager by the swapper to be be passed on to the hook
                      /// @return bytes4 The function selector for the hook
                      /// @return int128 The hook's delta in unspecified currency. Positive: the hook is owed/took currency, negative: the hook owes/sent currency
                      function afterSwap(
                          address sender,
                          PoolKey calldata key,
                          IPoolManager.SwapParams calldata params,
                          BalanceDelta delta,
                          bytes calldata hookData
                      ) external returns (bytes4, int128);
                      /// @notice The hook called before donate
                      /// @param sender The initial msg.sender for the donate call
                      /// @param key The key for the pool
                      /// @param amount0 The amount of token0 being donated
                      /// @param amount1 The amount of token1 being donated
                      /// @param hookData Arbitrary data handed into the PoolManager by the donor to be be passed on to the hook
                      /// @return bytes4 The function selector for the hook
                      function beforeDonate(
                          address sender,
                          PoolKey calldata key,
                          uint256 amount0,
                          uint256 amount1,
                          bytes calldata hookData
                      ) external returns (bytes4);
                      /// @notice The hook called after donate
                      /// @param sender The initial msg.sender for the donate call
                      /// @param key The key for the pool
                      /// @param amount0 The amount of token0 being donated
                      /// @param amount1 The amount of token1 being donated
                      /// @param hookData Arbitrary data handed into the PoolManager by the donor to be be passed on to the hook
                      /// @return bytes4 The function selector for the hook
                      function afterDonate(
                          address sender,
                          PoolKey calldata key,
                          uint256 amount0,
                          uint256 amount1,
                          bytes calldata hookData
                      ) external returns (bytes4);
                  }
                  // SPDX-License-Identifier: MIT
                  pragma solidity ^0.8.24;
                  import {Currency} from "../types/Currency.sol";
                  import {PoolKey} from "../types/PoolKey.sol";
                  import {IHooks} from "./IHooks.sol";
                  import {IERC6909Claims} from "./external/IERC6909Claims.sol";
                  import {IProtocolFees} from "./IProtocolFees.sol";
                  import {BalanceDelta} from "../types/BalanceDelta.sol";
                  import {PoolId} from "../types/PoolId.sol";
                  import {IExtsload} from "./IExtsload.sol";
                  import {IExttload} from "./IExttload.sol";
                  /// @notice Interface for the PoolManager
                  interface IPoolManager is IProtocolFees, IERC6909Claims, IExtsload, IExttload {
                      /// @notice Thrown when a currency is not netted out after the contract is unlocked
                      error CurrencyNotSettled();
                      /// @notice Thrown when trying to interact with a non-initialized pool
                      error PoolNotInitialized();
                      /// @notice Thrown when unlock is called, but the contract is already unlocked
                      error AlreadyUnlocked();
                      /// @notice Thrown when a function is called that requires the contract to be unlocked, but it is not
                      error ManagerLocked();
                      /// @notice Pools are limited to type(int16).max tickSpacing in #initialize, to prevent overflow
                      error TickSpacingTooLarge(int24 tickSpacing);
                      /// @notice Pools must have a positive non-zero tickSpacing passed to #initialize
                      error TickSpacingTooSmall(int24 tickSpacing);
                      /// @notice PoolKey must have currencies where address(currency0) < address(currency1)
                      error CurrenciesOutOfOrderOrEqual(address currency0, address currency1);
                      /// @notice Thrown when a call to updateDynamicLPFee is made by an address that is not the hook,
                      /// or on a pool that does not have a dynamic swap fee.
                      error UnauthorizedDynamicLPFeeUpdate();
                      /// @notice Thrown when trying to swap amount of 0
                      error SwapAmountCannotBeZero();
                      ///@notice Thrown when native currency is passed to a non native settlement
                      error NonzeroNativeValue();
                      /// @notice Thrown when `clear` is called with an amount that is not exactly equal to the open currency delta.
                      error MustClearExactPositiveDelta();
                      /// @notice Emitted when a new pool is initialized
                      /// @param id The abi encoded hash of the pool key struct for the new pool
                      /// @param currency0 The first currency of the pool by address sort order
                      /// @param currency1 The second currency of the pool by address sort order
                      /// @param fee The fee collected upon every swap in the pool, denominated in hundredths of a bip
                      /// @param tickSpacing The minimum number of ticks between initialized ticks
                      /// @param hooks The hooks contract address for the pool, or address(0) if none
                      /// @param sqrtPriceX96 The price of the pool on initialization
                      /// @param tick The initial tick of the pool corresponding to the initialized price
                      event Initialize(
                          PoolId indexed id,
                          Currency indexed currency0,
                          Currency indexed currency1,
                          uint24 fee,
                          int24 tickSpacing,
                          IHooks hooks,
                          uint160 sqrtPriceX96,
                          int24 tick
                      );
                      /// @notice Emitted when a liquidity position is modified
                      /// @param id The abi encoded hash of the pool key struct for the pool that was modified
                      /// @param sender The address that modified the pool
                      /// @param tickLower The lower tick of the position
                      /// @param tickUpper The upper tick of the position
                      /// @param liquidityDelta The amount of liquidity that was added or removed
                      /// @param salt The extra data to make positions unique
                      event ModifyLiquidity(
                          PoolId indexed id, address indexed sender, int24 tickLower, int24 tickUpper, int256 liquidityDelta, bytes32 salt
                      );
                      /// @notice Emitted for swaps between currency0 and currency1
                      /// @param id The abi encoded hash of the pool key struct for the pool that was modified
                      /// @param sender The address that initiated the swap call, and that received the callback
                      /// @param amount0 The delta of the currency0 balance of the pool
                      /// @param amount1 The delta of the currency1 balance of the pool
                      /// @param sqrtPriceX96 The sqrt(price) of the pool after the swap, as a Q64.96
                      /// @param liquidity The liquidity of the pool after the swap
                      /// @param tick The log base 1.0001 of the price of the pool after the swap
                      /// @param fee The swap fee in hundredths of a bip
                      event Swap(
                          PoolId indexed id,
                          address indexed sender,
                          int128 amount0,
                          int128 amount1,
                          uint160 sqrtPriceX96,
                          uint128 liquidity,
                          int24 tick,
                          uint24 fee
                      );
                      /// @notice Emitted for donations
                      /// @param id The abi encoded hash of the pool key struct for the pool that was donated to
                      /// @param sender The address that initiated the donate call
                      /// @param amount0 The amount donated in currency0
                      /// @param amount1 The amount donated in currency1
                      event Donate(PoolId indexed id, address indexed sender, uint256 amount0, uint256 amount1);
                      /// @notice All interactions on the contract that account deltas require unlocking. A caller that calls `unlock` must implement
                      /// `IUnlockCallback(msg.sender).unlockCallback(data)`, where they interact with the remaining functions on this contract.
                      /// @dev The only functions callable without an unlocking are `initialize` and `updateDynamicLPFee`
                      /// @param data Any data to pass to the callback, via `IUnlockCallback(msg.sender).unlockCallback(data)`
                      /// @return The data returned by the call to `IUnlockCallback(msg.sender).unlockCallback(data)`
                      function unlock(bytes calldata data) external returns (bytes memory);
                      /// @notice Initialize the state for a given pool ID
                      /// @dev A swap fee totaling MAX_SWAP_FEE (100%) makes exact output swaps impossible since the input is entirely consumed by the fee
                      /// @param key The pool key for the pool to initialize
                      /// @param sqrtPriceX96 The initial square root price
                      /// @return tick The initial tick of the pool
                      function initialize(PoolKey memory key, uint160 sqrtPriceX96) external returns (int24 tick);
                      struct ModifyLiquidityParams {
                          // the lower and upper tick of the position
                          int24 tickLower;
                          int24 tickUpper;
                          // how to modify the liquidity
                          int256 liquidityDelta;
                          // a value to set if you want unique liquidity positions at the same range
                          bytes32 salt;
                      }
                      /// @notice Modify the liquidity for the given pool
                      /// @dev Poke by calling with a zero liquidityDelta
                      /// @param key The pool to modify liquidity in
                      /// @param params The parameters for modifying the liquidity
                      /// @param hookData The data to pass through to the add/removeLiquidity hooks
                      /// @return callerDelta The balance delta of the caller of modifyLiquidity. This is the total of both principal, fee deltas, and hook deltas if applicable
                      /// @return feesAccrued The balance delta of the fees generated in the liquidity range. Returned for informational purposes
                      /// @dev Note that feesAccrued can be artificially inflated by a malicious actor and integrators should be careful using the value
                      /// For pools with a single liquidity position, actors can donate to themselves to inflate feeGrowthGlobal (and consequently feesAccrued)
                      /// atomically donating and collecting fees in the same unlockCallback may make the inflated value more extreme
                      function modifyLiquidity(PoolKey memory key, ModifyLiquidityParams memory params, bytes calldata hookData)
                          external
                          returns (BalanceDelta callerDelta, BalanceDelta feesAccrued);
                      struct SwapParams {
                          /// Whether to swap token0 for token1 or vice versa
                          bool zeroForOne;
                          /// The desired input amount if negative (exactIn), or the desired output amount if positive (exactOut)
                          int256 amountSpecified;
                          /// The sqrt price at which, if reached, the swap will stop executing
                          uint160 sqrtPriceLimitX96;
                      }
                      /// @notice Swap against the given pool
                      /// @param key The pool to swap in
                      /// @param params The parameters for swapping
                      /// @param hookData The data to pass through to the swap hooks
                      /// @return swapDelta The balance delta of the address swapping
                      /// @dev Swapping on low liquidity pools may cause unexpected swap amounts when liquidity available is less than amountSpecified.
                      /// Additionally note that if interacting with hooks that have the BEFORE_SWAP_RETURNS_DELTA_FLAG or AFTER_SWAP_RETURNS_DELTA_FLAG
                      /// the hook may alter the swap input/output. Integrators should perform checks on the returned swapDelta.
                      function swap(PoolKey memory key, SwapParams memory params, bytes calldata hookData)
                          external
                          returns (BalanceDelta swapDelta);
                      /// @notice Donate the given currency amounts to the in-range liquidity providers of a pool
                      /// @dev Calls to donate can be frontrun adding just-in-time liquidity, with the aim of receiving a portion donated funds.
                      /// Donors should keep this in mind when designing donation mechanisms.
                      /// @dev This function donates to in-range LPs at slot0.tick. In certain edge-cases of the swap algorithm, the `sqrtPrice` of
                      /// a pool can be at the lower boundary of tick `n`, but the `slot0.tick` of the pool is already `n - 1`. In this case a call to
                      /// `donate` would donate to tick `n - 1` (slot0.tick) not tick `n` (getTickAtSqrtPrice(slot0.sqrtPriceX96)).
                      /// Read the comments in `Pool.swap()` for more information about this.
                      /// @param key The key of the pool to donate to
                      /// @param amount0 The amount of currency0 to donate
                      /// @param amount1 The amount of currency1 to donate
                      /// @param hookData The data to pass through to the donate hooks
                      /// @return BalanceDelta The delta of the caller after the donate
                      function donate(PoolKey memory key, uint256 amount0, uint256 amount1, bytes calldata hookData)
                          external
                          returns (BalanceDelta);
                      /// @notice Writes the current ERC20 balance of the specified currency to transient storage
                      /// This is used to checkpoint balances for the manager and derive deltas for the caller.
                      /// @dev This MUST be called before any ERC20 tokens are sent into the contract, but can be skipped
                      /// for native tokens because the amount to settle is determined by the sent value.
                      /// However, if an ERC20 token has been synced and not settled, and the caller instead wants to settle
                      /// native funds, this function can be called with the native currency to then be able to settle the native currency
                      function sync(Currency currency) external;
                      /// @notice Called by the user to net out some value owed to the user
                      /// @dev Will revert if the requested amount is not available, consider using `mint` instead
                      /// @dev Can also be used as a mechanism for free flash loans
                      /// @param currency The currency to withdraw from the pool manager
                      /// @param to The address to withdraw to
                      /// @param amount The amount of currency to withdraw
                      function take(Currency currency, address to, uint256 amount) external;
                      /// @notice Called by the user to pay what is owed
                      /// @return paid The amount of currency settled
                      function settle() external payable returns (uint256 paid);
                      /// @notice Called by the user to pay on behalf of another address
                      /// @param recipient The address to credit for the payment
                      /// @return paid The amount of currency settled
                      function settleFor(address recipient) external payable returns (uint256 paid);
                      /// @notice WARNING - Any currency that is cleared, will be non-retrievable, and locked in the contract permanently.
                      /// A call to clear will zero out a positive balance WITHOUT a corresponding transfer.
                      /// @dev This could be used to clear a balance that is considered dust.
                      /// Additionally, the amount must be the exact positive balance. This is to enforce that the caller is aware of the amount being cleared.
                      function clear(Currency currency, uint256 amount) external;
                      /// @notice Called by the user to move value into ERC6909 balance
                      /// @param to The address to mint the tokens to
                      /// @param id The currency address to mint to ERC6909s, as a uint256
                      /// @param amount The amount of currency to mint
                      /// @dev The id is converted to a uint160 to correspond to a currency address
                      /// If the upper 12 bytes are not 0, they will be 0-ed out
                      function mint(address to, uint256 id, uint256 amount) external;
                      /// @notice Called by the user to move value from ERC6909 balance
                      /// @param from The address to burn the tokens from
                      /// @param id The currency address to burn from ERC6909s, as a uint256
                      /// @param amount The amount of currency to burn
                      /// @dev The id is converted to a uint160 to correspond to a currency address
                      /// If the upper 12 bytes are not 0, they will be 0-ed out
                      function burn(address from, uint256 id, uint256 amount) external;
                      /// @notice Updates the pools lp fees for the a pool that has enabled dynamic lp fees.
                      /// @dev A swap fee totaling MAX_SWAP_FEE (100%) makes exact output swaps impossible since the input is entirely consumed by the fee
                      /// @param key The key of the pool to update dynamic LP fees for
                      /// @param newDynamicLPFee The new dynamic pool LP fee
                      function updateDynamicLPFee(PoolKey memory key, uint24 newDynamicLPFee) external;
                  }
                  // SPDX-License-Identifier: MIT
                  pragma solidity ^0.8.0;
                  /// @notice Interface for the callback executed when an address unlocks the pool manager
                  interface IUnlockCallback {
                      /// @notice Called by the pool manager on `msg.sender` when the manager is unlocked
                      /// @param data The data that was passed to the call to unlock
                      /// @return Any data that you want to be returned from the unlock call
                      function unlockCallback(bytes calldata data) external returns (bytes memory);
                  }
                  // SPDX-License-Identifier: MIT
                  pragma solidity ^0.8.0;
                  import {Currency} from "./types/Currency.sol";
                  import {CurrencyReserves} from "./libraries/CurrencyReserves.sol";
                  import {IProtocolFees} from "./interfaces/IProtocolFees.sol";
                  import {PoolKey} from "./types/PoolKey.sol";
                  import {ProtocolFeeLibrary} from "./libraries/ProtocolFeeLibrary.sol";
                  import {Owned} from "solmate/src/auth/Owned.sol";
                  import {PoolId} from "./types/PoolId.sol";
                  import {Pool} from "./libraries/Pool.sol";
                  import {CustomRevert} from "./libraries/CustomRevert.sol";
                  /// @notice Contract handling the setting and accrual of protocol fees
                  abstract contract ProtocolFees is IProtocolFees, Owned {
                      using ProtocolFeeLibrary for uint24;
                      using Pool for Pool.State;
                      using CustomRevert for bytes4;
                      /// @inheritdoc IProtocolFees
                      mapping(Currency currency => uint256 amount) public protocolFeesAccrued;
                      /// @inheritdoc IProtocolFees
                      address public protocolFeeController;
                      constructor(address initialOwner) Owned(initialOwner) {}
                      /// @inheritdoc IProtocolFees
                      function setProtocolFeeController(address controller) external onlyOwner {
                          protocolFeeController = controller;
                          emit ProtocolFeeControllerUpdated(controller);
                      }
                      /// @inheritdoc IProtocolFees
                      function setProtocolFee(PoolKey memory key, uint24 newProtocolFee) external {
                          if (msg.sender != protocolFeeController) InvalidCaller.selector.revertWith();
                          if (!newProtocolFee.isValidProtocolFee()) ProtocolFeeTooLarge.selector.revertWith(newProtocolFee);
                          PoolId id = key.toId();
                          _getPool(id).setProtocolFee(newProtocolFee);
                          emit ProtocolFeeUpdated(id, newProtocolFee);
                      }
                      /// @inheritdoc IProtocolFees
                      function collectProtocolFees(address recipient, Currency currency, uint256 amount)
                          external
                          returns (uint256 amountCollected)
                      {
                          if (msg.sender != protocolFeeController) InvalidCaller.selector.revertWith();
                          if (!currency.isAddressZero() && CurrencyReserves.getSyncedCurrency() == currency) {
                              // prevent transfer between the sync and settle balanceOfs (native settle uses msg.value)
                              ProtocolFeeCurrencySynced.selector.revertWith();
                          }
                          amountCollected = (amount == 0) ? protocolFeesAccrued[currency] : amount;
                          protocolFeesAccrued[currency] -= amountCollected;
                          currency.transfer(recipient, amountCollected);
                      }
                      /// @dev abstract internal function to allow the ProtocolFees contract to access the lock
                      function _isUnlocked() internal virtual returns (bool);
                      /// @dev abstract internal function to allow the ProtocolFees contract to access pool state
                      /// @dev this is overridden in PoolManager.sol to give access to the _pools mapping
                      function _getPool(PoolId id) internal virtual returns (Pool.State storage);
                      function _updateProtocolFees(Currency currency, uint256 amount) internal {
                          unchecked {
                              protocolFeesAccrued[currency] += amount;
                          }
                      }
                  }
                  // SPDX-License-Identifier: MIT
                  pragma solidity ^0.8.0;
                  import {ERC6909} from "./ERC6909.sol";
                  /// @notice ERC6909Claims inherits ERC6909 and implements an internal burnFrom function
                  abstract contract ERC6909Claims is ERC6909 {
                      /// @notice Burn `amount` tokens of token type `id` from `from`.
                      /// @dev if sender is not `from` they must be an operator or have sufficient allowance.
                      /// @param from The address to burn tokens from.
                      /// @param id The currency to burn.
                      /// @param amount The amount to burn.
                      function _burnFrom(address from, uint256 id, uint256 amount) internal {
                          address sender = msg.sender;
                          if (from != sender && !isOperator[from][sender]) {
                              uint256 senderAllowance = allowance[from][sender][id];
                              if (senderAllowance != type(uint256).max) {
                                  allowance[from][sender][id] = senderAllowance - amount;
                              }
                          }
                          _burn(from, id, amount);
                      }
                  }
                  // SPDX-License-Identifier: MIT
                  pragma solidity ^0.8.0;
                  import {PoolKey} from "./PoolKey.sol";
                  type PoolId is bytes32;
                  /// @notice Library for computing the ID of a pool
                  library PoolIdLibrary {
                      /// @notice Returns value equal to keccak256(abi.encode(poolKey))
                      function toId(PoolKey memory poolKey) internal pure returns (PoolId poolId) {
                          assembly ("memory-safe") {
                              // 0xa0 represents the total size of the poolKey struct (5 slots of 32 bytes)
                              poolId := keccak256(poolKey, 0xa0)
                          }
                      }
                  }
                  // SPDX-License-Identifier: MIT
                  pragma solidity ^0.8.0;
                  import {SafeCast} from "../libraries/SafeCast.sol";
                  /// @dev Two `int128` values packed into a single `int256` where the upper 128 bits represent the amount0
                  /// and the lower 128 bits represent the amount1.
                  type BalanceDelta is int256;
                  using {add as +, sub as -, eq as ==, neq as !=} for BalanceDelta global;
                  using BalanceDeltaLibrary for BalanceDelta global;
                  using SafeCast for int256;
                  function toBalanceDelta(int128 _amount0, int128 _amount1) pure returns (BalanceDelta balanceDelta) {
                      assembly ("memory-safe") {
                          balanceDelta := or(shl(128, _amount0), and(sub(shl(128, 1), 1), _amount1))
                      }
                  }
                  function add(BalanceDelta a, BalanceDelta b) pure returns (BalanceDelta) {
                      int256 res0;
                      int256 res1;
                      assembly ("memory-safe") {
                          let a0 := sar(128, a)
                          let a1 := signextend(15, a)
                          let b0 := sar(128, b)
                          let b1 := signextend(15, b)
                          res0 := add(a0, b0)
                          res1 := add(a1, b1)
                      }
                      return toBalanceDelta(res0.toInt128(), res1.toInt128());
                  }
                  function sub(BalanceDelta a, BalanceDelta b) pure returns (BalanceDelta) {
                      int256 res0;
                      int256 res1;
                      assembly ("memory-safe") {
                          let a0 := sar(128, a)
                          let a1 := signextend(15, a)
                          let b0 := sar(128, b)
                          let b1 := signextend(15, b)
                          res0 := sub(a0, b0)
                          res1 := sub(a1, b1)
                      }
                      return toBalanceDelta(res0.toInt128(), res1.toInt128());
                  }
                  function eq(BalanceDelta a, BalanceDelta b) pure returns (bool) {
                      return BalanceDelta.unwrap(a) == BalanceDelta.unwrap(b);
                  }
                  function neq(BalanceDelta a, BalanceDelta b) pure returns (bool) {
                      return BalanceDelta.unwrap(a) != BalanceDelta.unwrap(b);
                  }
                  /// @notice Library for getting the amount0 and amount1 deltas from the BalanceDelta type
                  library BalanceDeltaLibrary {
                      /// @notice A BalanceDelta of 0
                      BalanceDelta public constant ZERO_DELTA = BalanceDelta.wrap(0);
                      function amount0(BalanceDelta balanceDelta) internal pure returns (int128 _amount0) {
                          assembly ("memory-safe") {
                              _amount0 := sar(128, balanceDelta)
                          }
                      }
                      function amount1(BalanceDelta balanceDelta) internal pure returns (int128 _amount1) {
                          assembly ("memory-safe") {
                              _amount1 := signextend(15, balanceDelta)
                          }
                      }
                  }
                  // SPDX-License-Identifier: MIT
                  pragma solidity ^0.8.0;
                  // Return type of the beforeSwap hook.
                  // Upper 128 bits is the delta in specified tokens. Lower 128 bits is delta in unspecified tokens (to match the afterSwap hook)
                  type BeforeSwapDelta is int256;
                  // Creates a BeforeSwapDelta from specified and unspecified
                  function toBeforeSwapDelta(int128 deltaSpecified, int128 deltaUnspecified)
                      pure
                      returns (BeforeSwapDelta beforeSwapDelta)
                  {
                      assembly ("memory-safe") {
                          beforeSwapDelta := or(shl(128, deltaSpecified), and(sub(shl(128, 1), 1), deltaUnspecified))
                      }
                  }
                  /// @notice Library for getting the specified and unspecified deltas from the BeforeSwapDelta type
                  library BeforeSwapDeltaLibrary {
                      /// @notice A BeforeSwapDelta of 0
                      BeforeSwapDelta public constant ZERO_DELTA = BeforeSwapDelta.wrap(0);
                      /// extracts int128 from the upper 128 bits of the BeforeSwapDelta
                      /// returned by beforeSwap
                      function getSpecifiedDelta(BeforeSwapDelta delta) internal pure returns (int128 deltaSpecified) {
                          assembly ("memory-safe") {
                              deltaSpecified := sar(128, delta)
                          }
                      }
                      /// extracts int128 from the lower 128 bits of the BeforeSwapDelta
                      /// returned by beforeSwap and afterSwap
                      function getUnspecifiedDelta(BeforeSwapDelta delta) internal pure returns (int128 deltaUnspecified) {
                          assembly ("memory-safe") {
                              deltaUnspecified := signextend(15, delta)
                          }
                      }
                  }
                  // SPDX-License-Identifier: BUSL-1.1
                  pragma solidity ^0.8.24;
                  /// @notice This is a temporary library that allows us to use transient storage (tstore/tload)
                  /// TODO: This library can be deleted when we have the transient keyword support in solidity.
                  library Lock {
                      // The slot holding the unlocked state, transiently. bytes32(uint256(keccak256("Unlocked")) - 1)
                      bytes32 internal constant IS_UNLOCKED_SLOT = 0xc090fc4683624cfc3884e9d8de5eca132f2d0ec062aff75d43c0465d5ceeab23;
                      function unlock() internal {
                          assembly ("memory-safe") {
                              // unlock
                              tstore(IS_UNLOCKED_SLOT, true)
                          }
                      }
                      function lock() internal {
                          assembly ("memory-safe") {
                              tstore(IS_UNLOCKED_SLOT, false)
                          }
                      }
                      function isUnlocked() internal view returns (bool unlocked) {
                          assembly ("memory-safe") {
                              unlocked := tload(IS_UNLOCKED_SLOT)
                          }
                      }
                  }
                  // SPDX-License-Identifier: BUSL-1.1
                  pragma solidity ^0.8.24;
                  import {Currency} from "../types/Currency.sol";
                  /// @title a library to store callers' currency deltas in transient storage
                  /// @dev this library implements the equivalent of a mapping, as transient storage can only be accessed in assembly
                  library CurrencyDelta {
                      /// @notice calculates which storage slot a delta should be stored in for a given account and currency
                      function _computeSlot(address target, Currency currency) internal pure returns (bytes32 hashSlot) {
                          assembly ("memory-safe") {
                              mstore(0, and(target, 0xffffffffffffffffffffffffffffffffffffffff))
                              mstore(32, and(currency, 0xffffffffffffffffffffffffffffffffffffffff))
                              hashSlot := keccak256(0, 64)
                          }
                      }
                      function getDelta(Currency currency, address target) internal view returns (int256 delta) {
                          bytes32 hashSlot = _computeSlot(target, currency);
                          assembly ("memory-safe") {
                              delta := tload(hashSlot)
                          }
                      }
                      /// @notice applies a new currency delta for a given account and currency
                      /// @return previous The prior value
                      /// @return next The modified result
                      function applyDelta(Currency currency, address target, int128 delta)
                          internal
                          returns (int256 previous, int256 next)
                      {
                          bytes32 hashSlot = _computeSlot(target, currency);
                          assembly ("memory-safe") {
                              previous := tload(hashSlot)
                          }
                          next = previous + delta;
                          assembly ("memory-safe") {
                              tstore(hashSlot, next)
                          }
                      }
                  }
                  // SPDX-License-Identifier: BUSL-1.1
                  pragma solidity ^0.8.24;
                  /// @notice This is a temporary library that allows us to use transient storage (tstore/tload)
                  /// for the nonzero delta count.
                  /// TODO: This library can be deleted when we have the transient keyword support in solidity.
                  library NonzeroDeltaCount {
                      // The slot holding the number of nonzero deltas. bytes32(uint256(keccak256("NonzeroDeltaCount")) - 1)
                      bytes32 internal constant NONZERO_DELTA_COUNT_SLOT =
                          0x7d4b3164c6e45b97e7d87b7125a44c5828d005af88f9d751cfd78729c5d99a0b;
                      function read() internal view returns (uint256 count) {
                          assembly ("memory-safe") {
                              count := tload(NONZERO_DELTA_COUNT_SLOT)
                          }
                      }
                      function increment() internal {
                          assembly ("memory-safe") {
                              let count := tload(NONZERO_DELTA_COUNT_SLOT)
                              count := add(count, 1)
                              tstore(NONZERO_DELTA_COUNT_SLOT, count)
                          }
                      }
                      /// @notice Potential to underflow. Ensure checks are performed by integrating contracts to ensure this does not happen.
                      /// Current usage ensures this will not happen because we call decrement with known boundaries (only up to the number of times we call increment).
                      function decrement() internal {
                          assembly ("memory-safe") {
                              let count := tload(NONZERO_DELTA_COUNT_SLOT)
                              count := sub(count, 1)
                              tstore(NONZERO_DELTA_COUNT_SLOT, count)
                          }
                      }
                  }
                  // SPDX-License-Identifier: BUSL-1.1
                  pragma solidity ^0.8.24;
                  import {Currency} from "../types/Currency.sol";
                  import {CustomRevert} from "./CustomRevert.sol";
                  library CurrencyReserves {
                      using CustomRevert for bytes4;
                      /// bytes32(uint256(keccak256("ReservesOf")) - 1)
                      bytes32 constant RESERVES_OF_SLOT = 0x1e0745a7db1623981f0b2a5d4232364c00787266eb75ad546f190e6cebe9bd95;
                      /// bytes32(uint256(keccak256("Currency")) - 1)
                      bytes32 constant CURRENCY_SLOT = 0x27e098c505d44ec3574004bca052aabf76bd35004c182099d8c575fb238593b9;
                      function getSyncedCurrency() internal view returns (Currency currency) {
                          assembly ("memory-safe") {
                              currency := tload(CURRENCY_SLOT)
                          }
                      }
                      function resetCurrency() internal {
                          assembly ("memory-safe") {
                              tstore(CURRENCY_SLOT, 0)
                          }
                      }
                      function syncCurrencyAndReserves(Currency currency, uint256 value) internal {
                          assembly ("memory-safe") {
                              tstore(CURRENCY_SLOT, and(currency, 0xffffffffffffffffffffffffffffffffffffffff))
                              tstore(RESERVES_OF_SLOT, value)
                          }
                      }
                      function getSyncedReserves() internal view returns (uint256 value) {
                          assembly ("memory-safe") {
                              value := tload(RESERVES_OF_SLOT)
                          }
                      }
                  }
                  // SPDX-License-Identifier: MIT
                  pragma solidity ^0.8.0;
                  import {IExtsload} from "./interfaces/IExtsload.sol";
                  /// @notice Enables public storage access for efficient state retrieval by external contracts.
                  /// https://eips.ethereum.org/EIPS/eip-2330#rationale
                  abstract contract Extsload is IExtsload {
                      /// @inheritdoc IExtsload
                      function extsload(bytes32 slot) external view returns (bytes32) {
                          assembly ("memory-safe") {
                              mstore(0, sload(slot))
                              return(0, 0x20)
                          }
                      }
                      /// @inheritdoc IExtsload
                      function extsload(bytes32 startSlot, uint256 nSlots) external view returns (bytes32[] memory) {
                          assembly ("memory-safe") {
                              let memptr := mload(0x40)
                              let start := memptr
                              // A left bit-shift of 5 is equivalent to multiplying by 32 but costs less gas.
                              let length := shl(5, nSlots)
                              // The abi offset of dynamic array in the returndata is 32.
                              mstore(memptr, 0x20)
                              // Store the length of the array returned
                              mstore(add(memptr, 0x20), nSlots)
                              // update memptr to the first location to hold a result
                              memptr := add(memptr, 0x40)
                              let end := add(memptr, length)
                              for {} 1 {} {
                                  mstore(memptr, sload(startSlot))
                                  memptr := add(memptr, 0x20)
                                  startSlot := add(startSlot, 1)
                                  if iszero(lt(memptr, end)) { break }
                              }
                              return(start, sub(end, start))
                          }
                      }
                      /// @inheritdoc IExtsload
                      function extsload(bytes32[] calldata slots) external view returns (bytes32[] memory) {
                          assembly ("memory-safe") {
                              let memptr := mload(0x40)
                              let start := memptr
                              // for abi encoding the response - the array will be found at 0x20
                              mstore(memptr, 0x20)
                              // next we store the length of the return array
                              mstore(add(memptr, 0x20), slots.length)
                              // update memptr to the first location to hold an array entry
                              memptr := add(memptr, 0x40)
                              // A left bit-shift of 5 is equivalent to multiplying by 32 but costs less gas.
                              let end := add(memptr, shl(5, slots.length))
                              let calldataptr := slots.offset
                              for {} 1 {} {
                                  mstore(memptr, sload(calldataload(calldataptr)))
                                  memptr := add(memptr, 0x20)
                                  calldataptr := add(calldataptr, 0x20)
                                  if iszero(lt(memptr, end)) { break }
                              }
                              return(start, sub(end, start))
                          }
                      }
                  }
                  // SPDX-License-Identifier: MIT
                  pragma solidity ^0.8.24;
                  import {IExttload} from "./interfaces/IExttload.sol";
                  /// @notice Enables public transient storage access for efficient state retrieval by external contracts.
                  /// https://eips.ethereum.org/EIPS/eip-2330#rationale
                  abstract contract Exttload is IExttload {
                      /// @inheritdoc IExttload
                      function exttload(bytes32 slot) external view returns (bytes32) {
                          assembly ("memory-safe") {
                              mstore(0, tload(slot))
                              return(0, 0x20)
                          }
                      }
                      /// @inheritdoc IExttload
                      function exttload(bytes32[] calldata slots) external view returns (bytes32[] memory) {
                          assembly ("memory-safe") {
                              let memptr := mload(0x40)
                              let start := memptr
                              // for abi encoding the response - the array will be found at 0x20
                              mstore(memptr, 0x20)
                              // next we store the length of the return array
                              mstore(add(memptr, 0x20), slots.length)
                              // update memptr to the first location to hold an array entry
                              memptr := add(memptr, 0x40)
                              // A left bit-shift of 5 is equivalent to multiplying by 32 but costs less gas.
                              let end := add(memptr, shl(5, slots.length))
                              let calldataptr := slots.offset
                              for {} 1 {} {
                                  mstore(memptr, tload(calldataload(calldataptr)))
                                  memptr := add(memptr, 0x20)
                                  calldataptr := add(calldataptr, 0x20)
                                  if iszero(lt(memptr, end)) { break }
                              }
                              return(start, sub(end, start))
                          }
                      }
                  }
                  // SPDX-License-Identifier: MIT
                  pragma solidity ^0.8.0;
                  /// @title Library for reverting with custom errors efficiently
                  /// @notice Contains functions for reverting with custom errors with different argument types efficiently
                  /// @dev To use this library, declare `using CustomRevert for bytes4;` and replace `revert CustomError()` with
                  /// `CustomError.selector.revertWith()`
                  /// @dev The functions may tamper with the free memory pointer but it is fine since the call context is exited immediately
                  library CustomRevert {
                      /// @dev ERC-7751 error for wrapping bubbled up reverts
                      error WrappedError(address target, bytes4 selector, bytes reason, bytes details);
                      /// @dev Reverts with the selector of a custom error in the scratch space
                      function revertWith(bytes4 selector) internal pure {
                          assembly ("memory-safe") {
                              mstore(0, selector)
                              revert(0, 0x04)
                          }
                      }
                      /// @dev Reverts with a custom error with an address argument in the scratch space
                      function revertWith(bytes4 selector, address addr) internal pure {
                          assembly ("memory-safe") {
                              mstore(0, selector)
                              mstore(0x04, and(addr, 0xffffffffffffffffffffffffffffffffffffffff))
                              revert(0, 0x24)
                          }
                      }
                      /// @dev Reverts with a custom error with an int24 argument in the scratch space
                      function revertWith(bytes4 selector, int24 value) internal pure {
                          assembly ("memory-safe") {
                              mstore(0, selector)
                              mstore(0x04, signextend(2, value))
                              revert(0, 0x24)
                          }
                      }
                      /// @dev Reverts with a custom error with a uint160 argument in the scratch space
                      function revertWith(bytes4 selector, uint160 value) internal pure {
                          assembly ("memory-safe") {
                              mstore(0, selector)
                              mstore(0x04, and(value, 0xffffffffffffffffffffffffffffffffffffffff))
                              revert(0, 0x24)
                          }
                      }
                      /// @dev Reverts with a custom error with two int24 arguments
                      function revertWith(bytes4 selector, int24 value1, int24 value2) internal pure {
                          assembly ("memory-safe") {
                              let fmp := mload(0x40)
                              mstore(fmp, selector)
                              mstore(add(fmp, 0x04), signextend(2, value1))
                              mstore(add(fmp, 0x24), signextend(2, value2))
                              revert(fmp, 0x44)
                          }
                      }
                      /// @dev Reverts with a custom error with two uint160 arguments
                      function revertWith(bytes4 selector, uint160 value1, uint160 value2) internal pure {
                          assembly ("memory-safe") {
                              let fmp := mload(0x40)
                              mstore(fmp, selector)
                              mstore(add(fmp, 0x04), and(value1, 0xffffffffffffffffffffffffffffffffffffffff))
                              mstore(add(fmp, 0x24), and(value2, 0xffffffffffffffffffffffffffffffffffffffff))
                              revert(fmp, 0x44)
                          }
                      }
                      /// @dev Reverts with a custom error with two address arguments
                      function revertWith(bytes4 selector, address value1, address value2) internal pure {
                          assembly ("memory-safe") {
                              let fmp := mload(0x40)
                              mstore(fmp, selector)
                              mstore(add(fmp, 0x04), and(value1, 0xffffffffffffffffffffffffffffffffffffffff))
                              mstore(add(fmp, 0x24), and(value2, 0xffffffffffffffffffffffffffffffffffffffff))
                              revert(fmp, 0x44)
                          }
                      }
                      /// @notice bubble up the revert message returned by a call and revert with a wrapped ERC-7751 error
                      /// @dev this method can be vulnerable to revert data bombs
                      function bubbleUpAndRevertWith(
                          address revertingContract,
                          bytes4 revertingFunctionSelector,
                          bytes4 additionalContext
                      ) internal pure {
                          bytes4 wrappedErrorSelector = WrappedError.selector;
                          assembly ("memory-safe") {
                              // Ensure the size of the revert data is a multiple of 32 bytes
                              let encodedDataSize := mul(div(add(returndatasize(), 31), 32), 32)
                              let fmp := mload(0x40)
                              // Encode wrapped error selector, address, function selector, offset, additional context, size, revert reason
                              mstore(fmp, wrappedErrorSelector)
                              mstore(add(fmp, 0x04), and(revertingContract, 0xffffffffffffffffffffffffffffffffffffffff))
                              mstore(
                                  add(fmp, 0x24),
                                  and(revertingFunctionSelector, 0xffffffff00000000000000000000000000000000000000000000000000000000)
                              )
                              // offset revert reason
                              mstore(add(fmp, 0x44), 0x80)
                              // offset additional context
                              mstore(add(fmp, 0x64), add(0xa0, encodedDataSize))
                              // size revert reason
                              mstore(add(fmp, 0x84), returndatasize())
                              // revert reason
                              returndatacopy(add(fmp, 0xa4), 0, returndatasize())
                              // size additional context
                              mstore(add(fmp, add(0xa4, encodedDataSize)), 0x04)
                              // additional context
                              mstore(
                                  add(fmp, add(0xc4, encodedDataSize)),
                                  and(additionalContext, 0xffffffff00000000000000000000000000000000000000000000000000000000)
                              )
                              revert(fmp, add(0xe4, encodedDataSize))
                          }
                      }
                  }
                  // SPDX-License-Identifier: MIT
                  pragma solidity ^0.8.0;
                  /// @notice Parses bytes returned from hooks and the byte selector used to check return selectors from hooks.
                  /// @dev parseSelector also is used to parse the expected selector
                  /// For parsing hook returns, note that all hooks return either bytes4 or (bytes4, 32-byte-delta) or (bytes4, 32-byte-delta, uint24).
                  library ParseBytes {
                      function parseSelector(bytes memory result) internal pure returns (bytes4 selector) {
                          // equivalent: (selector,) = abi.decode(result, (bytes4, int256));
                          assembly ("memory-safe") {
                              selector := mload(add(result, 0x20))
                          }
                      }
                      function parseFee(bytes memory result) internal pure returns (uint24 lpFee) {
                          // equivalent: (,, lpFee) = abi.decode(result, (bytes4, int256, uint24));
                          assembly ("memory-safe") {
                              lpFee := mload(add(result, 0x60))
                          }
                      }
                      function parseReturnDelta(bytes memory result) internal pure returns (int256 hookReturn) {
                          // equivalent: (, hookReturnDelta) = abi.decode(result, (bytes4, int256));
                          assembly ("memory-safe") {
                              hookReturn := mload(add(result, 0x40))
                          }
                      }
                  }
                  // SPDX-License-Identifier: MIT
                  pragma solidity ^0.8.0;
                  import {BitMath} from "./BitMath.sol";
                  /// @title Packed tick initialized state library
                  /// @notice Stores a packed mapping of tick index to its initialized state
                  /// @dev The mapping uses int16 for keys since ticks are represented as int24 and there are 256 (2^8) values per word.
                  library TickBitmap {
                      /// @notice Thrown when the tick is not enumerated by the tick spacing
                      /// @param tick the invalid tick
                      /// @param tickSpacing The tick spacing of the pool
                      error TickMisaligned(int24 tick, int24 tickSpacing);
                      /// @dev round towards negative infinity
                      function compress(int24 tick, int24 tickSpacing) internal pure returns (int24 compressed) {
                          // compressed = tick / tickSpacing;
                          // if (tick < 0 && tick % tickSpacing != 0) compressed--;
                          assembly ("memory-safe") {
                              tick := signextend(2, tick)
                              tickSpacing := signextend(2, tickSpacing)
                              compressed :=
                                  sub(
                                      sdiv(tick, tickSpacing),
                                      // if (tick < 0 && tick % tickSpacing != 0) then tick % tickSpacing < 0, vice versa
                                      slt(smod(tick, tickSpacing), 0)
                                  )
                          }
                      }
                      /// @notice Computes the position in the mapping where the initialized bit for a tick lives
                      /// @param tick The tick for which to compute the position
                      /// @return wordPos The key in the mapping containing the word in which the bit is stored
                      /// @return bitPos The bit position in the word where the flag is stored
                      function position(int24 tick) internal pure returns (int16 wordPos, uint8 bitPos) {
                          assembly ("memory-safe") {
                              // signed arithmetic shift right
                              wordPos := sar(8, signextend(2, tick))
                              bitPos := and(tick, 0xff)
                          }
                      }
                      /// @notice Flips the initialized state for a given tick from false to true, or vice versa
                      /// @param self The mapping in which to flip the tick
                      /// @param tick The tick to flip
                      /// @param tickSpacing The spacing between usable ticks
                      function flipTick(mapping(int16 => uint256) storage self, int24 tick, int24 tickSpacing) internal {
                          // Equivalent to the following Solidity:
                          //     if (tick % tickSpacing != 0) revert TickMisaligned(tick, tickSpacing);
                          //     (int16 wordPos, uint8 bitPos) = position(tick / tickSpacing);
                          //     uint256 mask = 1 << bitPos;
                          //     self[wordPos] ^= mask;
                          assembly ("memory-safe") {
                              tick := signextend(2, tick)
                              tickSpacing := signextend(2, tickSpacing)
                              // ensure that the tick is spaced
                              if smod(tick, tickSpacing) {
                                  let fmp := mload(0x40)
                                  mstore(fmp, 0xd4d8f3e6) // selector for TickMisaligned(int24,int24)
                                  mstore(add(fmp, 0x20), tick)
                                  mstore(add(fmp, 0x40), tickSpacing)
                                  revert(add(fmp, 0x1c), 0x44)
                              }
                              tick := sdiv(tick, tickSpacing)
                              // calculate the storage slot corresponding to the tick
                              // wordPos = tick >> 8
                              mstore(0, sar(8, tick))
                              mstore(0x20, self.slot)
                              // the slot of self[wordPos] is keccak256(abi.encode(wordPos, self.slot))
                              let slot := keccak256(0, 0x40)
                              // mask = 1 << bitPos = 1 << (tick % 256)
                              // self[wordPos] ^= mask
                              sstore(slot, xor(sload(slot), shl(and(tick, 0xff), 1)))
                          }
                      }
                      /// @notice Returns the next initialized tick contained in the same word (or adjacent word) as the tick that is either
                      /// to the left (less than or equal to) or right (greater than) of the given tick
                      /// @param self The mapping in which to compute the next initialized tick
                      /// @param tick The starting tick
                      /// @param tickSpacing The spacing between usable ticks
                      /// @param lte Whether to search for the next initialized tick to the left (less than or equal to the starting tick)
                      /// @return next The next initialized or uninitialized tick up to 256 ticks away from the current tick
                      /// @return initialized Whether the next tick is initialized, as the function only searches within up to 256 ticks
                      function nextInitializedTickWithinOneWord(
                          mapping(int16 => uint256) storage self,
                          int24 tick,
                          int24 tickSpacing,
                          bool lte
                      ) internal view returns (int24 next, bool initialized) {
                          unchecked {
                              int24 compressed = compress(tick, tickSpacing);
                              if (lte) {
                                  (int16 wordPos, uint8 bitPos) = position(compressed);
                                  // all the 1s at or to the right of the current bitPos
                                  uint256 mask = type(uint256).max >> (uint256(type(uint8).max) - bitPos);
                                  uint256 masked = self[wordPos] & mask;
                                  // if there are no initialized ticks to the right of or at the current tick, return rightmost in the word
                                  initialized = masked != 0;
                                  // overflow/underflow is possible, but prevented externally by limiting both tickSpacing and tick
                                  next = initialized
                                      ? (compressed - int24(uint24(bitPos - BitMath.mostSignificantBit(masked)))) * tickSpacing
                                      : (compressed - int24(uint24(bitPos))) * tickSpacing;
                              } else {
                                  // start from the word of the next tick, since the current tick state doesn't matter
                                  (int16 wordPos, uint8 bitPos) = position(++compressed);
                                  // all the 1s at or to the left of the bitPos
                                  uint256 mask = ~((1 << bitPos) - 1);
                                  uint256 masked = self[wordPos] & mask;
                                  // if there are no initialized ticks to the left of the current tick, return leftmost in the word
                                  initialized = masked != 0;
                                  // overflow/underflow is possible, but prevented externally by limiting both tickSpacing and tick
                                  next = initialized
                                      ? (compressed + int24(uint24(BitMath.leastSignificantBit(masked) - bitPos))) * tickSpacing
                                      : (compressed + int24(uint24(type(uint8).max - bitPos))) * tickSpacing;
                              }
                          }
                      }
                  }
                  // SPDX-License-Identifier: MIT
                  pragma solidity ^0.8.0;
                  /// @title Math functions that do not check inputs or outputs
                  /// @notice Contains methods that perform common math functions but do not do any overflow or underflow checks
                  library UnsafeMath {
                      /// @notice Returns ceil(x / y)
                      /// @dev division by 0 will return 0, and should be checked externally
                      /// @param x The dividend
                      /// @param y The divisor
                      /// @return z The quotient, ceil(x / y)
                      function divRoundingUp(uint256 x, uint256 y) internal pure returns (uint256 z) {
                          assembly ("memory-safe") {
                              z := add(div(x, y), gt(mod(x, y), 0))
                          }
                      }
                      /// @notice Calculates floor(a×b÷denominator)
                      /// @dev division by 0 will return 0, and should be checked externally
                      /// @param a The multiplicand
                      /// @param b The multiplier
                      /// @param denominator The divisor
                      /// @return result The 256-bit result, floor(a×b÷denominator)
                      function simpleMulDiv(uint256 a, uint256 b, uint256 denominator) internal pure returns (uint256 result) {
                          assembly ("memory-safe") {
                              result := div(mul(a, b), denominator)
                          }
                      }
                  }
                  // SPDX-License-Identifier: MIT
                  pragma solidity ^0.8.0;
                  /// @title FixedPoint128
                  /// @notice A library for handling binary fixed point numbers, see https://en.wikipedia.org/wiki/Q_(number_format)
                  library FixedPoint128 {
                      uint256 internal constant Q128 = 0x100000000000000000000000000000000;
                  }
                  // SPDX-License-Identifier: MIT
                  pragma solidity ^0.8.0;
                  import {SafeCast} from "./SafeCast.sol";
                  import {FullMath} from "./FullMath.sol";
                  import {UnsafeMath} from "./UnsafeMath.sol";
                  import {FixedPoint96} from "./FixedPoint96.sol";
                  /// @title Functions based on Q64.96 sqrt price and liquidity
                  /// @notice Contains the math that uses square root of price as a Q64.96 and liquidity to compute deltas
                  library SqrtPriceMath {
                      using SafeCast for uint256;
                      error InvalidPriceOrLiquidity();
                      error InvalidPrice();
                      error NotEnoughLiquidity();
                      error PriceOverflow();
                      /// @notice Gets the next sqrt price given a delta of currency0
                      /// @dev Always rounds up, because in the exact output case (increasing price) we need to move the price at least
                      /// far enough to get the desired output amount, and in the exact input case (decreasing price) we need to move the
                      /// price less in order to not send too much output.
                      /// The most precise formula for this is liquidity * sqrtPX96 / (liquidity +- amount * sqrtPX96),
                      /// if this is impossible because of overflow, we calculate liquidity / (liquidity / sqrtPX96 +- amount).
                      /// @param sqrtPX96 The starting price, i.e. before accounting for the currency0 delta
                      /// @param liquidity The amount of usable liquidity
                      /// @param amount How much of currency0 to add or remove from virtual reserves
                      /// @param add Whether to add or remove the amount of currency0
                      /// @return The price after adding or removing amount, depending on add
                      function getNextSqrtPriceFromAmount0RoundingUp(uint160 sqrtPX96, uint128 liquidity, uint256 amount, bool add)
                          internal
                          pure
                          returns (uint160)
                      {
                          // we short circuit amount == 0 because the result is otherwise not guaranteed to equal the input price
                          if (amount == 0) return sqrtPX96;
                          uint256 numerator1 = uint256(liquidity) << FixedPoint96.RESOLUTION;
                          if (add) {
                              unchecked {
                                  uint256 product = amount * sqrtPX96;
                                  if (product / amount == sqrtPX96) {
                                      uint256 denominator = numerator1 + product;
                                      if (denominator >= numerator1) {
                                          // always fits in 160 bits
                                          return uint160(FullMath.mulDivRoundingUp(numerator1, sqrtPX96, denominator));
                                      }
                                  }
                              }
                              // denominator is checked for overflow
                              return uint160(UnsafeMath.divRoundingUp(numerator1, (numerator1 / sqrtPX96) + amount));
                          } else {
                              unchecked {
                                  uint256 product = amount * sqrtPX96;
                                  // if the product overflows, we know the denominator underflows
                                  // in addition, we must check that the denominator does not underflow
                                  // equivalent: if (product / amount != sqrtPX96 || numerator1 <= product) revert PriceOverflow();
                                  assembly ("memory-safe") {
                                      if iszero(
                                          and(
                                              eq(div(product, amount), and(sqrtPX96, 0xffffffffffffffffffffffffffffffffffffffff)),
                                              gt(numerator1, product)
                                          )
                                      ) {
                                          mstore(0, 0xf5c787f1) // selector for PriceOverflow()
                                          revert(0x1c, 0x04)
                                      }
                                  }
                                  uint256 denominator = numerator1 - product;
                                  return FullMath.mulDivRoundingUp(numerator1, sqrtPX96, denominator).toUint160();
                              }
                          }
                      }
                      /// @notice Gets the next sqrt price given a delta of currency1
                      /// @dev Always rounds down, because in the exact output case (decreasing price) we need to move the price at least
                      /// far enough to get the desired output amount, and in the exact input case (increasing price) we need to move the
                      /// price less in order to not send too much output.
                      /// The formula we compute is within <1 wei of the lossless version: sqrtPX96 +- amount / liquidity
                      /// @param sqrtPX96 The starting price, i.e., before accounting for the currency1 delta
                      /// @param liquidity The amount of usable liquidity
                      /// @param amount How much of currency1 to add, or remove, from virtual reserves
                      /// @param add Whether to add, or remove, the amount of currency1
                      /// @return The price after adding or removing `amount`
                      function getNextSqrtPriceFromAmount1RoundingDown(uint160 sqrtPX96, uint128 liquidity, uint256 amount, bool add)
                          internal
                          pure
                          returns (uint160)
                      {
                          // if we're adding (subtracting), rounding down requires rounding the quotient down (up)
                          // in both cases, avoid a mulDiv for most inputs
                          if (add) {
                              uint256 quotient = (
                                  amount <= type(uint160).max
                                      ? (amount << FixedPoint96.RESOLUTION) / liquidity
                                      : FullMath.mulDiv(amount, FixedPoint96.Q96, liquidity)
                              );
                              return (uint256(sqrtPX96) + quotient).toUint160();
                          } else {
                              uint256 quotient = (
                                  amount <= type(uint160).max
                                      ? UnsafeMath.divRoundingUp(amount << FixedPoint96.RESOLUTION, liquidity)
                                      : FullMath.mulDivRoundingUp(amount, FixedPoint96.Q96, liquidity)
                              );
                              // equivalent: if (sqrtPX96 <= quotient) revert NotEnoughLiquidity();
                              assembly ("memory-safe") {
                                  if iszero(gt(and(sqrtPX96, 0xffffffffffffffffffffffffffffffffffffffff), quotient)) {
                                      mstore(0, 0x4323a555) // selector for NotEnoughLiquidity()
                                      revert(0x1c, 0x04)
                                  }
                              }
                              // always fits 160 bits
                              unchecked {
                                  return uint160(sqrtPX96 - quotient);
                              }
                          }
                      }
                      /// @notice Gets the next sqrt price given an input amount of currency0 or currency1
                      /// @dev Throws if price or liquidity are 0, or if the next price is out of bounds
                      /// @param sqrtPX96 The starting price, i.e., before accounting for the input amount
                      /// @param liquidity The amount of usable liquidity
                      /// @param amountIn How much of currency0, or currency1, is being swapped in
                      /// @param zeroForOne Whether the amount in is currency0 or currency1
                      /// @return uint160 The price after adding the input amount to currency0 or currency1
                      function getNextSqrtPriceFromInput(uint160 sqrtPX96, uint128 liquidity, uint256 amountIn, bool zeroForOne)
                          internal
                          pure
                          returns (uint160)
                      {
                          // equivalent: if (sqrtPX96 == 0 || liquidity == 0) revert InvalidPriceOrLiquidity();
                          assembly ("memory-safe") {
                              if or(
                                  iszero(and(sqrtPX96, 0xffffffffffffffffffffffffffffffffffffffff)),
                                  iszero(and(liquidity, 0xffffffffffffffffffffffffffffffff))
                              ) {
                                  mstore(0, 0x4f2461b8) // selector for InvalidPriceOrLiquidity()
                                  revert(0x1c, 0x04)
                              }
                          }
                          // round to make sure that we don't pass the target price
                          return zeroForOne
                              ? getNextSqrtPriceFromAmount0RoundingUp(sqrtPX96, liquidity, amountIn, true)
                              : getNextSqrtPriceFromAmount1RoundingDown(sqrtPX96, liquidity, amountIn, true);
                      }
                      /// @notice Gets the next sqrt price given an output amount of currency0 or currency1
                      /// @dev Throws if price or liquidity are 0 or the next price is out of bounds
                      /// @param sqrtPX96 The starting price before accounting for the output amount
                      /// @param liquidity The amount of usable liquidity
                      /// @param amountOut How much of currency0, or currency1, is being swapped out
                      /// @param zeroForOne Whether the amount out is currency1 or currency0
                      /// @return uint160 The price after removing the output amount of currency0 or currency1
                      function getNextSqrtPriceFromOutput(uint160 sqrtPX96, uint128 liquidity, uint256 amountOut, bool zeroForOne)
                          internal
                          pure
                          returns (uint160)
                      {
                          // equivalent: if (sqrtPX96 == 0 || liquidity == 0) revert InvalidPriceOrLiquidity();
                          assembly ("memory-safe") {
                              if or(
                                  iszero(and(sqrtPX96, 0xffffffffffffffffffffffffffffffffffffffff)),
                                  iszero(and(liquidity, 0xffffffffffffffffffffffffffffffff))
                              ) {
                                  mstore(0, 0x4f2461b8) // selector for InvalidPriceOrLiquidity()
                                  revert(0x1c, 0x04)
                              }
                          }
                          // round to make sure that we pass the target price
                          return zeroForOne
                              ? getNextSqrtPriceFromAmount1RoundingDown(sqrtPX96, liquidity, amountOut, false)
                              : getNextSqrtPriceFromAmount0RoundingUp(sqrtPX96, liquidity, amountOut, false);
                      }
                      /// @notice Gets the amount0 delta between two prices
                      /// @dev Calculates liquidity / sqrt(lower) - liquidity / sqrt(upper),
                      /// i.e. liquidity * (sqrt(upper) - sqrt(lower)) / (sqrt(upper) * sqrt(lower))
                      /// @param sqrtPriceAX96 A sqrt price
                      /// @param sqrtPriceBX96 Another sqrt price
                      /// @param liquidity The amount of usable liquidity
                      /// @param roundUp Whether to round the amount up or down
                      /// @return uint256 Amount of currency0 required to cover a position of size liquidity between the two passed prices
                      function getAmount0Delta(uint160 sqrtPriceAX96, uint160 sqrtPriceBX96, uint128 liquidity, bool roundUp)
                          internal
                          pure
                          returns (uint256)
                      {
                          unchecked {
                              if (sqrtPriceAX96 > sqrtPriceBX96) (sqrtPriceAX96, sqrtPriceBX96) = (sqrtPriceBX96, sqrtPriceAX96);
                              // equivalent: if (sqrtPriceAX96 == 0) revert InvalidPrice();
                              assembly ("memory-safe") {
                                  if iszero(and(sqrtPriceAX96, 0xffffffffffffffffffffffffffffffffffffffff)) {
                                      mstore(0, 0x00bfc921) // selector for InvalidPrice()
                                      revert(0x1c, 0x04)
                                  }
                              }
                              uint256 numerator1 = uint256(liquidity) << FixedPoint96.RESOLUTION;
                              uint256 numerator2 = sqrtPriceBX96 - sqrtPriceAX96;
                              return roundUp
                                  ? UnsafeMath.divRoundingUp(FullMath.mulDivRoundingUp(numerator1, numerator2, sqrtPriceBX96), sqrtPriceAX96)
                                  : FullMath.mulDiv(numerator1, numerator2, sqrtPriceBX96) / sqrtPriceAX96;
                          }
                      }
                      /// @notice Equivalent to: `a >= b ? a - b : b - a`
                      function absDiff(uint160 a, uint160 b) internal pure returns (uint256 res) {
                          assembly ("memory-safe") {
                              let diff :=
                                  sub(and(a, 0xffffffffffffffffffffffffffffffffffffffff), and(b, 0xffffffffffffffffffffffffffffffffffffffff))
                              // mask = 0 if a >= b else -1 (all 1s)
                              let mask := sar(255, diff)
                              // if a >= b, res = a - b = 0 ^ (a - b)
                              // if a < b, res = b - a = ~~(b - a) = ~(-(b - a) - 1) = ~(a - b - 1) = (-1) ^ (a - b - 1)
                              // either way, res = mask ^ (a - b + mask)
                              res := xor(mask, add(mask, diff))
                          }
                      }
                      /// @notice Gets the amount1 delta between two prices
                      /// @dev Calculates liquidity * (sqrt(upper) - sqrt(lower))
                      /// @param sqrtPriceAX96 A sqrt price
                      /// @param sqrtPriceBX96 Another sqrt price
                      /// @param liquidity The amount of usable liquidity
                      /// @param roundUp Whether to round the amount up, or down
                      /// @return amount1 Amount of currency1 required to cover a position of size liquidity between the two passed prices
                      function getAmount1Delta(uint160 sqrtPriceAX96, uint160 sqrtPriceBX96, uint128 liquidity, bool roundUp)
                          internal
                          pure
                          returns (uint256 amount1)
                      {
                          uint256 numerator = absDiff(sqrtPriceAX96, sqrtPriceBX96);
                          uint256 denominator = FixedPoint96.Q96;
                          uint256 _liquidity = uint256(liquidity);
                          /**
                           * Equivalent to:
                           *   amount1 = roundUp
                           *       ? FullMath.mulDivRoundingUp(liquidity, sqrtPriceBX96 - sqrtPriceAX96, FixedPoint96.Q96)
                           *       : FullMath.mulDiv(liquidity, sqrtPriceBX96 - sqrtPriceAX96, FixedPoint96.Q96);
                           * Cannot overflow because `type(uint128).max * type(uint160).max >> 96 < (1 << 192)`.
                           */
                          amount1 = FullMath.mulDiv(_liquidity, numerator, denominator);
                          assembly ("memory-safe") {
                              amount1 := add(amount1, and(gt(mulmod(_liquidity, numerator, denominator), 0), roundUp))
                          }
                      }
                      /// @notice Helper that gets signed currency0 delta
                      /// @param sqrtPriceAX96 A sqrt price
                      /// @param sqrtPriceBX96 Another sqrt price
                      /// @param liquidity The change in liquidity for which to compute the amount0 delta
                      /// @return int256 Amount of currency0 corresponding to the passed liquidityDelta between the two prices
                      function getAmount0Delta(uint160 sqrtPriceAX96, uint160 sqrtPriceBX96, int128 liquidity)
                          internal
                          pure
                          returns (int256)
                      {
                          unchecked {
                              return liquidity < 0
                                  ? getAmount0Delta(sqrtPriceAX96, sqrtPriceBX96, uint128(-liquidity), false).toInt256()
                                  : -getAmount0Delta(sqrtPriceAX96, sqrtPriceBX96, uint128(liquidity), true).toInt256();
                          }
                      }
                      /// @notice Helper that gets signed currency1 delta
                      /// @param sqrtPriceAX96 A sqrt price
                      /// @param sqrtPriceBX96 Another sqrt price
                      /// @param liquidity The change in liquidity for which to compute the amount1 delta
                      /// @return int256 Amount of currency1 corresponding to the passed liquidityDelta between the two prices
                      function getAmount1Delta(uint160 sqrtPriceAX96, uint160 sqrtPriceBX96, int128 liquidity)
                          internal
                          pure
                          returns (int256)
                      {
                          unchecked {
                              return liquidity < 0
                                  ? getAmount1Delta(sqrtPriceAX96, sqrtPriceBX96, uint128(-liquidity), false).toInt256()
                                  : -getAmount1Delta(sqrtPriceAX96, sqrtPriceBX96, uint128(liquidity), true).toInt256();
                          }
                      }
                  }
                  // SPDX-License-Identifier: MIT
                  pragma solidity ^0.8.0;
                  import {FullMath} from "./FullMath.sol";
                  import {SqrtPriceMath} from "./SqrtPriceMath.sol";
                  /// @title Computes the result of a swap within ticks
                  /// @notice Contains methods for computing the result of a swap within a single tick price range, i.e., a single tick.
                  library SwapMath {
                      /// @notice the swap fee is represented in hundredths of a bip, so the max is 100%
                      /// @dev the swap fee is the total fee on a swap, including both LP and Protocol fee
                      uint256 internal constant MAX_SWAP_FEE = 1e6;
                      /// @notice Computes the sqrt price target for the next swap step
                      /// @param zeroForOne The direction of the swap, true for currency0 to currency1, false for currency1 to currency0
                      /// @param sqrtPriceNextX96 The Q64.96 sqrt price for the next initialized tick
                      /// @param sqrtPriceLimitX96 The Q64.96 sqrt price limit. If zero for one, the price cannot be less than this value
                      /// after the swap. If one for zero, the price cannot be greater than this value after the swap
                      /// @return sqrtPriceTargetX96 The price target for the next swap step
                      function getSqrtPriceTarget(bool zeroForOne, uint160 sqrtPriceNextX96, uint160 sqrtPriceLimitX96)
                          internal
                          pure
                          returns (uint160 sqrtPriceTargetX96)
                      {
                          assembly ("memory-safe") {
                              // a flag to toggle between sqrtPriceNextX96 and sqrtPriceLimitX96
                              // when zeroForOne == true, nextOrLimit reduces to sqrtPriceNextX96 >= sqrtPriceLimitX96
                              // sqrtPriceTargetX96 = max(sqrtPriceNextX96, sqrtPriceLimitX96)
                              // when zeroForOne == false, nextOrLimit reduces to sqrtPriceNextX96 < sqrtPriceLimitX96
                              // sqrtPriceTargetX96 = min(sqrtPriceNextX96, sqrtPriceLimitX96)
                              sqrtPriceNextX96 := and(sqrtPriceNextX96, 0xffffffffffffffffffffffffffffffffffffffff)
                              sqrtPriceLimitX96 := and(sqrtPriceLimitX96, 0xffffffffffffffffffffffffffffffffffffffff)
                              let nextOrLimit := xor(lt(sqrtPriceNextX96, sqrtPriceLimitX96), and(zeroForOne, 0x1))
                              let symDiff := xor(sqrtPriceNextX96, sqrtPriceLimitX96)
                              sqrtPriceTargetX96 := xor(sqrtPriceLimitX96, mul(symDiff, nextOrLimit))
                          }
                      }
                      /// @notice Computes the result of swapping some amount in, or amount out, given the parameters of the swap
                      /// @dev If the swap's amountSpecified is negative, the combined fee and input amount will never exceed the absolute value of the remaining amount.
                      /// @param sqrtPriceCurrentX96 The current sqrt price of the pool
                      /// @param sqrtPriceTargetX96 The price that cannot be exceeded, from which the direction of the swap is inferred
                      /// @param liquidity The usable liquidity
                      /// @param amountRemaining How much input or output amount is remaining to be swapped in/out
                      /// @param feePips The fee taken from the input amount, expressed in hundredths of a bip
                      /// @return sqrtPriceNextX96 The price after swapping the amount in/out, not to exceed the price target
                      /// @return amountIn The amount to be swapped in, of either currency0 or currency1, based on the direction of the swap
                      /// @return amountOut The amount to be received, of either currency0 or currency1, based on the direction of the swap
                      /// @return feeAmount The amount of input that will be taken as a fee
                      /// @dev feePips must be no larger than MAX_SWAP_FEE for this function. We ensure that before setting a fee using LPFeeLibrary.isValid.
                      function computeSwapStep(
                          uint160 sqrtPriceCurrentX96,
                          uint160 sqrtPriceTargetX96,
                          uint128 liquidity,
                          int256 amountRemaining,
                          uint24 feePips
                      ) internal pure returns (uint160 sqrtPriceNextX96, uint256 amountIn, uint256 amountOut, uint256 feeAmount) {
                          unchecked {
                              uint256 _feePips = feePips; // upcast once and cache
                              bool zeroForOne = sqrtPriceCurrentX96 >= sqrtPriceTargetX96;
                              bool exactIn = amountRemaining < 0;
                              if (exactIn) {
                                  uint256 amountRemainingLessFee =
                                      FullMath.mulDiv(uint256(-amountRemaining), MAX_SWAP_FEE - _feePips, MAX_SWAP_FEE);
                                  amountIn = zeroForOne
                                      ? SqrtPriceMath.getAmount0Delta(sqrtPriceTargetX96, sqrtPriceCurrentX96, liquidity, true)
                                      : SqrtPriceMath.getAmount1Delta(sqrtPriceCurrentX96, sqrtPriceTargetX96, liquidity, true);
                                  if (amountRemainingLessFee >= amountIn) {
                                      // `amountIn` is capped by the target price
                                      sqrtPriceNextX96 = sqrtPriceTargetX96;
                                      feeAmount = _feePips == MAX_SWAP_FEE
                                          ? amountIn // amountIn is always 0 here, as amountRemainingLessFee == 0 and amountRemainingLessFee >= amountIn
                                          : FullMath.mulDivRoundingUp(amountIn, _feePips, MAX_SWAP_FEE - _feePips);
                                  } else {
                                      // exhaust the remaining amount
                                      amountIn = amountRemainingLessFee;
                                      sqrtPriceNextX96 = SqrtPriceMath.getNextSqrtPriceFromInput(
                                          sqrtPriceCurrentX96, liquidity, amountRemainingLessFee, zeroForOne
                                      );
                                      // we didn't reach the target, so take the remainder of the maximum input as fee
                                      feeAmount = uint256(-amountRemaining) - amountIn;
                                  }
                                  amountOut = zeroForOne
                                      ? SqrtPriceMath.getAmount1Delta(sqrtPriceNextX96, sqrtPriceCurrentX96, liquidity, false)
                                      : SqrtPriceMath.getAmount0Delta(sqrtPriceCurrentX96, sqrtPriceNextX96, liquidity, false);
                              } else {
                                  amountOut = zeroForOne
                                      ? SqrtPriceMath.getAmount1Delta(sqrtPriceTargetX96, sqrtPriceCurrentX96, liquidity, false)
                                      : SqrtPriceMath.getAmount0Delta(sqrtPriceCurrentX96, sqrtPriceTargetX96, liquidity, false);
                                  if (uint256(amountRemaining) >= amountOut) {
                                      // `amountOut` is capped by the target price
                                      sqrtPriceNextX96 = sqrtPriceTargetX96;
                                  } else {
                                      // cap the output amount to not exceed the remaining output amount
                                      amountOut = uint256(amountRemaining);
                                      sqrtPriceNextX96 =
                                          SqrtPriceMath.getNextSqrtPriceFromOutput(sqrtPriceCurrentX96, liquidity, amountOut, zeroForOne);
                                  }
                                  amountIn = zeroForOne
                                      ? SqrtPriceMath.getAmount0Delta(sqrtPriceNextX96, sqrtPriceCurrentX96, liquidity, true)
                                      : SqrtPriceMath.getAmount1Delta(sqrtPriceCurrentX96, sqrtPriceNextX96, liquidity, true);
                                  // `feePips` cannot be `MAX_SWAP_FEE` for exact out
                                  feeAmount = FullMath.mulDivRoundingUp(amountIn, _feePips, MAX_SWAP_FEE - _feePips);
                              }
                          }
                      }
                  }
                  // SPDX-License-Identifier: MIT
                  pragma solidity ^0.8.0;
                  /**
                   * @dev Slot0 is a packed version of solidity structure.
                   * Using the packaged version saves gas by not storing the structure fields in memory slots.
                   *
                   * Layout:
                   * 24 bits empty | 24 bits lpFee | 12 bits protocolFee 1->0 | 12 bits protocolFee 0->1 | 24 bits tick | 160 bits sqrtPriceX96
                   *
                   * Fields in the direction from the least significant bit:
                   *
                   * The current price
                   * uint160 sqrtPriceX96;
                   *
                   * The current tick
                   * int24 tick;
                   *
                   * Protocol fee, expressed in hundredths of a bip, upper 12 bits are for 1->0, and the lower 12 are for 0->1
                   * the maximum is 1000 - meaning the maximum protocol fee is 0.1%
                   * the protocolFee is taken from the input first, then the lpFee is taken from the remaining input
                   * uint24 protocolFee;
                   *
                   * The current LP fee of the pool. If the pool is dynamic, this does not include the dynamic fee flag.
                   * uint24 lpFee;
                   */
                  type Slot0 is bytes32;
                  using Slot0Library for Slot0 global;
                  /// @notice Library for getting and setting values in the Slot0 type
                  library Slot0Library {
                      uint160 internal constant MASK_160_BITS = 0x00FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
                      uint24 internal constant MASK_24_BITS = 0xFFFFFF;
                      uint8 internal constant TICK_OFFSET = 160;
                      uint8 internal constant PROTOCOL_FEE_OFFSET = 184;
                      uint8 internal constant LP_FEE_OFFSET = 208;
                      // #### GETTERS ####
                      function sqrtPriceX96(Slot0 _packed) internal pure returns (uint160 _sqrtPriceX96) {
                          assembly ("memory-safe") {
                              _sqrtPriceX96 := and(MASK_160_BITS, _packed)
                          }
                      }
                      function tick(Slot0 _packed) internal pure returns (int24 _tick) {
                          assembly ("memory-safe") {
                              _tick := signextend(2, shr(TICK_OFFSET, _packed))
                          }
                      }
                      function protocolFee(Slot0 _packed) internal pure returns (uint24 _protocolFee) {
                          assembly ("memory-safe") {
                              _protocolFee := and(MASK_24_BITS, shr(PROTOCOL_FEE_OFFSET, _packed))
                          }
                      }
                      function lpFee(Slot0 _packed) internal pure returns (uint24 _lpFee) {
                          assembly ("memory-safe") {
                              _lpFee := and(MASK_24_BITS, shr(LP_FEE_OFFSET, _packed))
                          }
                      }
                      // #### SETTERS ####
                      function setSqrtPriceX96(Slot0 _packed, uint160 _sqrtPriceX96) internal pure returns (Slot0 _result) {
                          assembly ("memory-safe") {
                              _result := or(and(not(MASK_160_BITS), _packed), and(MASK_160_BITS, _sqrtPriceX96))
                          }
                      }
                      function setTick(Slot0 _packed, int24 _tick) internal pure returns (Slot0 _result) {
                          assembly ("memory-safe") {
                              _result := or(and(not(shl(TICK_OFFSET, MASK_24_BITS)), _packed), shl(TICK_OFFSET, and(MASK_24_BITS, _tick)))
                          }
                      }
                      function setProtocolFee(Slot0 _packed, uint24 _protocolFee) internal pure returns (Slot0 _result) {
                          assembly ("memory-safe") {
                              _result :=
                                  or(
                                      and(not(shl(PROTOCOL_FEE_OFFSET, MASK_24_BITS)), _packed),
                                      shl(PROTOCOL_FEE_OFFSET, and(MASK_24_BITS, _protocolFee))
                                  )
                          }
                      }
                      function setLpFee(Slot0 _packed, uint24 _lpFee) internal pure returns (Slot0 _result) {
                          assembly ("memory-safe") {
                              _result :=
                                  or(and(not(shl(LP_FEE_OFFSET, MASK_24_BITS)), _packed), shl(LP_FEE_OFFSET, and(MASK_24_BITS, _lpFee)))
                          }
                      }
                  }
                  // SPDX-License-Identifier: MIT
                  pragma solidity ^0.8.0;
                  /// @notice library of functions related to protocol fees
                  library ProtocolFeeLibrary {
                      /// @notice Max protocol fee is 0.1% (1000 pips)
                      /// @dev Increasing these values could lead to overflow in Pool.swap
                      uint16 public constant MAX_PROTOCOL_FEE = 1000;
                      /// @notice Thresholds used for optimized bounds checks on protocol fees
                      uint24 internal constant FEE_0_THRESHOLD = 1001;
                      uint24 internal constant FEE_1_THRESHOLD = 1001 << 12;
                      /// @notice the protocol fee is represented in hundredths of a bip
                      uint256 internal constant PIPS_DENOMINATOR = 1_000_000;
                      function getZeroForOneFee(uint24 self) internal pure returns (uint16) {
                          return uint16(self & 0xfff);
                      }
                      function getOneForZeroFee(uint24 self) internal pure returns (uint16) {
                          return uint16(self >> 12);
                      }
                      function isValidProtocolFee(uint24 self) internal pure returns (bool valid) {
                          // Equivalent to: getZeroForOneFee(self) <= MAX_PROTOCOL_FEE && getOneForZeroFee(self) <= MAX_PROTOCOL_FEE
                          assembly ("memory-safe") {
                              let isZeroForOneFeeOk := lt(and(self, 0xfff), FEE_0_THRESHOLD)
                              let isOneForZeroFeeOk := lt(and(self, 0xfff000), FEE_1_THRESHOLD)
                              valid := and(isZeroForOneFeeOk, isOneForZeroFeeOk)
                          }
                      }
                      // The protocol fee is taken from the input amount first and then the LP fee is taken from the remaining
                      // The swap fee is capped at 100%
                      // Equivalent to protocolFee + lpFee(1_000_000 - protocolFee) / 1_000_000 (rounded up)
                      /// @dev here `self` is just a single direction's protocol fee, not a packed type of 2 protocol fees
                      function calculateSwapFee(uint16 self, uint24 lpFee) internal pure returns (uint24 swapFee) {
                          // protocolFee + lpFee - (protocolFee * lpFee / 1_000_000)
                          assembly ("memory-safe") {
                              self := and(self, 0xfff)
                              lpFee := and(lpFee, 0xffffff)
                              let numerator := mul(self, lpFee)
                              swapFee := sub(add(self, lpFee), div(numerator, PIPS_DENOMINATOR))
                          }
                      }
                  }
                  // SPDX-License-Identifier: MIT
                  pragma solidity ^0.8.0;
                  /// @title Math library for liquidity
                  library LiquidityMath {
                      /// @notice Add a signed liquidity delta to liquidity and revert if it overflows or underflows
                      /// @param x The liquidity before change
                      /// @param y The delta by which liquidity should be changed
                      /// @return z The liquidity delta
                      function addDelta(uint128 x, int128 y) internal pure returns (uint128 z) {
                          assembly ("memory-safe") {
                              z := add(and(x, 0xffffffffffffffffffffffffffffffff), signextend(15, y))
                              if shr(128, z) {
                                  // revert SafeCastOverflow()
                                  mstore(0, 0x93dafdf1)
                                  revert(0x1c, 0x04)
                              }
                          }
                      }
                  }
                  // SPDX-License-Identifier: MIT
                  pragma solidity ^0.8.0;
                  /// @title Contains 512-bit math functions
                  /// @notice Facilitates multiplication and division that can have overflow of an intermediate value without any loss of precision
                  /// @dev Handles "phantom overflow" i.e., allows multiplication and division where an intermediate value overflows 256 bits
                  library FullMath {
                      /// @notice Calculates floor(a×b÷denominator) with full precision. Throws if result overflows a uint256 or denominator == 0
                      /// @param a The multiplicand
                      /// @param b The multiplier
                      /// @param denominator The divisor
                      /// @return result The 256-bit result
                      /// @dev Credit to Remco Bloemen under MIT license https://xn--2-umb.com/21/muldiv
                      function mulDiv(uint256 a, uint256 b, uint256 denominator) internal pure returns (uint256 result) {
                          unchecked {
                              // 512-bit multiply [prod1 prod0] = a * b
                              // Compute the product mod 2**256 and mod 2**256 - 1
                              // then use the Chinese Remainder Theorem to reconstruct
                              // the 512 bit result. The result is stored in two 256
                              // variables such that product = prod1 * 2**256 + prod0
                              uint256 prod0 = a * b; // Least significant 256 bits of the product
                              uint256 prod1; // Most significant 256 bits of the product
                              assembly ("memory-safe") {
                                  let mm := mulmod(a, b, not(0))
                                  prod1 := sub(sub(mm, prod0), lt(mm, prod0))
                              }
                              // Make sure the result is less than 2**256.
                              // Also prevents denominator == 0
                              require(denominator > prod1);
                              // Handle non-overflow cases, 256 by 256 division
                              if (prod1 == 0) {
                                  assembly ("memory-safe") {
                                      result := div(prod0, denominator)
                                  }
                                  return result;
                              }
                              ///////////////////////////////////////////////
                              // 512 by 256 division.
                              ///////////////////////////////////////////////
                              // Make division exact by subtracting the remainder from [prod1 prod0]
                              // Compute remainder using mulmod
                              uint256 remainder;
                              assembly ("memory-safe") {
                                  remainder := mulmod(a, b, denominator)
                              }
                              // Subtract 256 bit number from 512 bit number
                              assembly ("memory-safe") {
                                  prod1 := sub(prod1, gt(remainder, prod0))
                                  prod0 := sub(prod0, remainder)
                              }
                              // Factor powers of two out of denominator
                              // Compute largest power of two divisor of denominator.
                              // Always >= 1.
                              uint256 twos = (0 - denominator) & denominator;
                              // Divide denominator by power of two
                              assembly ("memory-safe") {
                                  denominator := div(denominator, twos)
                              }
                              // Divide [prod1 prod0] by the factors of two
                              assembly ("memory-safe") {
                                  prod0 := div(prod0, twos)
                              }
                              // Shift in bits from prod1 into prod0. For this we need
                              // to flip `twos` such that it is 2**256 / twos.
                              // If twos is zero, then it becomes one
                              assembly ("memory-safe") {
                                  twos := add(div(sub(0, twos), twos), 1)
                              }
                              prod0 |= prod1 * twos;
                              // Invert denominator mod 2**256
                              // Now that denominator is an odd number, it has an inverse
                              // modulo 2**256 such that denominator * inv = 1 mod 2**256.
                              // Compute the inverse by starting with a seed that is correct
                              // correct for four bits. That is, denominator * inv = 1 mod 2**4
                              uint256 inv = (3 * denominator) ^ 2;
                              // Now use Newton-Raphson iteration to improve the precision.
                              // Thanks to Hensel's lifting lemma, this also works in modular
                              // arithmetic, doubling the correct bits in each step.
                              inv *= 2 - denominator * inv; // inverse mod 2**8
                              inv *= 2 - denominator * inv; // inverse mod 2**16
                              inv *= 2 - denominator * inv; // inverse mod 2**32
                              inv *= 2 - denominator * inv; // inverse mod 2**64
                              inv *= 2 - denominator * inv; // inverse mod 2**128
                              inv *= 2 - denominator * inv; // inverse mod 2**256
                              // Because the division is now exact we can divide by multiplying
                              // with the modular inverse of denominator. This will give us the
                              // correct result modulo 2**256. Since the preconditions guarantee
                              // that the outcome is less than 2**256, this is the final result.
                              // We don't need to compute the high bits of the result and prod1
                              // is no longer required.
                              result = prod0 * inv;
                              return result;
                          }
                      }
                      /// @notice Calculates ceil(a×b÷denominator) with full precision. Throws if result overflows a uint256 or denominator == 0
                      /// @param a The multiplicand
                      /// @param b The multiplier
                      /// @param denominator The divisor
                      /// @return result The 256-bit result
                      function mulDivRoundingUp(uint256 a, uint256 b, uint256 denominator) internal pure returns (uint256 result) {
                          unchecked {
                              result = mulDiv(a, b, denominator);
                              if (mulmod(a, b, denominator) != 0) {
                                  require(++result > 0);
                              }
                          }
                      }
                  }
                  // SPDX-License-Identifier: MIT
                  pragma solidity ^0.8.0;
                  /// @title Minimal ERC20 interface for Uniswap
                  /// @notice Contains a subset of the full ERC20 interface that is used in Uniswap V3
                  interface IERC20Minimal {
                      /// @notice Returns an account's balance in the token
                      /// @param account The account for which to look up the number of tokens it has, i.e. its balance
                      /// @return The number of tokens held by the account
                      function balanceOf(address account) external view returns (uint256);
                      /// @notice Transfers the amount of token from the `msg.sender` to the recipient
                      /// @param recipient The account that will receive the amount transferred
                      /// @param amount The number of tokens to send from the sender to the recipient
                      /// @return Returns true for a successful transfer, false for an unsuccessful transfer
                      function transfer(address recipient, uint256 amount) external returns (bool);
                      /// @notice Returns the current allowance given to a spender by an owner
                      /// @param owner The account of the token owner
                      /// @param spender The account of the token spender
                      /// @return The current allowance granted by `owner` to `spender`
                      function allowance(address owner, address spender) external view returns (uint256);
                      /// @notice Sets the allowance of a spender from the `msg.sender` to the value `amount`
                      /// @param spender The account which will be allowed to spend a given amount of the owners tokens
                      /// @param amount The amount of tokens allowed to be used by `spender`
                      /// @return Returns true for a successful approval, false for unsuccessful
                      function approve(address spender, uint256 amount) external returns (bool);
                      /// @notice Transfers `amount` tokens from `sender` to `recipient` up to the allowance given to the `msg.sender`
                      /// @param sender The account from which the transfer will be initiated
                      /// @param recipient The recipient of the transfer
                      /// @param amount The amount of the transfer
                      /// @return Returns true for a successful transfer, false for unsuccessful
                      function transferFrom(address sender, address recipient, uint256 amount) external returns (bool);
                      /// @notice Event emitted when tokens are transferred from one address to another, either via `#transfer` or `#transferFrom`.
                      /// @param from The account from which the tokens were sent, i.e. the balance decreased
                      /// @param to The account to which the tokens were sent, i.e. the balance increased
                      /// @param value The amount of tokens that were transferred
                      event Transfer(address indexed from, address indexed to, uint256 value);
                      /// @notice Event emitted when the approval amount for the spender of a given owner's tokens changes.
                      /// @param owner The account that approved spending of its tokens
                      /// @param spender The account for which the spending allowance was modified
                      /// @param value The new allowance from the owner to the spender
                      event Approval(address indexed owner, address indexed spender, uint256 value);
                  }
                  // SPDX-License-Identifier: MIT
                  pragma solidity ^0.8.0;
                  /// @title BitMath
                  /// @dev This library provides functionality for computing bit properties of an unsigned integer
                  /// @author Solady (https://github.com/Vectorized/solady/blob/8200a70e8dc2a77ecb074fc2e99a2a0d36547522/src/utils/LibBit.sol)
                  library BitMath {
                      /// @notice Returns the index of the most significant bit of the number,
                      ///     where the least significant bit is at index 0 and the most significant bit is at index 255
                      /// @param x the value for which to compute the most significant bit, must be greater than 0
                      /// @return r the index of the most significant bit
                      function mostSignificantBit(uint256 x) internal pure returns (uint8 r) {
                          require(x > 0);
                          assembly ("memory-safe") {
                              r := shl(7, lt(0xffffffffffffffffffffffffffffffff, x))
                              r := or(r, shl(6, lt(0xffffffffffffffff, shr(r, x))))
                              r := or(r, shl(5, lt(0xffffffff, shr(r, x))))
                              r := or(r, shl(4, lt(0xffff, shr(r, x))))
                              r := or(r, shl(3, lt(0xff, shr(r, x))))
                              // forgefmt: disable-next-item
                              r := or(r, byte(and(0x1f, shr(shr(r, x), 0x8421084210842108cc6318c6db6d54be)),
                                  0x0706060506020500060203020504000106050205030304010505030400000000))
                          }
                      }
                      /// @notice Returns the index of the least significant bit of the number,
                      ///     where the least significant bit is at index 0 and the most significant bit is at index 255
                      /// @param x the value for which to compute the least significant bit, must be greater than 0
                      /// @return r the index of the least significant bit
                      function leastSignificantBit(uint256 x) internal pure returns (uint8 r) {
                          require(x > 0);
                          assembly ("memory-safe") {
                              // Isolate the least significant bit.
                              x := and(x, sub(0, x))
                              // For the upper 3 bits of the result, use a De Bruijn-like lookup.
                              // Credit to adhusson: https://blog.adhusson.com/cheap-find-first-set-evm/
                              // forgefmt: disable-next-item
                              r := shl(5, shr(252, shl(shl(2, shr(250, mul(x,
                                  0xb6db6db6ddddddddd34d34d349249249210842108c6318c639ce739cffffffff))),
                                  0x8040405543005266443200005020610674053026020000107506200176117077)))
                              // For the lower 5 bits of the result, use a De Bruijn lookup.
                              // forgefmt: disable-next-item
                              r := or(r, byte(and(div(0xd76453e0, shr(r, x)), 0x1f),
                                  0x001f0d1e100c1d070f090b19131c1706010e11080a1a141802121b1503160405))
                          }
                      }
                  }
                  // SPDX-License-Identifier: MIT
                  pragma solidity ^0.8.0;
                  /// @notice Interface for claims over a contract balance, wrapped as a ERC6909
                  interface IERC6909Claims {
                      /*//////////////////////////////////////////////////////////////
                                                   EVENTS
                      //////////////////////////////////////////////////////////////*/
                      event OperatorSet(address indexed owner, address indexed operator, bool approved);
                      event Approval(address indexed owner, address indexed spender, uint256 indexed id, uint256 amount);
                      event Transfer(address caller, address indexed from, address indexed to, uint256 indexed id, uint256 amount);
                      /*//////////////////////////////////////////////////////////////
                                                   FUNCTIONS
                      //////////////////////////////////////////////////////////////*/
                      /// @notice Owner balance of an id.
                      /// @param owner The address of the owner.
                      /// @param id The id of the token.
                      /// @return amount The balance of the token.
                      function balanceOf(address owner, uint256 id) external view returns (uint256 amount);
                      /// @notice Spender allowance of an id.
                      /// @param owner The address of the owner.
                      /// @param spender The address of the spender.
                      /// @param id The id of the token.
                      /// @return amount The allowance of the token.
                      function allowance(address owner, address spender, uint256 id) external view returns (uint256 amount);
                      /// @notice Checks if a spender is approved by an owner as an operator
                      /// @param owner The address of the owner.
                      /// @param spender The address of the spender.
                      /// @return approved The approval status.
                      function isOperator(address owner, address spender) external view returns (bool approved);
                      /// @notice Transfers an amount of an id from the caller to a receiver.
                      /// @param receiver The address of the receiver.
                      /// @param id The id of the token.
                      /// @param amount The amount of the token.
                      /// @return bool True, always, unless the function reverts
                      function transfer(address receiver, uint256 id, uint256 amount) external returns (bool);
                      /// @notice Transfers an amount of an id from a sender to a receiver.
                      /// @param sender The address of the sender.
                      /// @param receiver The address of the receiver.
                      /// @param id The id of the token.
                      /// @param amount The amount of the token.
                      /// @return bool True, always, unless the function reverts
                      function transferFrom(address sender, address receiver, uint256 id, uint256 amount) external returns (bool);
                      /// @notice Approves an amount of an id to a spender.
                      /// @param spender The address of the spender.
                      /// @param id The id of the token.
                      /// @param amount The amount of the token.
                      /// @return bool True, always
                      function approve(address spender, uint256 id, uint256 amount) external returns (bool);
                      /// @notice Sets or removes an operator for the caller.
                      /// @param operator The address of the operator.
                      /// @param approved The approval status.
                      /// @return bool True, always
                      function setOperator(address operator, bool approved) external returns (bool);
                  }
                  // SPDX-License-Identifier: MIT
                  pragma solidity ^0.8.0;
                  import {Currency} from "../types/Currency.sol";
                  import {PoolId} from "../types/PoolId.sol";
                  import {PoolKey} from "../types/PoolKey.sol";
                  /// @notice Interface for all protocol-fee related functions in the pool manager
                  interface IProtocolFees {
                      /// @notice Thrown when protocol fee is set too high
                      error ProtocolFeeTooLarge(uint24 fee);
                      /// @notice Thrown when collectProtocolFees or setProtocolFee is not called by the controller.
                      error InvalidCaller();
                      /// @notice Thrown when collectProtocolFees is attempted on a token that is synced.
                      error ProtocolFeeCurrencySynced();
                      /// @notice Emitted when the protocol fee controller address is updated in setProtocolFeeController.
                      event ProtocolFeeControllerUpdated(address indexed protocolFeeController);
                      /// @notice Emitted when the protocol fee is updated for a pool.
                      event ProtocolFeeUpdated(PoolId indexed id, uint24 protocolFee);
                      /// @notice Given a currency address, returns the protocol fees accrued in that currency
                      /// @param currency The currency to check
                      /// @return amount The amount of protocol fees accrued in the currency
                      function protocolFeesAccrued(Currency currency) external view returns (uint256 amount);
                      /// @notice Sets the protocol fee for the given pool
                      /// @param key The key of the pool to set a protocol fee for
                      /// @param newProtocolFee The fee to set
                      function setProtocolFee(PoolKey memory key, uint24 newProtocolFee) external;
                      /// @notice Sets the protocol fee controller
                      /// @param controller The new protocol fee controller
                      function setProtocolFeeController(address controller) external;
                      /// @notice Collects the protocol fees for a given recipient and currency, returning the amount collected
                      /// @dev This will revert if the contract is unlocked
                      /// @param recipient The address to receive the protocol fees
                      /// @param currency The currency to withdraw
                      /// @param amount The amount of currency to withdraw
                      /// @return amountCollected The amount of currency successfully withdrawn
                      function collectProtocolFees(address recipient, Currency currency, uint256 amount)
                          external
                          returns (uint256 amountCollected);
                      /// @notice Returns the current protocol fee controller address
                      /// @return address The current protocol fee controller address
                      function protocolFeeController() external view returns (address);
                  }
                  // SPDX-License-Identifier: MIT
                  pragma solidity ^0.8.0;
                  /// @notice Interface for functions to access any storage slot in a contract
                  interface IExtsload {
                      /// @notice Called by external contracts to access granular pool state
                      /// @param slot Key of slot to sload
                      /// @return value The value of the slot as bytes32
                      function extsload(bytes32 slot) external view returns (bytes32 value);
                      /// @notice Called by external contracts to access granular pool state
                      /// @param startSlot Key of slot to start sloading from
                      /// @param nSlots Number of slots to load into return value
                      /// @return values List of loaded values.
                      function extsload(bytes32 startSlot, uint256 nSlots) external view returns (bytes32[] memory values);
                      /// @notice Called by external contracts to access sparse pool state
                      /// @param slots List of slots to SLOAD from.
                      /// @return values List of loaded values.
                      function extsload(bytes32[] calldata slots) external view returns (bytes32[] memory values);
                  }
                  // SPDX-License-Identifier: MIT
                  pragma solidity ^0.8.24;
                  /// @notice Interface for functions to access any transient storage slot in a contract
                  interface IExttload {
                      /// @notice Called by external contracts to access transient storage of the contract
                      /// @param slot Key of slot to tload
                      /// @return value The value of the slot as bytes32
                      function exttload(bytes32 slot) external view returns (bytes32 value);
                      /// @notice Called by external contracts to access sparse transient pool state
                      /// @param slots List of slots to tload
                      /// @return values List of loaded values
                      function exttload(bytes32[] calldata slots) external view returns (bytes32[] memory values);
                  }
                  // SPDX-License-Identifier: AGPL-3.0-only
                  pragma solidity >=0.8.0;
                  /// @notice Simple single owner authorization mixin.
                  /// @author Solmate (https://github.com/transmissions11/solmate/blob/main/src/auth/Owned.sol)
                  abstract contract Owned {
                      /*//////////////////////////////////////////////////////////////
                                                   EVENTS
                      //////////////////////////////////////////////////////////////*/
                      event OwnershipTransferred(address indexed user, address indexed newOwner);
                      /*//////////////////////////////////////////////////////////////
                                              OWNERSHIP STORAGE
                      //////////////////////////////////////////////////////////////*/
                      address public owner;
                      modifier onlyOwner() virtual {
                          require(msg.sender == owner, "UNAUTHORIZED");
                          _;
                      }
                      /*//////////////////////////////////////////////////////////////
                                                 CONSTRUCTOR
                      //////////////////////////////////////////////////////////////*/
                      constructor(address _owner) {
                          owner = _owner;
                          emit OwnershipTransferred(address(0), _owner);
                      }
                      /*//////////////////////////////////////////////////////////////
                                               OWNERSHIP LOGIC
                      //////////////////////////////////////////////////////////////*/
                      function transferOwnership(address newOwner) public virtual onlyOwner {
                          owner = newOwner;
                          emit OwnershipTransferred(msg.sender, newOwner);
                      }
                  }
                  // SPDX-License-Identifier: MIT
                  pragma solidity ^0.8.0;
                  import {IERC6909Claims} from "./interfaces/external/IERC6909Claims.sol";
                  /// @notice Minimalist and gas efficient standard ERC6909 implementation.
                  /// @author Solmate (https://github.com/transmissions11/solmate/blob/main/src/tokens/ERC6909.sol)
                  /// @dev Copied from the commit at 4b47a19038b798b4a33d9749d25e570443520647
                  /// @dev This contract has been modified from the implementation at the above link.
                  abstract contract ERC6909 is IERC6909Claims {
                      /*//////////////////////////////////////////////////////////////
                                               ERC6909 STORAGE
                      //////////////////////////////////////////////////////////////*/
                      mapping(address owner => mapping(address operator => bool isOperator)) public isOperator;
                      mapping(address owner => mapping(uint256 id => uint256 balance)) public balanceOf;
                      mapping(address owner => mapping(address spender => mapping(uint256 id => uint256 amount))) public allowance;
                      /*//////////////////////////////////////////////////////////////
                                                ERC6909 LOGIC
                      //////////////////////////////////////////////////////////////*/
                      function transfer(address receiver, uint256 id, uint256 amount) public virtual returns (bool) {
                          balanceOf[msg.sender][id] -= amount;
                          balanceOf[receiver][id] += amount;
                          emit Transfer(msg.sender, msg.sender, receiver, id, amount);
                          return true;
                      }
                      function transferFrom(address sender, address receiver, uint256 id, uint256 amount) public virtual returns (bool) {
                          if (msg.sender != sender && !isOperator[sender][msg.sender]) {
                              uint256 allowed = allowance[sender][msg.sender][id];
                              if (allowed != type(uint256).max) allowance[sender][msg.sender][id] = allowed - amount;
                          }
                          balanceOf[sender][id] -= amount;
                          balanceOf[receiver][id] += amount;
                          emit Transfer(msg.sender, sender, receiver, id, amount);
                          return true;
                      }
                      function approve(address spender, uint256 id, uint256 amount) public virtual returns (bool) {
                          allowance[msg.sender][spender][id] = amount;
                          emit Approval(msg.sender, spender, id, amount);
                          return true;
                      }
                      function setOperator(address operator, bool approved) public virtual returns (bool) {
                          isOperator[msg.sender][operator] = approved;
                          emit OperatorSet(msg.sender, operator, approved);
                          return true;
                      }
                      /*//////////////////////////////////////////////////////////////
                                                ERC165 LOGIC
                      //////////////////////////////////////////////////////////////*/
                      function supportsInterface(bytes4 interfaceId) public view virtual returns (bool) {
                          return interfaceId == 0x01ffc9a7 // ERC165 Interface ID for ERC165
                              || interfaceId == 0x0f632fb3; // ERC165 Interface ID for ERC6909
                      }
                      /*//////////////////////////////////////////////////////////////
                                          INTERNAL MINT/BURN LOGIC
                      //////////////////////////////////////////////////////////////*/
                      function _mint(address receiver, uint256 id, uint256 amount) internal virtual {
                          balanceOf[receiver][id] += amount;
                          emit Transfer(msg.sender, address(0), receiver, id, amount);
                      }
                      function _burn(address sender, uint256 id, uint256 amount) internal virtual {
                          balanceOf[sender][id] -= amount;
                          emit Transfer(msg.sender, sender, address(0), id, amount);
                      }
                  }
                  // SPDX-License-Identifier: MIT
                  pragma solidity ^0.8.0;
                  /// @title FixedPoint96
                  /// @notice A library for handling binary fixed point numbers, see https://en.wikipedia.org/wiki/Q_(number_format)
                  /// @dev Used in SqrtPriceMath.sol
                  library FixedPoint96 {
                      uint8 internal constant RESOLUTION = 96;
                      uint256 internal constant Q96 = 0x1000000000000000000000000;
                  }
                  

                  File 2 of 3: WETH9
                  // Copyright (C) 2015, 2016, 2017 Dapphub
                  
                  // This program is free software: you can redistribute it and/or modify
                  // it under the terms of the GNU General Public License as published by
                  // the Free Software Foundation, either version 3 of the License, or
                  // (at your option) any later version.
                  
                  // This program is distributed in the hope that it will be useful,
                  // but WITHOUT ANY WARRANTY; without even the implied warranty of
                  // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
                  // GNU General Public License for more details.
                  
                  // You should have received a copy of the GNU General Public License
                  // along with this program.  If not, see <http://www.gnu.org/licenses/>.
                  
                  pragma solidity ^0.4.18;
                  
                  contract WETH9 {
                      string public name     = "Wrapped Ether";
                      string public symbol   = "WETH";
                      uint8  public decimals = 18;
                  
                      event  Approval(address indexed src, address indexed guy, uint wad);
                      event  Transfer(address indexed src, address indexed dst, uint wad);
                      event  Deposit(address indexed dst, uint wad);
                      event  Withdrawal(address indexed src, uint wad);
                  
                      mapping (address => uint)                       public  balanceOf;
                      mapping (address => mapping (address => uint))  public  allowance;
                  
                      function() public payable {
                          deposit();
                      }
                      function deposit() public payable {
                          balanceOf[msg.sender] += msg.value;
                          Deposit(msg.sender, msg.value);
                      }
                      function withdraw(uint wad) public {
                          require(balanceOf[msg.sender] >= wad);
                          balanceOf[msg.sender] -= wad;
                          msg.sender.transfer(wad);
                          Withdrawal(msg.sender, wad);
                      }
                  
                      function totalSupply() public view returns (uint) {
                          return this.balance;
                      }
                  
                      function approve(address guy, uint wad) public returns (bool) {
                          allowance[msg.sender][guy] = wad;
                          Approval(msg.sender, guy, wad);
                          return true;
                      }
                  
                      function transfer(address dst, uint wad) public returns (bool) {
                          return transferFrom(msg.sender, dst, wad);
                      }
                  
                      function transferFrom(address src, address dst, uint wad)
                          public
                          returns (bool)
                      {
                          require(balanceOf[src] >= wad);
                  
                          if (src != msg.sender && allowance[src][msg.sender] != uint(-1)) {
                              require(allowance[src][msg.sender] >= wad);
                              allowance[src][msg.sender] -= wad;
                          }
                  
                          balanceOf[src] -= wad;
                          balanceOf[dst] += wad;
                  
                          Transfer(src, dst, wad);
                  
                          return true;
                      }
                  }
                  
                  
                  /*
                                      GNU GENERAL PUBLIC LICENSE
                                         Version 3, 29 June 2007
                  
                   Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>
                   Everyone is permitted to copy and distribute verbatim copies
                   of this license document, but changing it is not allowed.
                  
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                  any other work released this way by its authors.  You can apply it to
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                  File 3 of 3: TetherToken
                  pragma solidity ^0.4.17;
                  
                  /**
                   * @title SafeMath
                   * @dev Math operations with safety checks that throw on error
                   */
                  library SafeMath {
                      function mul(uint256 a, uint256 b) internal pure returns (uint256) {
                          if (a == 0) {
                              return 0;
                          }
                          uint256 c = a * b;
                          assert(c / a == b);
                          return c;
                      }
                  
                      function div(uint256 a, uint256 b) internal pure returns (uint256) {
                          // assert(b > 0); // Solidity automatically throws when dividing by 0
                          uint256 c = a / b;
                          // assert(a == b * c + a % b); // There is no case in which this doesn't hold
                          return c;
                      }
                  
                      function sub(uint256 a, uint256 b) internal pure returns (uint256) {
                          assert(b <= a);
                          return a - b;
                      }
                  
                      function add(uint256 a, uint256 b) internal pure returns (uint256) {
                          uint256 c = a + b;
                          assert(c >= a);
                          return c;
                      }
                  }
                  
                  /**
                   * @title Ownable
                   * @dev The Ownable contract has an owner address, and provides basic authorization control
                   * functions, this simplifies the implementation of "user permissions".
                   */
                  contract Ownable {
                      address public owner;
                  
                      /**
                        * @dev The Ownable constructor sets the original `owner` of the contract to the sender
                        * account.
                        */
                      function Ownable() public {
                          owner = msg.sender;
                      }
                  
                      /**
                        * @dev Throws if called by any account other than the owner.
                        */
                      modifier onlyOwner() {
                          require(msg.sender == owner);
                          _;
                      }
                  
                      /**
                      * @dev Allows the current owner to transfer control of the contract to a newOwner.
                      * @param newOwner The address to transfer ownership to.
                      */
                      function transferOwnership(address newOwner) public onlyOwner {
                          if (newOwner != address(0)) {
                              owner = newOwner;
                          }
                      }
                  
                  }
                  
                  /**
                   * @title ERC20Basic
                   * @dev Simpler version of ERC20 interface
                   * @dev see https://github.com/ethereum/EIPs/issues/20
                   */
                  contract ERC20Basic {
                      uint public _totalSupply;
                      function totalSupply() public constant returns (uint);
                      function balanceOf(address who) public constant returns (uint);
                      function transfer(address to, uint value) public;
                      event Transfer(address indexed from, address indexed to, uint value);
                  }
                  
                  /**
                   * @title ERC20 interface
                   * @dev see https://github.com/ethereum/EIPs/issues/20
                   */
                  contract ERC20 is ERC20Basic {
                      function allowance(address owner, address spender) public constant returns (uint);
                      function transferFrom(address from, address to, uint value) public;
                      function approve(address spender, uint value) public;
                      event Approval(address indexed owner, address indexed spender, uint value);
                  }
                  
                  /**
                   * @title Basic token
                   * @dev Basic version of StandardToken, with no allowances.
                   */
                  contract BasicToken is Ownable, ERC20Basic {
                      using SafeMath for uint;
                  
                      mapping(address => uint) public balances;
                  
                      // additional variables for use if transaction fees ever became necessary
                      uint public basisPointsRate = 0;
                      uint public maximumFee = 0;
                  
                      /**
                      * @dev Fix for the ERC20 short address attack.
                      */
                      modifier onlyPayloadSize(uint size) {
                          require(!(msg.data.length < size + 4));
                          _;
                      }
                  
                      /**
                      * @dev transfer token for a specified address
                      * @param _to The address to transfer to.
                      * @param _value The amount to be transferred.
                      */
                      function transfer(address _to, uint _value) public onlyPayloadSize(2 * 32) {
                          uint fee = (_value.mul(basisPointsRate)).div(10000);
                          if (fee > maximumFee) {
                              fee = maximumFee;
                          }
                          uint sendAmount = _value.sub(fee);
                          balances[msg.sender] = balances[msg.sender].sub(_value);
                          balances[_to] = balances[_to].add(sendAmount);
                          if (fee > 0) {
                              balances[owner] = balances[owner].add(fee);
                              Transfer(msg.sender, owner, fee);
                          }
                          Transfer(msg.sender, _to, sendAmount);
                      }
                  
                      /**
                      * @dev Gets the balance of the specified address.
                      * @param _owner The address to query the the balance of.
                      * @return An uint representing the amount owned by the passed address.
                      */
                      function balanceOf(address _owner) public constant returns (uint balance) {
                          return balances[_owner];
                      }
                  
                  }
                  
                  /**
                   * @title Standard ERC20 token
                   *
                   * @dev Implementation of the basic standard token.
                   * @dev https://github.com/ethereum/EIPs/issues/20
                   * @dev Based oncode by FirstBlood: https://github.com/Firstbloodio/token/blob/master/smart_contract/FirstBloodToken.sol
                   */
                  contract StandardToken is BasicToken, ERC20 {
                  
                      mapping (address => mapping (address => uint)) public allowed;
                  
                      uint public constant MAX_UINT = 2**256 - 1;
                  
                      /**
                      * @dev Transfer tokens from one address to another
                      * @param _from address The address which you want to send tokens from
                      * @param _to address The address which you want to transfer to
                      * @param _value uint the amount of tokens to be transferred
                      */
                      function transferFrom(address _from, address _to, uint _value) public onlyPayloadSize(3 * 32) {
                          var _allowance = allowed[_from][msg.sender];
                  
                          // Check is not needed because sub(_allowance, _value) will already throw if this condition is not met
                          // if (_value > _allowance) throw;
                  
                          uint fee = (_value.mul(basisPointsRate)).div(10000);
                          if (fee > maximumFee) {
                              fee = maximumFee;
                          }
                          if (_allowance < MAX_UINT) {
                              allowed[_from][msg.sender] = _allowance.sub(_value);
                          }
                          uint sendAmount = _value.sub(fee);
                          balances[_from] = balances[_from].sub(_value);
                          balances[_to] = balances[_to].add(sendAmount);
                          if (fee > 0) {
                              balances[owner] = balances[owner].add(fee);
                              Transfer(_from, owner, fee);
                          }
                          Transfer(_from, _to, sendAmount);
                      }
                  
                      /**
                      * @dev Approve the passed address to spend the specified amount of tokens on behalf of msg.sender.
                      * @param _spender The address which will spend the funds.
                      * @param _value The amount of tokens to be spent.
                      */
                      function approve(address _spender, uint _value) public onlyPayloadSize(2 * 32) {
                  
                          // To change the approve amount you first have to reduce the addresses`
                          //  allowance to zero by calling `approve(_spender, 0)` if it is not
                          //  already 0 to mitigate the race condition described here:
                          //  https://github.com/ethereum/EIPs/issues/20#issuecomment-263524729
                          require(!((_value != 0) && (allowed[msg.sender][_spender] != 0)));
                  
                          allowed[msg.sender][_spender] = _value;
                          Approval(msg.sender, _spender, _value);
                      }
                  
                      /**
                      * @dev Function to check the amount of tokens than an owner allowed to a spender.
                      * @param _owner address The address which owns the funds.
                      * @param _spender address The address which will spend the funds.
                      * @return A uint specifying the amount of tokens still available for the spender.
                      */
                      function allowance(address _owner, address _spender) public constant returns (uint remaining) {
                          return allowed[_owner][_spender];
                      }
                  
                  }
                  
                  
                  /**
                   * @title Pausable
                   * @dev Base contract which allows children to implement an emergency stop mechanism.
                   */
                  contract Pausable is Ownable {
                    event Pause();
                    event Unpause();
                  
                    bool public paused = false;
                  
                  
                    /**
                     * @dev Modifier to make a function callable only when the contract is not paused.
                     */
                    modifier whenNotPaused() {
                      require(!paused);
                      _;
                    }
                  
                    /**
                     * @dev Modifier to make a function callable only when the contract is paused.
                     */
                    modifier whenPaused() {
                      require(paused);
                      _;
                    }
                  
                    /**
                     * @dev called by the owner to pause, triggers stopped state
                     */
                    function pause() onlyOwner whenNotPaused public {
                      paused = true;
                      Pause();
                    }
                  
                    /**
                     * @dev called by the owner to unpause, returns to normal state
                     */
                    function unpause() onlyOwner whenPaused public {
                      paused = false;
                      Unpause();
                    }
                  }
                  
                  contract BlackList is Ownable, BasicToken {
                  
                      /////// Getters to allow the same blacklist to be used also by other contracts (including upgraded Tether) ///////
                      function getBlackListStatus(address _maker) external constant returns (bool) {
                          return isBlackListed[_maker];
                      }
                  
                      function getOwner() external constant returns (address) {
                          return owner;
                      }
                  
                      mapping (address => bool) public isBlackListed;
                      
                      function addBlackList (address _evilUser) public onlyOwner {
                          isBlackListed[_evilUser] = true;
                          AddedBlackList(_evilUser);
                      }
                  
                      function removeBlackList (address _clearedUser) public onlyOwner {
                          isBlackListed[_clearedUser] = false;
                          RemovedBlackList(_clearedUser);
                      }
                  
                      function destroyBlackFunds (address _blackListedUser) public onlyOwner {
                          require(isBlackListed[_blackListedUser]);
                          uint dirtyFunds = balanceOf(_blackListedUser);
                          balances[_blackListedUser] = 0;
                          _totalSupply -= dirtyFunds;
                          DestroyedBlackFunds(_blackListedUser, dirtyFunds);
                      }
                  
                      event DestroyedBlackFunds(address _blackListedUser, uint _balance);
                  
                      event AddedBlackList(address _user);
                  
                      event RemovedBlackList(address _user);
                  
                  }
                  
                  contract UpgradedStandardToken is StandardToken{
                      // those methods are called by the legacy contract
                      // and they must ensure msg.sender to be the contract address
                      function transferByLegacy(address from, address to, uint value) public;
                      function transferFromByLegacy(address sender, address from, address spender, uint value) public;
                      function approveByLegacy(address from, address spender, uint value) public;
                  }
                  
                  contract TetherToken is Pausable, StandardToken, BlackList {
                  
                      string public name;
                      string public symbol;
                      uint public decimals;
                      address public upgradedAddress;
                      bool public deprecated;
                  
                      //  The contract can be initialized with a number of tokens
                      //  All the tokens are deposited to the owner address
                      //
                      // @param _balance Initial supply of the contract
                      // @param _name Token Name
                      // @param _symbol Token symbol
                      // @param _decimals Token decimals
                      function TetherToken(uint _initialSupply, string _name, string _symbol, uint _decimals) public {
                          _totalSupply = _initialSupply;
                          name = _name;
                          symbol = _symbol;
                          decimals = _decimals;
                          balances[owner] = _initialSupply;
                          deprecated = false;
                      }
                  
                      // Forward ERC20 methods to upgraded contract if this one is deprecated
                      function transfer(address _to, uint _value) public whenNotPaused {
                          require(!isBlackListed[msg.sender]);
                          if (deprecated) {
                              return UpgradedStandardToken(upgradedAddress).transferByLegacy(msg.sender, _to, _value);
                          } else {
                              return super.transfer(_to, _value);
                          }
                      }
                  
                      // Forward ERC20 methods to upgraded contract if this one is deprecated
                      function transferFrom(address _from, address _to, uint _value) public whenNotPaused {
                          require(!isBlackListed[_from]);
                          if (deprecated) {
                              return UpgradedStandardToken(upgradedAddress).transferFromByLegacy(msg.sender, _from, _to, _value);
                          } else {
                              return super.transferFrom(_from, _to, _value);
                          }
                      }
                  
                      // Forward ERC20 methods to upgraded contract if this one is deprecated
                      function balanceOf(address who) public constant returns (uint) {
                          if (deprecated) {
                              return UpgradedStandardToken(upgradedAddress).balanceOf(who);
                          } else {
                              return super.balanceOf(who);
                          }
                      }
                  
                      // Forward ERC20 methods to upgraded contract if this one is deprecated
                      function approve(address _spender, uint _value) public onlyPayloadSize(2 * 32) {
                          if (deprecated) {
                              return UpgradedStandardToken(upgradedAddress).approveByLegacy(msg.sender, _spender, _value);
                          } else {
                              return super.approve(_spender, _value);
                          }
                      }
                  
                      // Forward ERC20 methods to upgraded contract if this one is deprecated
                      function allowance(address _owner, address _spender) public constant returns (uint remaining) {
                          if (deprecated) {
                              return StandardToken(upgradedAddress).allowance(_owner, _spender);
                          } else {
                              return super.allowance(_owner, _spender);
                          }
                      }
                  
                      // deprecate current contract in favour of a new one
                      function deprecate(address _upgradedAddress) public onlyOwner {
                          deprecated = true;
                          upgradedAddress = _upgradedAddress;
                          Deprecate(_upgradedAddress);
                      }
                  
                      // deprecate current contract if favour of a new one
                      function totalSupply() public constant returns (uint) {
                          if (deprecated) {
                              return StandardToken(upgradedAddress).totalSupply();
                          } else {
                              return _totalSupply;
                          }
                      }
                  
                      // Issue a new amount of tokens
                      // these tokens are deposited into the owner address
                      //
                      // @param _amount Number of tokens to be issued
                      function issue(uint amount) public onlyOwner {
                          require(_totalSupply + amount > _totalSupply);
                          require(balances[owner] + amount > balances[owner]);
                  
                          balances[owner] += amount;
                          _totalSupply += amount;
                          Issue(amount);
                      }
                  
                      // Redeem tokens.
                      // These tokens are withdrawn from the owner address
                      // if the balance must be enough to cover the redeem
                      // or the call will fail.
                      // @param _amount Number of tokens to be issued
                      function redeem(uint amount) public onlyOwner {
                          require(_totalSupply >= amount);
                          require(balances[owner] >= amount);
                  
                          _totalSupply -= amount;
                          balances[owner] -= amount;
                          Redeem(amount);
                      }
                  
                      function setParams(uint newBasisPoints, uint newMaxFee) public onlyOwner {
                          // Ensure transparency by hardcoding limit beyond which fees can never be added
                          require(newBasisPoints < 20);
                          require(newMaxFee < 50);
                  
                          basisPointsRate = newBasisPoints;
                          maximumFee = newMaxFee.mul(10**decimals);
                  
                          Params(basisPointsRate, maximumFee);
                      }
                  
                      // Called when new token are issued
                      event Issue(uint amount);
                  
                      // Called when tokens are redeemed
                      event Redeem(uint amount);
                  
                      // Called when contract is deprecated
                      event Deprecate(address newAddress);
                  
                      // Called if contract ever adds fees
                      event Params(uint feeBasisPoints, uint maxFee);
                  }