// SPDX-License-Identifier: MIT
pragma solidity ^0.8.23;

library BasisPoints {
  uint256 public constant MAX_BPS = 10_000;

  /*
   * @notice Calculate the basis points of a given amount
   * @param amount The amount to calculate basis points from
   * @param basisPoints The basis points to calculate
   * @return The basis points of the given amount
   */
  function calculate(
    uint256 amount,
    uint256 basisPoints
  ) internal pure returns (uint256) {
    require(basisPoints <= MAX_BPS, "Basis points cannot exceed 10_000");
    return (amount * basisPoints) / MAX_BPS;
  }
}

// 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 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 a uint256 argument in the scratch space
  function revertWith(bytes4 selector, uint256 value) internal pure {
    assembly ("memory-safe") {
      mstore(0, selector)
      mstore(0x04, value)
      revert(0, 0x24)
    }
  }

  /// @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)
    }
  }
}

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.4;

/// @notice Simple ERC20 + EIP-2612 implementation.
/// @author Solady (https://github.com/vectorized/solady/blob/main/src/tokens/ERC20.sol)
/// @author Modified from Solmate (https://github.com/transmissions11/solmate/blob/main/src/tokens/ERC20.sol)
/// @author Modified from OpenZeppelin (https://github.com/OpenZeppelin/openzeppelin-contracts/blob/master/contracts/token/ERC20/ERC20.sol)
///
/// @dev Note:
/// - The ERC20 standard allows minting and transferring to and from the zero address,
///   minting and transferring zero tokens, as well as self-approvals.
///   For performance, this implementation WILL NOT revert for such actions.
///   Please add any checks with overrides if desired.
/// - The `permit` function uses the ecrecover precompile (0x1).
///
/// If you are overriding:
/// - NEVER violate the ERC20 invariant:
///   the total sum of all balances must be equal to `totalSupply()`.
/// - Check that the overridden function is actually used in the function you want to
///   change the behavior of. Much of the code has been manually inlined for performance.
abstract contract ERC20 {
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                       CUSTOM ERRORS                        */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev The total supply has overflowed.
    error TotalSupplyOverflow();

    /// @dev The allowance has overflowed.
    error AllowanceOverflow();

    /// @dev The allowance has underflowed.
    error AllowanceUnderflow();

    /// @dev Insufficient balance.
    error InsufficientBalance();

    /// @dev Insufficient allowance.
    error InsufficientAllowance();

    /// @dev The permit is invalid.
    error InvalidPermit();

    /// @dev The permit has expired.
    error PermitExpired();

    /// @dev The allowance of Permit2 is fixed at infinity.
    error Permit2AllowanceIsFixedAtInfinity();

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                           EVENTS                           */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Emitted when `amount` tokens is transferred from `from` to `to`.
    event Transfer(address indexed from, address indexed to, uint256 amount);

    /// @dev Emitted when `amount` tokens is approved by `owner` to be used by `spender`.
    event Approval(address indexed owner, address indexed spender, uint256 amount);

    /// @dev `keccak256(bytes("Transfer(address,address,uint256)"))`.
    uint256 private constant _TRANSFER_EVENT_SIGNATURE =
        0xddf252ad1be2c89b69c2b068fc378daa952ba7f163c4a11628f55a4df523b3ef;

    /// @dev `keccak256(bytes("Approval(address,address,uint256)"))`.
    uint256 private constant _APPROVAL_EVENT_SIGNATURE =
        0x8c5be1e5ebec7d5bd14f71427d1e84f3dd0314c0f7b2291e5b200ac8c7c3b925;

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                          STORAGE                           */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev The storage slot for the total supply.
    uint256 private constant _TOTAL_SUPPLY_SLOT = 0x05345cdf77eb68f44c;

    /// @dev The balance slot of `owner` is given by:
    /// ```
    ///     mstore(0x0c, _BALANCE_SLOT_SEED)
    ///     mstore(0x00, owner)
    ///     let balanceSlot := keccak256(0x0c, 0x20)
    /// ```
    uint256 private constant _BALANCE_SLOT_SEED = 0x87a211a2;

    /// @dev The allowance slot of (`owner`, `spender`) is given by:
    /// ```
    ///     mstore(0x20, spender)
    ///     mstore(0x0c, _ALLOWANCE_SLOT_SEED)
    ///     mstore(0x00, owner)
    ///     let allowanceSlot := keccak256(0x0c, 0x34)
    /// ```
    uint256 private constant _ALLOWANCE_SLOT_SEED = 0x7f5e9f20;

    /// @dev The nonce slot of `owner` is given by:
    /// ```
    ///     mstore(0x0c, _NONCES_SLOT_SEED)
    ///     mstore(0x00, owner)
    ///     let nonceSlot := keccak256(0x0c, 0x20)
    /// ```
    uint256 private constant _NONCES_SLOT_SEED = 0x38377508;

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                         CONSTANTS                          */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev `(_NONCES_SLOT_SEED << 16) | 0x1901`.
    uint256 private constant _NONCES_SLOT_SEED_WITH_SIGNATURE_PREFIX = 0x383775081901;

    /// @dev `keccak256("EIP712Domain(string name,string version,uint256 chainId,address verifyingContract)")`.
    bytes32 private constant _DOMAIN_TYPEHASH =
        0x8b73c3c69bb8fe3d512ecc4cf759cc79239f7b179b0ffacaa9a75d522b39400f;

    /// @dev `keccak256("1")`.
    /// If you need to use a different version, override `_versionHash`.
    bytes32 private constant _DEFAULT_VERSION_HASH =
        0xc89efdaa54c0f20c7adf612882df0950f5a951637e0307cdcb4c672f298b8bc6;

    /// @dev `keccak256("Permit(address owner,address spender,uint256 value,uint256 nonce,uint256 deadline)")`.
    bytes32 private constant _PERMIT_TYPEHASH =
        0x6e71edae12b1b97f4d1f60370fef10105fa2faae0126114a169c64845d6126c9;

    /// @dev The canonical Permit2 address.
    /// For signature-based allowance granting for single transaction ERC20 `transferFrom`.
    /// To enable, override `_givePermit2InfiniteAllowance()`.
    /// [Github](https://github.com/Uniswap/permit2)
    /// [Etherscan](https://etherscan.io/address/0x000000000022D473030F116dDEE9F6B43aC78BA3)
    address internal constant _PERMIT2 = 0x000000000022D473030F116dDEE9F6B43aC78BA3;

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                       ERC20 METADATA                       */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Returns the name of the token.
    function name() public view virtual returns (string memory);

    /// @dev Returns the symbol of the token.
    function symbol() public view virtual returns (string memory);

    /// @dev Returns the decimals places of the token.
    function decimals() public view virtual returns (uint8) {
        return 18;
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                           ERC20                            */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Returns the amount of tokens in existence.
    function totalSupply() public view virtual returns (uint256 result) {
        /// @solidity memory-safe-assembly
        assembly {
            result := sload(_TOTAL_SUPPLY_SLOT)
        }
    }

    /// @dev Returns the amount of tokens owned by `owner`.
    function balanceOf(address owner) public view virtual returns (uint256 result) {
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x0c, _BALANCE_SLOT_SEED)
            mstore(0x00, owner)
            result := sload(keccak256(0x0c, 0x20))
        }
    }

    /// @dev Returns the amount of tokens that `spender` can spend on behalf of `owner`.
    function allowance(address owner, address spender)
        public
        view
        virtual
        returns (uint256 result)
    {
        if (_givePermit2InfiniteAllowance()) {
            if (spender == _PERMIT2) return type(uint256).max;
        }
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x20, spender)
            mstore(0x0c, _ALLOWANCE_SLOT_SEED)
            mstore(0x00, owner)
            result := sload(keccak256(0x0c, 0x34))
        }
    }

    /// @dev Sets `amount` as the allowance of `spender` over the caller's tokens.
    ///
    /// Emits a {Approval} event.
    function approve(address spender, uint256 amount) public virtual returns (bool) {
        if (_givePermit2InfiniteAllowance()) {
            /// @solidity memory-safe-assembly
            assembly {
                // If `spender == _PERMIT2 && amount != type(uint256).max`.
                if iszero(or(xor(shr(96, shl(96, spender)), _PERMIT2), iszero(not(amount)))) {
                    mstore(0x00, 0x3f68539a) // `Permit2AllowanceIsFixedAtInfinity()`.
                    revert(0x1c, 0x04)
                }
            }
        }
        /// @solidity memory-safe-assembly
        assembly {
            // Compute the allowance slot and store the amount.
            mstore(0x20, spender)
            mstore(0x0c, _ALLOWANCE_SLOT_SEED)
            mstore(0x00, caller())
            sstore(keccak256(0x0c, 0x34), amount)
            // Emit the {Approval} event.
            mstore(0x00, amount)
            log3(0x00, 0x20, _APPROVAL_EVENT_SIGNATURE, caller(), shr(96, mload(0x2c)))
        }
        return true;
    }

    /// @dev Transfer `amount` tokens from the caller to `to`.
    ///
    /// Requirements:
    /// - `from` must at least have `amount`.
    ///
    /// Emits a {Transfer} event.
    function transfer(address to, uint256 amount) public virtual returns (bool) {
        _beforeTokenTransfer(msg.sender, to, amount);
        /// @solidity memory-safe-assembly
        assembly {
            // Compute the balance slot and load its value.
            mstore(0x0c, _BALANCE_SLOT_SEED)
            mstore(0x00, caller())
            let fromBalanceSlot := keccak256(0x0c, 0x20)
            let fromBalance := sload(fromBalanceSlot)
            // Revert if insufficient balance.
            if gt(amount, fromBalance) {
                mstore(0x00, 0xf4d678b8) // `InsufficientBalance()`.
                revert(0x1c, 0x04)
            }
            // Subtract and store the updated balance.
            sstore(fromBalanceSlot, sub(fromBalance, amount))
            // Compute the balance slot of `to`.
            mstore(0x00, to)
            let toBalanceSlot := keccak256(0x0c, 0x20)
            // Add and store the updated balance of `to`.
            // Will not overflow because the sum of all user balances
            // cannot exceed the maximum uint256 value.
            sstore(toBalanceSlot, add(sload(toBalanceSlot), amount))
            // Emit the {Transfer} event.
            mstore(0x20, amount)
            log3(0x20, 0x20, _TRANSFER_EVENT_SIGNATURE, caller(), shr(96, mload(0x0c)))
        }
        _afterTokenTransfer(msg.sender, to, amount);
        return true;
    }

    /// @dev Transfers `amount` tokens from `from` to `to`.
    ///
    /// Note: Does not update the allowance if it is the maximum uint256 value.
    ///
    /// Requirements:
    /// - `from` must at least have `amount`.
    /// - The caller must have at least `amount` of allowance to transfer the tokens of `from`.
    ///
    /// Emits a {Transfer} event.
    function transferFrom(address from, address to, uint256 amount) public virtual returns (bool) {
        _beforeTokenTransfer(from, to, amount);
        // Code duplication is for zero-cost abstraction if possible.
        if (_givePermit2InfiniteAllowance()) {
            /// @solidity memory-safe-assembly
            assembly {
                let from_ := shl(96, from)
                if iszero(eq(caller(), _PERMIT2)) {
                    // Compute the allowance slot and load its value.
                    mstore(0x20, caller())
                    mstore(0x0c, or(from_, _ALLOWANCE_SLOT_SEED))
                    let allowanceSlot := keccak256(0x0c, 0x34)
                    let allowance_ := sload(allowanceSlot)
                    // If the allowance is not the maximum uint256 value.
                    if not(allowance_) {
                        // Revert if the amount to be transferred exceeds the allowance.
                        if gt(amount, allowance_) {
                            mstore(0x00, 0x13be252b) // `InsufficientAllowance()`.
                            revert(0x1c, 0x04)
                        }
                        // Subtract and store the updated allowance.
                        sstore(allowanceSlot, sub(allowance_, amount))
                    }
                }
                // Compute the balance slot and load its value.
                mstore(0x0c, or(from_, _BALANCE_SLOT_SEED))
                let fromBalanceSlot := keccak256(0x0c, 0x20)
                let fromBalance := sload(fromBalanceSlot)
                // Revert if insufficient balance.
                if gt(amount, fromBalance) {
                    mstore(0x00, 0xf4d678b8) // `InsufficientBalance()`.
                    revert(0x1c, 0x04)
                }
                // Subtract and store the updated balance.
                sstore(fromBalanceSlot, sub(fromBalance, amount))
                // Compute the balance slot of `to`.
                mstore(0x00, to)
                let toBalanceSlot := keccak256(0x0c, 0x20)
                // Add and store the updated balance of `to`.
                // Will not overflow because the sum of all user balances
                // cannot exceed the maximum uint256 value.
                sstore(toBalanceSlot, add(sload(toBalanceSlot), amount))
                // Emit the {Transfer} event.
                mstore(0x20, amount)
                log3(0x20, 0x20, _TRANSFER_EVENT_SIGNATURE, shr(96, from_), shr(96, mload(0x0c)))
            }
        } else {
            /// @solidity memory-safe-assembly
            assembly {
                let from_ := shl(96, from)
                // Compute the allowance slot and load its value.
                mstore(0x20, caller())
                mstore(0x0c, or(from_, _ALLOWANCE_SLOT_SEED))
                let allowanceSlot := keccak256(0x0c, 0x34)
                let allowance_ := sload(allowanceSlot)
                // If the allowance is not the maximum uint256 value.
                if not(allowance_) {
                    // Revert if the amount to be transferred exceeds the allowance.
                    if gt(amount, allowance_) {
                        mstore(0x00, 0x13be252b) // `InsufficientAllowance()`.
                        revert(0x1c, 0x04)
                    }
                    // Subtract and store the updated allowance.
                    sstore(allowanceSlot, sub(allowance_, amount))
                }
                // Compute the balance slot and load its value.
                mstore(0x0c, or(from_, _BALANCE_SLOT_SEED))
                let fromBalanceSlot := keccak256(0x0c, 0x20)
                let fromBalance := sload(fromBalanceSlot)
                // Revert if insufficient balance.
                if gt(amount, fromBalance) {
                    mstore(0x00, 0xf4d678b8) // `InsufficientBalance()`.
                    revert(0x1c, 0x04)
                }
                // Subtract and store the updated balance.
                sstore(fromBalanceSlot, sub(fromBalance, amount))
                // Compute the balance slot of `to`.
                mstore(0x00, to)
                let toBalanceSlot := keccak256(0x0c, 0x20)
                // Add and store the updated balance of `to`.
                // Will not overflow because the sum of all user balances
                // cannot exceed the maximum uint256 value.
                sstore(toBalanceSlot, add(sload(toBalanceSlot), amount))
                // Emit the {Transfer} event.
                mstore(0x20, amount)
                log3(0x20, 0x20, _TRANSFER_EVENT_SIGNATURE, shr(96, from_), shr(96, mload(0x0c)))
            }
        }
        _afterTokenTransfer(from, to, amount);
        return true;
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                          EIP-2612                          */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev For more performance, override to return the constant value
    /// of `keccak256(bytes(name()))` if `name()` will never change.
    function _constantNameHash() internal view virtual returns (bytes32 result) {}

    /// @dev If you need a different value, override this function.
    function _versionHash() internal view virtual returns (bytes32 result) {
        result = _DEFAULT_VERSION_HASH;
    }

    /// @dev For inheriting contracts to increment the nonce.
    function _incrementNonce(address owner) internal virtual {
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x0c, _NONCES_SLOT_SEED)
            mstore(0x00, owner)
            let nonceSlot := keccak256(0x0c, 0x20)
            sstore(nonceSlot, add(1, sload(nonceSlot)))
        }
    }

    /// @dev Returns the current nonce for `owner`.
    /// This value is used to compute the signature for EIP-2612 permit.
    function nonces(address owner) public view virtual returns (uint256 result) {
        /// @solidity memory-safe-assembly
        assembly {
            // Compute the nonce slot and load its value.
            mstore(0x0c, _NONCES_SLOT_SEED)
            mstore(0x00, owner)
            result := sload(keccak256(0x0c, 0x20))
        }
    }

    /// @dev Sets `value` as the allowance of `spender` over the tokens of `owner`,
    /// authorized by a signed approval by `owner`.
    ///
    /// Emits a {Approval} event.
    function permit(
        address owner,
        address spender,
        uint256 value,
        uint256 deadline,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) public virtual {
        if (_givePermit2InfiniteAllowance()) {
            /// @solidity memory-safe-assembly
            assembly {
                // If `spender == _PERMIT2 && value != type(uint256).max`.
                if iszero(or(xor(shr(96, shl(96, spender)), _PERMIT2), iszero(not(value)))) {
                    mstore(0x00, 0x3f68539a) // `Permit2AllowanceIsFixedAtInfinity()`.
                    revert(0x1c, 0x04)
                }
            }
        }
        bytes32 nameHash = _constantNameHash();
        //  We simply calculate it on-the-fly to allow for cases where the `name` may change.
        if (nameHash == bytes32(0)) nameHash = keccak256(bytes(name()));
        bytes32 versionHash = _versionHash();
        /// @solidity memory-safe-assembly
        assembly {
            // Revert if the block timestamp is greater than `deadline`.
            if gt(timestamp(), deadline) {
                mstore(0x00, 0x1a15a3cc) // `PermitExpired()`.
                revert(0x1c, 0x04)
            }
            let m := mload(0x40) // Grab the free memory pointer.
            // Clean the upper 96 bits.
            owner := shr(96, shl(96, owner))
            spender := shr(96, shl(96, spender))
            // Compute the nonce slot and load its value.
            mstore(0x0e, _NONCES_SLOT_SEED_WITH_SIGNATURE_PREFIX)
            mstore(0x00, owner)
            let nonceSlot := keccak256(0x0c, 0x20)
            let nonceValue := sload(nonceSlot)
            // Prepare the domain separator.
            mstore(m, _DOMAIN_TYPEHASH)
            mstore(add(m, 0x20), nameHash)
            mstore(add(m, 0x40), versionHash)
            mstore(add(m, 0x60), chainid())
            mstore(add(m, 0x80), address())
            mstore(0x2e, keccak256(m, 0xa0))
            // Prepare the struct hash.
            mstore(m, _PERMIT_TYPEHASH)
            mstore(add(m, 0x20), owner)
            mstore(add(m, 0x40), spender)
            mstore(add(m, 0x60), value)
            mstore(add(m, 0x80), nonceValue)
            mstore(add(m, 0xa0), deadline)
            mstore(0x4e, keccak256(m, 0xc0))
            // Prepare the ecrecover calldata.
            mstore(0x00, keccak256(0x2c, 0x42))
            mstore(0x20, and(0xff, v))
            mstore(0x40, r)
            mstore(0x60, s)
            let t := staticcall(gas(), 1, 0x00, 0x80, 0x20, 0x20)
            // If the ecrecover fails, the returndatasize will be 0x00,
            // `owner` will be checked if it equals the hash at 0x00,
            // which evaluates to false (i.e. 0), and we will revert.
            // If the ecrecover succeeds, the returndatasize will be 0x20,
            // `owner` will be compared against the returned address at 0x20.
            if iszero(eq(mload(returndatasize()), owner)) {
                mstore(0x00, 0xddafbaef) // `InvalidPermit()`.
                revert(0x1c, 0x04)
            }
            // Increment and store the updated nonce.
            sstore(nonceSlot, add(nonceValue, t)) // `t` is 1 if ecrecover succeeds.
            // Compute the allowance slot and store the value.
            // The `owner` is already at slot 0x20.
            mstore(0x40, or(shl(160, _ALLOWANCE_SLOT_SEED), spender))
            sstore(keccak256(0x2c, 0x34), value)
            // Emit the {Approval} event.
            log3(add(m, 0x60), 0x20, _APPROVAL_EVENT_SIGNATURE, owner, spender)
            mstore(0x40, m) // Restore the free memory pointer.
            mstore(0x60, 0) // Restore the zero pointer.
        }
    }

    /// @dev Returns the EIP-712 domain separator for the EIP-2612 permit.
    function DOMAIN_SEPARATOR() public view virtual returns (bytes32 result) {
        bytes32 nameHash = _constantNameHash();
        //  We simply calculate it on-the-fly to allow for cases where the `name` may change.
        if (nameHash == bytes32(0)) nameHash = keccak256(bytes(name()));
        bytes32 versionHash = _versionHash();
        /// @solidity memory-safe-assembly
        assembly {
            let m := mload(0x40) // Grab the free memory pointer.
            mstore(m, _DOMAIN_TYPEHASH)
            mstore(add(m, 0x20), nameHash)
            mstore(add(m, 0x40), versionHash)
            mstore(add(m, 0x60), chainid())
            mstore(add(m, 0x80), address())
            result := keccak256(m, 0xa0)
        }
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                  INTERNAL MINT FUNCTIONS                   */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Mints `amount` tokens to `to`, increasing the total supply.
    ///
    /// Emits a {Transfer} event.
    function _mint(address to, uint256 amount) internal virtual {
        _beforeTokenTransfer(address(0), to, amount);
        /// @solidity memory-safe-assembly
        assembly {
            let totalSupplyBefore := sload(_TOTAL_SUPPLY_SLOT)
            let totalSupplyAfter := add(totalSupplyBefore, amount)
            // Revert if the total supply overflows.
            if lt(totalSupplyAfter, totalSupplyBefore) {
                mstore(0x00, 0xe5cfe957) // `TotalSupplyOverflow()`.
                revert(0x1c, 0x04)
            }
            // Store the updated total supply.
            sstore(_TOTAL_SUPPLY_SLOT, totalSupplyAfter)
            // Compute the balance slot and load its value.
            mstore(0x0c, _BALANCE_SLOT_SEED)
            mstore(0x00, to)
            let toBalanceSlot := keccak256(0x0c, 0x20)
            // Add and store the updated balance.
            sstore(toBalanceSlot, add(sload(toBalanceSlot), amount))
            // Emit the {Transfer} event.
            mstore(0x20, amount)
            log3(0x20, 0x20, _TRANSFER_EVENT_SIGNATURE, 0, shr(96, mload(0x0c)))
        }
        _afterTokenTransfer(address(0), to, amount);
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                  INTERNAL BURN FUNCTIONS                   */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Burns `amount` tokens from `from`, reducing the total supply.
    ///
    /// Emits a {Transfer} event.
    function _burn(address from, uint256 amount) internal virtual {
        _beforeTokenTransfer(from, address(0), amount);
        /// @solidity memory-safe-assembly
        assembly {
            // Compute the balance slot and load its value.
            mstore(0x0c, _BALANCE_SLOT_SEED)
            mstore(0x00, from)
            let fromBalanceSlot := keccak256(0x0c, 0x20)
            let fromBalance := sload(fromBalanceSlot)
            // Revert if insufficient balance.
            if gt(amount, fromBalance) {
                mstore(0x00, 0xf4d678b8) // `InsufficientBalance()`.
                revert(0x1c, 0x04)
            }
            // Subtract and store the updated balance.
            sstore(fromBalanceSlot, sub(fromBalance, amount))
            // Subtract and store the updated total supply.
            sstore(_TOTAL_SUPPLY_SLOT, sub(sload(_TOTAL_SUPPLY_SLOT), amount))
            // Emit the {Transfer} event.
            mstore(0x00, amount)
            log3(0x00, 0x20, _TRANSFER_EVENT_SIGNATURE, shr(96, shl(96, from)), 0)
        }
        _afterTokenTransfer(from, address(0), amount);
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                INTERNAL TRANSFER FUNCTIONS                 */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Moves `amount` of tokens from `from` to `to`.
    function _transfer(address from, address to, uint256 amount) internal virtual {
        _beforeTokenTransfer(from, to, amount);
        /// @solidity memory-safe-assembly
        assembly {
            let from_ := shl(96, from)
            // Compute the balance slot and load its value.
            mstore(0x0c, or(from_, _BALANCE_SLOT_SEED))
            let fromBalanceSlot := keccak256(0x0c, 0x20)
            let fromBalance := sload(fromBalanceSlot)
            // Revert if insufficient balance.
            if gt(amount, fromBalance) {
                mstore(0x00, 0xf4d678b8) // `InsufficientBalance()`.
                revert(0x1c, 0x04)
            }
            // Subtract and store the updated balance.
            sstore(fromBalanceSlot, sub(fromBalance, amount))
            // Compute the balance slot of `to`.
            mstore(0x00, to)
            let toBalanceSlot := keccak256(0x0c, 0x20)
            // Add and store the updated balance of `to`.
            // Will not overflow because the sum of all user balances
            // cannot exceed the maximum uint256 value.
            sstore(toBalanceSlot, add(sload(toBalanceSlot), amount))
            // Emit the {Transfer} event.
            mstore(0x20, amount)
            log3(0x20, 0x20, _TRANSFER_EVENT_SIGNATURE, shr(96, from_), shr(96, mload(0x0c)))
        }
        _afterTokenTransfer(from, to, amount);
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                INTERNAL ALLOWANCE FUNCTIONS                */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Updates the allowance of `owner` for `spender` based on spent `amount`.
    function _spendAllowance(address owner, address spender, uint256 amount) internal virtual {
        if (_givePermit2InfiniteAllowance()) {
            if (spender == _PERMIT2) return; // Do nothing, as allowance is infinite.
        }
        /// @solidity memory-safe-assembly
        assembly {
            // Compute the allowance slot and load its value.
            mstore(0x20, spender)
            mstore(0x0c, _ALLOWANCE_SLOT_SEED)
            mstore(0x00, owner)
            let allowanceSlot := keccak256(0x0c, 0x34)
            let allowance_ := sload(allowanceSlot)
            // If the allowance is not the maximum uint256 value.
            if not(allowance_) {
                // Revert if the amount to be transferred exceeds the allowance.
                if gt(amount, allowance_) {
                    mstore(0x00, 0x13be252b) // `InsufficientAllowance()`.
                    revert(0x1c, 0x04)
                }
                // Subtract and store the updated allowance.
                sstore(allowanceSlot, sub(allowance_, amount))
            }
        }
    }

    /// @dev Sets `amount` as the allowance of `spender` over the tokens of `owner`.
    ///
    /// Emits a {Approval} event.
    function _approve(address owner, address spender, uint256 amount) internal virtual {
        if (_givePermit2InfiniteAllowance()) {
            /// @solidity memory-safe-assembly
            assembly {
                // If `spender == _PERMIT2 && amount != type(uint256).max`.
                if iszero(or(xor(shr(96, shl(96, spender)), _PERMIT2), iszero(not(amount)))) {
                    mstore(0x00, 0x3f68539a) // `Permit2AllowanceIsFixedAtInfinity()`.
                    revert(0x1c, 0x04)
                }
            }
        }
        /// @solidity memory-safe-assembly
        assembly {
            let owner_ := shl(96, owner)
            // Compute the allowance slot and store the amount.
            mstore(0x20, spender)
            mstore(0x0c, or(owner_, _ALLOWANCE_SLOT_SEED))
            sstore(keccak256(0x0c, 0x34), amount)
            // Emit the {Approval} event.
            mstore(0x00, amount)
            log3(0x00, 0x20, _APPROVAL_EVENT_SIGNATURE, shr(96, owner_), shr(96, mload(0x2c)))
        }
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                     HOOKS TO OVERRIDE                      */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Hook that is called before any transfer of tokens.
    /// This includes minting and burning.
    function _beforeTokenTransfer(address from, address to, uint256 amount) internal virtual {}

    /// @dev Hook that is called after any transfer of tokens.
    /// This includes minting and burning.
    function _afterTokenTransfer(address from, address to, uint256 amount) internal virtual {}

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                          PERMIT2                           */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Returns whether to fix the Permit2 contract's allowance at infinity.
    ///
    /// This value should be kept constant after contract initialization,
    /// or else the actual allowance values may not match with the {Approval} events.
    /// For best performance, return a compile-time constant for zero-cost abstraction.
    function _givePermit2InfiniteAllowance() internal view virtual returns (bool) {
        return false;
    }
}

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.4;

import {ERC20} from "./ERC20.sol";

/// @notice ERC20 with votes based on ERC5805 and ERC6372.
/// @author Solady (https://github.com/vectorized/solady/blob/main/src/tokens/ERC20Votes.sol)
/// @author Modified from OpenZeppelin (https://github.com/OpenZeppelin/openzeppelin-contracts/blob/master/contracts/token/ERC20/extensions/ERC20Votes.sol)
abstract contract ERC20Votes is ERC20 {
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                       CUSTOM ERRORS                        */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev The timepoint is in the future.
    error ERC5805FutureLookup();

    /// @dev The ERC5805 signature to set a delegate has expired.
    error ERC5805DelegateSignatureExpired();

    /// @dev The ERC5805 signature to set a delegate is invalid.
    error ERC5805DelegateInvalidSignature();

    /// @dev Out-of-bounds access for the checkpoints.
    error ERC5805CheckpointIndexOutOfBounds();

    /// @dev Arithmetic overflow when pushing a new checkpoint.
    error ERC5805CheckpointValueOverflow();

    /// @dev Arithmetic underflow when pushing a new checkpoint.
    error ERC5805CheckpointValueUnderflow();

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                           EVENTS                           */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev The delegate of `delegator` is changed from `from` to `to`.
    event DelegateChanged(address indexed delegator, address indexed from, address indexed to);

    /// @dev The votes balance of `delegate` is changed from `oldValue` to `newValue`.
    event DelegateVotesChanged(address indexed delegate, uint256 oldValue, uint256 newValue);

    /// @dev `keccak256(bytes("DelegateChanged(address,address,address)"))`.
    uint256 private constant _DELEGATE_CHANGED_EVENT_SIGNATURE =
        0x3134e8a2e6d97e929a7e54011ea5485d7d196dd5f0ba4d4ef95803e8e3fc257f;

    /// @dev `keccak256(bytes("DelegateVotesChanged(address,uint256,uint256)"))`.
    uint256 private constant _DELEGATE_VOTES_CHANGED_EVENT_SIGNATURE =
        0xdec2bacdd2f05b59de34da9b523dff8be42e5e38e818c82fdb0bae774387a724;

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                         CONSTANTS                          */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev `keccak256("EIP712Domain(string name,string version,uint256 chainId,address verifyingContract)")`.
    bytes32 private constant _DOMAIN_TYPEHASH =
        0x8b73c3c69bb8fe3d512ecc4cf759cc79239f7b179b0ffacaa9a75d522b39400f;

    /// @dev `keccak256("Delegation(address delegatee,uint256 nonce,uint256 expiry)")`.
    bytes32 private constant _ERC5805_DELEGATION_TYPEHASH =
        0xe48329057bfd03d55e49b547132e39cffd9c1820ad7b9d4c5307691425d15adf;

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                          STORAGE                           */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev The slot of a delegate is given by:
    /// ```
    ///     mstore(0x04, _ERC20_VOTES_MASTER_SLOT_SEED)
    ///     mstore(0x00, account)
    ///     let delegateSlot := keccak256(0x0c, 0x18)
    /// ```
    /// The checkpoints length slot of a delegate is given by:
    /// ```
    ///     mstore(0x04, _ERC20_VOTES_MASTER_SLOT_SEED)
    ///     mstore(0x00, delegate)
    ///     let lengthSlot := keccak256(0x0c, 0x17)
    ///     let length := and(0xffffffffffff, shr(48, sload(lengthSlot)))
    /// ```
    /// The total checkpoints length slot is `_ERC20_VOTES_MASTER_SLOT_SEED << 96`.
    ///
    /// The `i`-th checkpoint slot is given by:
    /// ```
    ///     let checkpointSlot := add(i, lengthSlot)
    ///     let key := and(sload(checkpointSlot), 0xffffffffffff)
    ///     let value := shr(96, sload(checkpointSlot))
    ///     if eq(value, address()) { value := sload(not(checkpointSlot)) }
    /// ```
    uint256 private constant _ERC20_VOTES_MASTER_SLOT_SEED = 0xff466c9f;

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                          ERC6372                           */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Returns the clock mode.
    function CLOCK_MODE() public view virtual returns (string memory) {
        return "mode=blocknumber&from=default";
    }

    /// @dev Returns the current clock.
    function clock() public view virtual returns (uint48 result) {
        /// @solidity memory-safe-assembly
        assembly {
            result := number()
            // Branch-less out-of-gas revert if `block.number >= 2 ** 48`.
            returndatacopy(returndatasize(), returndatasize(), sub(0, shr(48, number())))
        }
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                          ERC5805                           */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Returns the latest amount of voting units for `account`.
    function getVotes(address account) public view virtual returns (uint256) {
        return _checkpointLatest(_delegateCheckpointsSlot(account));
    }

    /// @dev Returns the latest amount of voting units `account` has before `timepoint`.
    function getPastVotes(address account, uint256 timepoint)
        public
        view
        virtual
        returns (uint256)
    {
        if (timepoint >= clock()) _revertERC5805FutureLookup();
        return _checkpointUpperLookupRecent(_delegateCheckpointsSlot(account), timepoint);
    }

    /// @dev Returns the current voting delegate of `delegator`.
    function delegates(address delegator) public view virtual returns (address result) {
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x04, _ERC20_VOTES_MASTER_SLOT_SEED)
            mstore(0x00, delegator)
            result := sload(keccak256(0x0c, 0x18))
        }
    }

    /// @dev Set the voting delegate of the caller to `delegatee`.
    function delegate(address delegatee) public virtual {
        _delegate(msg.sender, delegatee);
    }

    /// @dev Sets the voting delegate of the signature signer to `delegatee`.
    function delegateBySig(
        address delegatee,
        uint256 nonce,
        uint256 expiry,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) public virtual {
        address signer;
        bytes32 nameHash = _constantNameHash();
        //  We simply calculate it on-the-fly to allow for cases where the `name` may change.
        if (nameHash == bytes32(0)) nameHash = keccak256(bytes(name()));
        bytes32 versionHash = _versionHash();
        /// @solidity memory-safe-assembly
        assembly {
            if gt(timestamp(), expiry) {
                mstore(0x00, 0x3480e9e1) // `ERC5805DelegateSignatureExpired()`.
                revert(0x1c, 0x04)
            }
            let m := mload(0x40)
            // Prepare the struct hash.
            mstore(0x00, _ERC5805_DELEGATION_TYPEHASH)
            mstore(0x20, shr(96, shl(96, delegatee)))
            mstore(0x40, nonce)
            mstore(0x60, expiry)
            mstore(0x40, keccak256(0x00, 0x80))
            mstore(0x00, 0x1901) // Store "\x19\x01".
            // Prepare the domain separator.
            mstore(m, _DOMAIN_TYPEHASH)
            mstore(add(m, 0x20), nameHash)
            mstore(add(m, 0x40), versionHash)
            mstore(add(m, 0x60), chainid())
            mstore(add(m, 0x80), address())
            mstore(0x20, keccak256(m, 0xa0))
            // Prepare the ecrecover calldata.
            mstore(0x00, keccak256(0x1e, 0x42))
            mstore(0x20, and(0xff, v))
            mstore(0x40, r)
            mstore(0x60, s)
            signer := mload(staticcall(gas(), 1, 0x00, 0x80, 0x01, 0x20))
            mstore(0x40, m) // Restore the free memory pointer.
            mstore(0x60, 0) // Restore the zero pointer.
            // `returndatasize()` will be `0x20` upon success, and `0x00` otherwise.
            expiry := iszero(returndatasize()) // Reuse `expiry` to denote `ecrecover` failure.
        }
        if ((nonces(signer) ^ nonce) | expiry != 0) {
            /// @solidity memory-safe-assembly
            assembly {
                mstore(0x00, 0x1838d95c) // `ERC5805DelegateInvalidSignature()`.
                revert(0x1c, 0x04)
            }
        }
        _incrementNonce(signer);
        _delegate(signer, delegatee);
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*              OTHER VOTE PUBLIC VIEW FUNCTIONS              */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Returns the number of checkpoints for `account`.
    function checkpointCount(address account) public view virtual returns (uint256 result) {
        result = _delegateCheckpointsSlot(account);
        /// @solidity memory-safe-assembly
        assembly {
            result := shr(208, shl(160, sload(result)))
        }
    }

    /// @dev Returns the voting checkpoint for `account` at index `i`.
    function checkpointAt(address account, uint256 i)
        public
        view
        virtual
        returns (uint48 checkpointClock, uint256 checkpointValue)
    {
        uint256 lengthSlot = _delegateCheckpointsSlot(account);
        /// @solidity memory-safe-assembly
        assembly {
            if iszero(lt(i, shr(208, shl(160, sload(lengthSlot))))) {
                mstore(0x00, 0x86df9d10) // `ERC5805CheckpointIndexOutOfBounds()`.
                revert(0x1c, 0x04)
            }
            let checkpointPacked := sload(add(i, lengthSlot))
            checkpointClock := and(0xffffffffffff, checkpointPacked)
            checkpointValue := shr(96, checkpointPacked)
            if eq(checkpointValue, address()) { checkpointValue := sload(not(add(i, lengthSlot))) }
        }
    }

    /// @dev Returns the latest amount of total voting units.
    function getVotesTotalSupply() public view virtual returns (uint256) {
        return _checkpointLatest(_ERC20_VOTES_MASTER_SLOT_SEED << 96);
    }

    /// @dev Returns the latest amount of total voting units before `timepoint`.
    function getPastVotesTotalSupply(uint256 timepoint) public view virtual returns (uint256) {
        if (timepoint >= clock()) _revertERC5805FutureLookup();
        return _checkpointUpperLookupRecent(_ERC20_VOTES_MASTER_SLOT_SEED << 96, timepoint);
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                     INTERNAL FUNCTIONS                     */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Returns the amount of voting units `delegator` has control over.
    /// Override if you need a different formula.
    function _getVotingUnits(address delegator) internal view virtual returns (uint256) {
        return balanceOf(delegator);
    }

    /// @dev ERC20 after token transfer internal hook.
    function _afterTokenTransfer(address from, address to, uint256 amount)
        internal
        virtual
        override
    {
        _transferVotingUnits(from, to, amount);
    }

    /// @dev Used in `_afterTokenTransfer(address from, address to, uint256 amount)`.
    function _transferVotingUnits(address from, address to, uint256 amount) internal virtual {
        if (from == address(0)) {
            _checkpointPushDiff(_ERC20_VOTES_MASTER_SLOT_SEED << 96, clock(), amount, true);
        }
        if (to == address(0)) {
            _checkpointPushDiff(_ERC20_VOTES_MASTER_SLOT_SEED << 96, clock(), amount, false);
        }
        _moveDelegateVotes(delegates(from), delegates(to), amount);
    }

    /// @dev Transfer `amount` of delegated votes from `from` to `to`.
    /// Emits a {DelegateVotesChanged} event for each change of delegated votes.
    function _moveDelegateVotes(address from, address to, uint256 amount) internal virtual {
        if (amount == uint256(0)) return;
        (uint256 fromCleaned, uint256 toCleaned) = (uint256(uint160(from)), uint256(uint160(to)));
        if (fromCleaned == toCleaned) return;
        if (fromCleaned != 0) {
            (uint256 oldValue, uint256 newValue) =
                _checkpointPushDiff(_delegateCheckpointsSlot(from), clock(), amount, false);
            /// @solidity memory-safe-assembly
            assembly {
                // Emit the {DelegateVotesChanged} event.
                mstore(0x00, oldValue)
                mstore(0x20, newValue)
                log2(0x00, 0x40, _DELEGATE_VOTES_CHANGED_EVENT_SIGNATURE, fromCleaned)
            }
        }
        if (toCleaned != 0) {
            (uint256 oldValue, uint256 newValue) =
                _checkpointPushDiff(_delegateCheckpointsSlot(to), clock(), amount, true);
            /// @solidity memory-safe-assembly
            assembly {
                // Emit the {DelegateVotesChanged} event.
                mstore(0x00, oldValue)
                mstore(0x20, newValue)
                log2(0x00, 0x40, _DELEGATE_VOTES_CHANGED_EVENT_SIGNATURE, toCleaned)
            }
        }
    }

    /// @dev Delegates all of `account`'s voting units to `delegatee`.
    /// Emits the {DelegateChanged} and {DelegateVotesChanged} events.
    function _delegate(address account, address delegatee) internal virtual {
        address from;
        /// @solidity memory-safe-assembly
        assembly {
            let to := shr(96, shl(96, delegatee))
            mstore(0x04, _ERC20_VOTES_MASTER_SLOT_SEED)
            mstore(0x00, account)
            let delegateSlot := keccak256(0x0c, 0x18)
            from := sload(delegateSlot)
            sstore(delegateSlot, to)
            // Emit the {DelegateChanged} event.
            log4(0x00, 0x00, _DELEGATE_CHANGED_EVENT_SIGNATURE, shr(96, mload(0x0c)), from, to)
        }
        _moveDelegateVotes(from, delegatee, _getVotingUnits(account));
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                      PRIVATE HELPERS                       */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Returns the delegate checkpoints slot for `account`.
    function _delegateCheckpointsSlot(address account) private pure returns (uint256 result) {
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x04, _ERC20_VOTES_MASTER_SLOT_SEED)
            mstore(0x00, account)
            result := keccak256(0x0c, 0x17)
        }
    }

    /// @dev Pushes a checkpoint.
    function _checkpointPushDiff(uint256 lengthSlot, uint256 key, uint256 amount, bool isAdd)
        private
        returns (uint256 oldValue, uint256 newValue)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let lengthSlotPacked := sload(lengthSlot)
            for { let n := shr(208, shl(160, lengthSlotPacked)) } 1 {} {
                if iszero(n) {
                    if iszero(or(isAdd, iszero(amount))) {
                        mstore(0x00, 0x5915f686) // `ERC5805CheckpointValueUnderflow()`.
                        revert(0x1c, 0x04)
                    }
                    newValue := amount
                    if iszero(or(eq(newValue, address()), shr(160, newValue))) {
                        sstore(lengthSlot, or(or(key, shl(48, 1)), shl(96, newValue)))
                        break
                    }
                    sstore(lengthSlot, or(or(key, shl(48, 1)), shl(96, address())))
                    sstore(not(lengthSlot), newValue)
                    break
                }
                let checkpointSlot := add(sub(n, 1), lengthSlot)
                let lastPacked := sload(checkpointSlot)
                oldValue := shr(96, lastPacked)
                if eq(oldValue, address()) { oldValue := sload(not(checkpointSlot)) }
                for {} 1 {} {
                    if iszero(isAdd) {
                        newValue := sub(oldValue, amount)
                        if iszero(gt(newValue, oldValue)) { break }
                        mstore(0x00, 0x5915f686) // `ERC5805CheckpointValueUnderflow()`.
                        revert(0x1c, 0x04)
                    }
                    newValue := add(oldValue, amount)
                    if iszero(lt(newValue, oldValue)) { break }
                    mstore(0x00, 0x9dbbeb75) // `ERC5805CheckpointValueOverflow()`.
                    revert(0x1c, 0x04)
                }
                let lastKey := and(0xffffffffffff, lastPacked)
                if iszero(eq(lastKey, key)) {
                    n := add(1, n)
                    checkpointSlot := add(1, checkpointSlot)
                    sstore(lengthSlot, add(shl(48, 1), lengthSlotPacked))
                }
                if or(gt(lastKey, key), shr(48, n)) { invalid() }
                if iszero(or(eq(newValue, address()), shr(160, newValue))) {
                    sstore(checkpointSlot, or(or(key, shl(48, n)), shl(96, newValue)))
                    break
                }
                sstore(checkpointSlot, or(or(key, shl(48, n)), shl(96, address())))
                sstore(not(checkpointSlot), newValue)
                break
            }
        }
    }

    /// @dev Returns the latest value in the checkpoints.
    function _checkpointLatest(uint256 lengthSlot) private view returns (uint256 result) {
        /// @solidity memory-safe-assembly
        assembly {
            result := shr(208, shl(160, sload(lengthSlot)))
            if result {
                lengthSlot := add(sub(result, 1), lengthSlot) // Reuse for `checkpointSlot`.
                result := shr(96, sload(lengthSlot))
                if eq(result, address()) { result := sload(not(lengthSlot)) }
            }
        }
    }

    /// @dev Returns the value in the checkpoints with the largest key that is less than `key`.
    function _checkpointUpperLookupRecent(uint256 lengthSlot, uint256 key)
        private
        view
        returns (uint256 result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let l := 0 // Low.
            let h := shr(208, shl(160, sload(lengthSlot))) // High.
            // Start the binary search nearer to the right to optimize for recent checkpoints.
            for {} iszero(lt(h, 6)) {} {
                let m := shl(4, lt(0xffff, h))
                m := shl(shr(1, or(m, shl(3, lt(0xff, shr(m, h))))), 16)
                m := shr(1, add(m, div(h, m)))
                m := shr(1, add(m, div(h, m)))
                m := shr(1, add(m, div(h, m)))
                m := shr(1, add(m, div(h, m)))
                m := shr(1, add(m, div(h, m)))
                m := sub(h, shr(1, add(m, div(h, m)))) // Approx `h - sqrt(h)`.
                if iszero(lt(key, and(sload(add(m, lengthSlot)), 0xffffffffffff))) {
                    l := add(1, m)
                    break
                }
                h := m
                break
            }
            // Binary search.
            for {} lt(l, h) {} {
                let m := shr(1, add(l, h)) // Won't overflow in practice.
                if iszero(lt(key, and(sload(add(m, lengthSlot)), 0xffffffffffff))) {
                    l := add(1, m)
                    continue
                }
                h := m
            }
            let checkpointSlot := add(sub(h, 1), lengthSlot)
            result := mul(iszero(iszero(h)), shr(96, sload(checkpointSlot)))
            if eq(result, address()) { result := sload(not(checkpointSlot)) }
        }
    }

    /// @dev Reverts with `ERC5805FutureLookup()`.
    function _revertERC5805FutureLookup() private pure {
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x00, 0xf9874464) // `ERC5805FutureLookup()`.
            revert(0x1c, 0x04)
        }
    }
}

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.4;

/// @notice Library for managing enumerable sets in storage.
/// @author Solady (https://github.com/vectorized/solady/blob/main/src/utils/EnumerableSetLib.sol)
///
/// @dev Note:
/// In many applications, the number of elements in an enumerable set is small.
/// This enumerable set implementation avoids storing the length and indices
/// for up to 3 elements. Once the length exceeds 3 for the first time, the length
/// and indices will be initialized. The amortized cost of adding elements is O(1).
///
/// The AddressSet implementation packs the length with the 0th entry.
library EnumerableSetLib {
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                       CUSTOM ERRORS                        */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev The index must be less than the length.
    error IndexOutOfBounds();

    /// @dev The value cannot be the zero sentinel.
    error ValueIsZeroSentinel();

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                         CONSTANTS                          */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev A sentinel value to denote the zero value in storage.
    /// No elements can be equal to this value.
    /// `uint72(bytes9(keccak256(bytes("_ZERO_SENTINEL"))))`.
    uint256 private constant _ZERO_SENTINEL = 0xfbb67fda52d4bfb8bf;

    /// @dev The storage layout is given by:
    /// ```
    ///     mstore(0x04, _ENUMERABLE_ADDRESS_SET_SLOT_SEED)
    ///     mstore(0x00, set.slot)
    ///     let rootSlot := keccak256(0x00, 0x24)
    ///     mstore(0x20, rootSlot)
    ///     mstore(0x00, shr(96, shl(96, value)))
    ///     let positionSlot := keccak256(0x00, 0x40)
    ///     let valueSlot := add(rootSlot, sload(positionSlot))
    ///     let valueInStorage := shr(96, sload(valueSlot))
    ///     let lazyLength := shr(160, shl(160, sload(rootSlot)))
    /// ```
    uint256 private constant _ENUMERABLE_ADDRESS_SET_SLOT_SEED = 0x978aab92;

    /// @dev The storage layout is given by:
    /// ```
    ///     mstore(0x04, _ENUMERABLE_WORD_SET_SLOT_SEED)
    ///     mstore(0x00, set.slot)
    ///     let rootSlot := keccak256(0x00, 0x24)
    ///     mstore(0x20, rootSlot)
    ///     mstore(0x00, value)
    ///     let positionSlot := keccak256(0x00, 0x40)
    ///     let valueSlot := add(rootSlot, sload(positionSlot))
    ///     let valueInStorage := sload(valueSlot)
    ///     let lazyLength := sload(not(rootSlot))
    /// ```
    uint256 private constant _ENUMERABLE_WORD_SET_SLOT_SEED = 0x18fb5864;

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                          STRUCTS                           */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev An enumerable address set in storage.
    struct AddressSet {
        uint256 _spacer;
    }

    /// @dev An enumerable bytes32 set in storage.
    struct Bytes32Set {
        uint256 _spacer;
    }

    /// @dev An enumerable uint256 set in storage.
    struct Uint256Set {
        uint256 _spacer;
    }

    /// @dev An enumerable int256 set in storage.
    struct Int256Set {
        uint256 _spacer;
    }

    /// @dev An enumerable uint8 set in storage. Useful for enums.
    struct Uint8Set {
        uint256 data;
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                     GETTERS / SETTERS                      */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Returns the number of elements in the set.
    function length(AddressSet storage set) internal view returns (uint256 result) {
        bytes32 rootSlot = _rootSlot(set);
        /// @solidity memory-safe-assembly
        assembly {
            let rootPacked := sload(rootSlot)
            let n := shr(160, shl(160, rootPacked))
            result := shr(1, n)
            for {} iszero(or(iszero(shr(96, rootPacked)), n)) {} {
                result := 1
                if iszero(sload(add(rootSlot, result))) { break }
                result := 2
                if iszero(sload(add(rootSlot, result))) { break }
                result := 3
                break
            }
        }
    }

    /// @dev Returns the number of elements in the set.
    function length(Bytes32Set storage set) internal view returns (uint256 result) {
        bytes32 rootSlot = _rootSlot(set);
        /// @solidity memory-safe-assembly
        assembly {
            let n := sload(not(rootSlot))
            result := shr(1, n)
            for {} iszero(n) {} {
                result := 0
                if iszero(sload(add(rootSlot, result))) { break }
                result := 1
                if iszero(sload(add(rootSlot, result))) { break }
                result := 2
                if iszero(sload(add(rootSlot, result))) { break }
                result := 3
                break
            }
        }
    }

    /// @dev Returns the number of elements in the set.
    function length(Uint256Set storage set) internal view returns (uint256 result) {
        result = length(_toBytes32Set(set));
    }

    /// @dev Returns the number of elements in the set.
    function length(Int256Set storage set) internal view returns (uint256 result) {
        result = length(_toBytes32Set(set));
    }

    /// @dev Returns the number of elements in the set.
    function length(Uint8Set storage set) internal view returns (uint256 result) {
        /// @solidity memory-safe-assembly
        assembly {
            for { let packed := sload(set.slot) } packed { result := add(1, result) } {
                packed := xor(packed, and(packed, add(1, not(packed))))
            }
        }
    }

    /// @dev Returns whether `value` is in the set.
    function contains(AddressSet storage set, address value) internal view returns (bool result) {
        bytes32 rootSlot = _rootSlot(set);
        /// @solidity memory-safe-assembly
        assembly {
            value := shr(96, shl(96, value))
            if eq(value, _ZERO_SENTINEL) {
                mstore(0x00, 0xf5a267f1) // `ValueIsZeroSentinel()`.
                revert(0x1c, 0x04)
            }
            if iszero(value) { value := _ZERO_SENTINEL }
            let rootPacked := sload(rootSlot)
            for {} 1 {} {
                if iszero(shr(160, shl(160, rootPacked))) {
                    result := 1
                    if eq(shr(96, rootPacked), value) { break }
                    if eq(shr(96, sload(add(rootSlot, 1))), value) { break }
                    if eq(shr(96, sload(add(rootSlot, 2))), value) { break }
                    result := 0
                    break
                }
                mstore(0x20, rootSlot)
                mstore(0x00, value)
                result := iszero(iszero(sload(keccak256(0x00, 0x40))))
                break
            }
        }
    }

    /// @dev Returns whether `value` is in the set.
    function contains(Bytes32Set storage set, bytes32 value) internal view returns (bool result) {
        bytes32 rootSlot = _rootSlot(set);
        /// @solidity memory-safe-assembly
        assembly {
            if eq(value, _ZERO_SENTINEL) {
                mstore(0x00, 0xf5a267f1) // `ValueIsZeroSentinel()`.
                revert(0x1c, 0x04)
            }
            if iszero(value) { value := _ZERO_SENTINEL }
            for {} 1 {} {
                if iszero(sload(not(rootSlot))) {
                    result := 1
                    if eq(sload(rootSlot), value) { break }
                    if eq(sload(add(rootSlot, 1)), value) { break }
                    if eq(sload(add(rootSlot, 2)), value) { break }
                    result := 0
                    break
                }
                mstore(0x20, rootSlot)
                mstore(0x00, value)
                result := iszero(iszero(sload(keccak256(0x00, 0x40))))
                break
            }
        }
    }

    /// @dev Returns whether `value` is in the set.
    function contains(Uint256Set storage set, uint256 value) internal view returns (bool result) {
        result = contains(_toBytes32Set(set), bytes32(value));
    }

    /// @dev Returns whether `value` is in the set.
    function contains(Int256Set storage set, int256 value) internal view returns (bool result) {
        result = contains(_toBytes32Set(set), bytes32(uint256(value)));
    }

    /// @dev Returns whether `value` is in the set.
    function contains(Uint8Set storage set, uint8 value) internal view returns (bool result) {
        /// @solidity memory-safe-assembly
        assembly {
            result := and(1, shr(and(0xff, value), sload(set.slot)))
        }
    }

    /// @dev Adds `value` to the set. Returns whether `value` was not in the set.
    function add(AddressSet storage set, address value) internal returns (bool result) {
        bytes32 rootSlot = _rootSlot(set);
        /// @solidity memory-safe-assembly
        assembly {
            value := shr(96, shl(96, value))
            if eq(value, _ZERO_SENTINEL) {
                mstore(0x00, 0xf5a267f1) // `ValueIsZeroSentinel()`.
                revert(0x1c, 0x04)
            }
            if iszero(value) { value := _ZERO_SENTINEL }
            let rootPacked := sload(rootSlot)
            for { let n := shr(160, shl(160, rootPacked)) } 1 {} {
                mstore(0x20, rootSlot)
                if iszero(n) {
                    let v0 := shr(96, rootPacked)
                    if iszero(v0) {
                        sstore(rootSlot, shl(96, value))
                        result := 1
                        break
                    }
                    if eq(v0, value) { break }
                    let v1 := shr(96, sload(add(rootSlot, 1)))
                    if iszero(v1) {
                        sstore(add(rootSlot, 1), shl(96, value))
                        result := 1
                        break
                    }
                    if eq(v1, value) { break }
                    let v2 := shr(96, sload(add(rootSlot, 2)))
                    if iszero(v2) {
                        sstore(add(rootSlot, 2), shl(96, value))
                        result := 1
                        break
                    }
                    if eq(v2, value) { break }
                    mstore(0x00, v0)
                    sstore(keccak256(0x00, 0x40), 1)
                    mstore(0x00, v1)
                    sstore(keccak256(0x00, 0x40), 2)
                    mstore(0x00, v2)
                    sstore(keccak256(0x00, 0x40), 3)
                    rootPacked := or(rootPacked, 7)
                    n := 7
                }
                mstore(0x00, value)
                let p := keccak256(0x00, 0x40)
                if iszero(sload(p)) {
                    n := shr(1, n)
                    result := 1
                    sstore(p, add(1, n))
                    if iszero(n) {
                        sstore(rootSlot, or(3, shl(96, value)))
                        break
                    }
                    sstore(add(rootSlot, n), shl(96, value))
                    sstore(rootSlot, add(2, rootPacked))
                    break
                }
                break
            }
        }
    }

    /// @dev Adds `value` to the set. Returns whether `value` was not in the set.
    function add(Bytes32Set storage set, bytes32 value) internal returns (bool result) {
        bytes32 rootSlot = _rootSlot(set);
        /// @solidity memory-safe-assembly
        assembly {
            if eq(value, _ZERO_SENTINEL) {
                mstore(0x00, 0xf5a267f1) // `ValueIsZeroSentinel()`.
                revert(0x1c, 0x04)
            }
            if iszero(value) { value := _ZERO_SENTINEL }
            for { let n := sload(not(rootSlot)) } 1 {} {
                mstore(0x20, rootSlot)
                if iszero(n) {
                    let v0 := sload(rootSlot)
                    if iszero(v0) {
                        sstore(rootSlot, value)
                        result := 1
                        break
                    }
                    if eq(v0, value) { break }
                    let v1 := sload(add(rootSlot, 1))
                    if iszero(v1) {
                        sstore(add(rootSlot, 1), value)
                        result := 1
                        break
                    }
                    if eq(v1, value) { break }
                    let v2 := sload(add(rootSlot, 2))
                    if iszero(v2) {
                        sstore(add(rootSlot, 2), value)
                        result := 1
                        break
                    }
                    if eq(v2, value) { break }
                    mstore(0x00, v0)
                    sstore(keccak256(0x00, 0x40), 1)
                    mstore(0x00, v1)
                    sstore(keccak256(0x00, 0x40), 2)
                    mstore(0x00, v2)
                    sstore(keccak256(0x00, 0x40), 3)
                    n := 7
                }
                mstore(0x00, value)
                let p := keccak256(0x00, 0x40)
                if iszero(sload(p)) {
                    n := shr(1, n)
                    sstore(add(rootSlot, n), value)
                    sstore(p, add(1, n))
                    sstore(not(rootSlot), or(1, shl(1, add(1, n))))
                    result := 1
                    break
                }
                break
            }
        }
    }

    /// @dev Adds `value` to the set. Returns whether `value` was not in the set.
    function add(Uint256Set storage set, uint256 value) internal returns (bool result) {
        result = add(_toBytes32Set(set), bytes32(value));
    }

    /// @dev Adds `value` to the set. Returns whether `value` was not in the set.
    function add(Int256Set storage set, int256 value) internal returns (bool result) {
        result = add(_toBytes32Set(set), bytes32(uint256(value)));
    }

    /// @dev Adds `value` to the set. Returns whether `value` was not in the set.
    function add(Uint8Set storage set, uint8 value) internal returns (bool result) {
        /// @solidity memory-safe-assembly
        assembly {
            result := sload(set.slot)
            let mask := shl(and(0xff, value), 1)
            sstore(set.slot, or(result, mask))
            result := iszero(and(result, mask))
        }
    }

    /// @dev Removes `value` from the set. Returns whether `value` was in the set.
    function remove(AddressSet storage set, address value) internal returns (bool result) {
        bytes32 rootSlot = _rootSlot(set);
        /// @solidity memory-safe-assembly
        assembly {
            value := shr(96, shl(96, value))
            if eq(value, _ZERO_SENTINEL) {
                mstore(0x00, 0xf5a267f1) // `ValueIsZeroSentinel()`.
                revert(0x1c, 0x04)
            }
            if iszero(value) { value := _ZERO_SENTINEL }
            let rootPacked := sload(rootSlot)
            for { let n := shr(160, shl(160, rootPacked)) } 1 {} {
                if iszero(n) {
                    result := 1
                    if eq(shr(96, rootPacked), value) {
                        sstore(rootSlot, sload(add(rootSlot, 1)))
                        sstore(add(rootSlot, 1), sload(add(rootSlot, 2)))
                        sstore(add(rootSlot, 2), 0)
                        break
                    }
                    if eq(shr(96, sload(add(rootSlot, 1))), value) {
                        sstore(add(rootSlot, 1), sload(add(rootSlot, 2)))
                        sstore(add(rootSlot, 2), 0)
                        break
                    }
                    if eq(shr(96, sload(add(rootSlot, 2))), value) {
                        sstore(add(rootSlot, 2), 0)
                        break
                    }
                    result := 0
                    break
                }
                mstore(0x20, rootSlot)
                mstore(0x00, value)
                let p := keccak256(0x00, 0x40)
                let position := sload(p)
                if iszero(position) { break }
                n := sub(shr(1, n), 1)
                if iszero(eq(sub(position, 1), n)) {
                    let lastValue := shr(96, sload(add(rootSlot, n)))
                    sstore(add(rootSlot, sub(position, 1)), shl(96, lastValue))
                    sstore(add(rootSlot, n), 0)
                    mstore(0x00, lastValue)
                    sstore(keccak256(0x00, 0x40), position)
                }
                sstore(rootSlot, or(shl(96, shr(96, sload(rootSlot))), or(shl(1, n), 1)))
                sstore(p, 0)
                result := 1
                break
            }
        }
    }

    /// @dev Removes `value` from the set. Returns whether `value` was in the set.
    function remove(Bytes32Set storage set, bytes32 value) internal returns (bool result) {
        bytes32 rootSlot = _rootSlot(set);
        /// @solidity memory-safe-assembly
        assembly {
            if eq(value, _ZERO_SENTINEL) {
                mstore(0x00, 0xf5a267f1) // `ValueIsZeroSentinel()`.
                revert(0x1c, 0x04)
            }
            if iszero(value) { value := _ZERO_SENTINEL }
            for { let n := sload(not(rootSlot)) } 1 {} {
                if iszero(n) {
                    result := 1
                    if eq(sload(rootSlot), value) {
                        sstore(rootSlot, sload(add(rootSlot, 1)))
                        sstore(add(rootSlot, 1), sload(add(rootSlot, 2)))
                        sstore(add(rootSlot, 2), 0)
                        break
                    }
                    if eq(sload(add(rootSlot, 1)), value) {
                        sstore(add(rootSlot, 1), sload(add(rootSlot, 2)))
                        sstore(add(rootSlot, 2), 0)
                        break
                    }
                    if eq(sload(add(rootSlot, 2)), value) {
                        sstore(add(rootSlot, 2), 0)
                        break
                    }
                    result := 0
                    break
                }
                mstore(0x20, rootSlot)
                mstore(0x00, value)
                let p := keccak256(0x00, 0x40)
                let position := sload(p)
                if iszero(position) { break }
                n := sub(shr(1, n), 1)
                if iszero(eq(sub(position, 1), n)) {
                    let lastValue := sload(add(rootSlot, n))
                    sstore(add(rootSlot, sub(position, 1)), lastValue)
                    sstore(add(rootSlot, n), 0)
                    mstore(0x00, lastValue)
                    sstore(keccak256(0x00, 0x40), position)
                }
                sstore(not(rootSlot), or(shl(1, n), 1))
                sstore(p, 0)
                result := 1
                break
            }
        }
    }

    /// @dev Removes `value` from the set. Returns whether `value` was in the set.
    function remove(Uint256Set storage set, uint256 value) internal returns (bool result) {
        result = remove(_toBytes32Set(set), bytes32(value));
    }

    /// @dev Removes `value` from the set. Returns whether `value` was in the set.
    function remove(Int256Set storage set, int256 value) internal returns (bool result) {
        result = remove(_toBytes32Set(set), bytes32(uint256(value)));
    }

    /// @dev Removes `value` from the set. Returns whether `value` was in the set.
    function remove(Uint8Set storage set, uint8 value) internal returns (bool result) {
        /// @solidity memory-safe-assembly
        assembly {
            result := sload(set.slot)
            let mask := shl(and(0xff, value), 1)
            sstore(set.slot, and(result, not(mask)))
            result := iszero(iszero(and(result, mask)))
        }
    }

    /// @dev Returns all of the values in the set.
    /// Note: This can consume more gas than the block gas limit for large sets.
    function values(AddressSet storage set) internal view returns (address[] memory result) {
        bytes32 rootSlot = _rootSlot(set);
        /// @solidity memory-safe-assembly
        assembly {
            let zs := _ZERO_SENTINEL
            let rootPacked := sload(rootSlot)
            let n := shr(160, shl(160, rootPacked))
            result := mload(0x40)
            let o := add(0x20, result)
            let v := shr(96, rootPacked)
            mstore(o, mul(v, iszero(eq(v, zs))))
            for {} 1 {} {
                if iszero(n) {
                    if v {
                        n := 1
                        v := shr(96, sload(add(rootSlot, n)))
                        if v {
                            n := 2
                            mstore(add(o, 0x20), mul(v, iszero(eq(v, zs))))
                            v := shr(96, sload(add(rootSlot, n)))
                            if v {
                                n := 3
                                mstore(add(o, 0x40), mul(v, iszero(eq(v, zs))))
                            }
                        }
                    }
                    break
                }
                n := shr(1, n)
                for { let i := 1 } lt(i, n) { i := add(i, 1) } {
                    v := shr(96, sload(add(rootSlot, i)))
                    mstore(add(o, shl(5, i)), mul(v, iszero(eq(v, zs))))
                }
                break
            }
            mstore(result, n)
            mstore(0x40, add(o, shl(5, n)))
        }
    }

    /// @dev Returns all of the values in the set.
    /// Note: This can consume more gas than the block gas limit for large sets.
    function values(Bytes32Set storage set) internal view returns (bytes32[] memory result) {
        bytes32 rootSlot = _rootSlot(set);
        /// @solidity memory-safe-assembly
        assembly {
            let zs := _ZERO_SENTINEL
            let n := sload(not(rootSlot))
            result := mload(0x40)
            let o := add(0x20, result)
            for {} 1 {} {
                if iszero(n) {
                    let v := sload(rootSlot)
                    if v {
                        n := 1
                        mstore(o, mul(v, iszero(eq(v, zs))))
                        v := sload(add(rootSlot, n))
                        if v {
                            n := 2
                            mstore(add(o, 0x20), mul(v, iszero(eq(v, zs))))
                            v := sload(add(rootSlot, n))
                            if v {
                                n := 3
                                mstore(add(o, 0x40), mul(v, iszero(eq(v, zs))))
                            }
                        }
                    }
                    break
                }
                n := shr(1, n)
                for { let i := 0 } lt(i, n) { i := add(i, 1) } {
                    let v := sload(add(rootSlot, i))
                    mstore(add(o, shl(5, i)), mul(v, iszero(eq(v, zs))))
                }
                break
            }
            mstore(result, n)
            mstore(0x40, add(o, shl(5, n)))
        }
    }

    /// @dev Returns all of the values in the set.
    /// Note: This can consume more gas than the block gas limit for large sets.
    function values(Uint256Set storage set) internal view returns (uint256[] memory result) {
        result = _toUints(values(_toBytes32Set(set)));
    }

    /// @dev Returns all of the values in the set.
    /// Note: This can consume more gas than the block gas limit for large sets.
    function values(Int256Set storage set) internal view returns (int256[] memory result) {
        result = _toInts(values(_toBytes32Set(set)));
    }

    /// @dev Returns all of the values in the set.
    function values(Uint8Set storage set) internal view returns (uint8[] memory result) {
        /// @solidity memory-safe-assembly
        assembly {
            result := mload(0x40)
            let ptr := add(result, 0x20)
            let o := 0
            for { let packed := sload(set.slot) } packed {} {
                if iszero(and(packed, 0xffff)) {
                    o := add(o, 16)
                    packed := shr(16, packed)
                    continue
                }
                mstore(ptr, o)
                ptr := add(ptr, shl(5, and(packed, 1)))
                o := add(o, 1)
                packed := shr(1, packed)
            }
            mstore(result, shr(5, sub(ptr, add(result, 0x20))))
            mstore(0x40, ptr)
        }
    }

    /// @dev Returns the element at index `i` in the set. Reverts if `i` is out-of-bounds.
    function at(AddressSet storage set, uint256 i) internal view returns (address result) {
        bytes32 rootSlot = _rootSlot(set);
        /// @solidity memory-safe-assembly
        assembly {
            result := shr(96, sload(add(rootSlot, i)))
            result := mul(result, iszero(eq(result, _ZERO_SENTINEL)))
        }
        if (i >= length(set)) revert IndexOutOfBounds();
    }

    /// @dev Returns the element at index `i` in the set. Reverts if `i` is out-of-bounds.
    function at(Bytes32Set storage set, uint256 i) internal view returns (bytes32 result) {
        result = _rootSlot(set);
        /// @solidity memory-safe-assembly
        assembly {
            result := sload(add(result, i))
            result := mul(result, iszero(eq(result, _ZERO_SENTINEL)))
        }
        if (i >= length(set)) revert IndexOutOfBounds();
    }

    /// @dev Returns the element at index `i` in the set. Reverts if `i` is out-of-bounds.
    function at(Uint256Set storage set, uint256 i) internal view returns (uint256 result) {
        result = uint256(at(_toBytes32Set(set), i));
    }

    /// @dev Returns the element at index `i` in the set. Reverts if `i` is out-of-bounds.
    function at(Int256Set storage set, uint256 i) internal view returns (int256 result) {
        result = int256(uint256(at(_toBytes32Set(set), i)));
    }

    /// @dev Returns the element at index `i` in the set. Reverts if `i` is out-of-bounds.
    function at(Uint8Set storage set, uint256 i) internal view returns (uint8 result) {
        /// @solidity memory-safe-assembly
        assembly {
            let packed := sload(set.slot)
            for {} 1 {
                mstore(0x00, 0x4e23d035) // `IndexOutOfBounds()`.
                revert(0x1c, 0x04)
            } {
                if iszero(lt(i, 256)) { continue }
                for { let j := 0 } iszero(eq(i, j)) {} {
                    packed := xor(packed, and(packed, add(1, not(packed))))
                    j := add(j, 1)
                }
                if iszero(packed) { continue }
                break
            }
            // Find first set subroutine, optimized for smaller bytecode size.
            let x := and(packed, add(1, not(packed)))
            let r := shl(7, iszero(iszero(shr(128, x))))
            r := or(r, shl(6, iszero(iszero(shr(64, shr(r, x))))))
            r := or(r, shl(5, lt(0xffffffff, shr(r, x))))
            // For the lower 5 bits of the result, use a De Bruijn lookup.
            // forgefmt: disable-next-item
            result := or(r, byte(and(div(0xd76453e0, shr(r, x)), 0x1f),
                0x001f0d1e100c1d070f090b19131c1706010e11080a1a141802121b1503160405))
        }
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                      PRIVATE HELPERS                       */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Returns the root slot.
    function _rootSlot(AddressSet storage s) private pure returns (bytes32 r) {
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x04, _ENUMERABLE_ADDRESS_SET_SLOT_SEED)
            mstore(0x00, s.slot)
            r := keccak256(0x00, 0x24)
        }
    }

    /// @dev Returns the root slot.
    function _rootSlot(Bytes32Set storage s) private pure returns (bytes32 r) {
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x04, _ENUMERABLE_WORD_SET_SLOT_SEED)
            mstore(0x00, s.slot)
            r := keccak256(0x00, 0x24)
        }
    }

    /// @dev Casts to a Bytes32Set.
    function _toBytes32Set(Uint256Set storage s) private pure returns (Bytes32Set storage c) {
        /// @solidity memory-safe-assembly
        assembly {
            c.slot := s.slot
        }
    }

    /// @dev Casts to a Bytes32Set.
    function _toBytes32Set(Int256Set storage s) private pure returns (Bytes32Set storage c) {
        /// @solidity memory-safe-assembly
        assembly {
            c.slot := s.slot
        }
    }

    /// @dev Casts to a uint256 array.
    function _toUints(bytes32[] memory a) private pure returns (uint256[] memory c) {
        /// @solidity memory-safe-assembly
        assembly {
            c := a
        }
    }

    /// @dev Casts to a int256 array.
    function _toInts(bytes32[] memory a) private pure returns (int256[] memory c) {
        /// @solidity memory-safe-assembly
        assembly {
            c := a
        }
    }
}

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.4;

/// @notice Arithmetic library with operations for fixed-point numbers.
/// @author Solady (https://github.com/vectorized/solady/blob/main/src/utils/FixedPointMathLib.sol)
/// @author Modified from Solmate (https://github.com/transmissions11/solmate/blob/main/src/utils/FixedPointMathLib.sol)
library FixedPointMathLib {
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                       CUSTOM ERRORS                        */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev The operation failed, as the output exceeds the maximum value of uint256.
    error ExpOverflow();

    /// @dev The operation failed, as the output exceeds the maximum value of uint256.
    error FactorialOverflow();

    /// @dev The operation failed, due to an overflow.
    error RPowOverflow();

    /// @dev The mantissa is too big to fit.
    error MantissaOverflow();

    /// @dev The operation failed, due to an multiplication overflow.
    error MulWadFailed();

    /// @dev The operation failed, due to an multiplication overflow.
    error SMulWadFailed();

    /// @dev The operation failed, either due to a multiplication overflow, or a division by a zero.
    error DivWadFailed();

    /// @dev The operation failed, either due to a multiplication overflow, or a division by a zero.
    error SDivWadFailed();

    /// @dev The operation failed, either due to a multiplication overflow, or a division by a zero.
    error MulDivFailed();

    /// @dev The division failed, as the denominator is zero.
    error DivFailed();

    /// @dev The full precision multiply-divide operation failed, either due
    /// to the result being larger than 256 bits, or a division by a zero.
    error FullMulDivFailed();

    /// @dev The output is undefined, as the input is less-than-or-equal to zero.
    error LnWadUndefined();

    /// @dev The input outside the acceptable domain.
    error OutOfDomain();

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                         CONSTANTS                          */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev The scalar of ETH and most ERC20s.
    uint256 internal constant WAD = 1e18;

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*              SIMPLIFIED FIXED POINT OPERATIONS             */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Equivalent to `(x * y) / WAD` rounded down.
    function mulWad(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            // Equivalent to `require(y == 0 || x <= type(uint256).max / y)`.
            if gt(x, div(not(0), y)) {
                if y {
                    mstore(0x00, 0xbac65e5b) // `MulWadFailed()`.
                    revert(0x1c, 0x04)
                }
            }
            z := div(mul(x, y), WAD)
        }
    }

    /// @dev Equivalent to `(x * y) / WAD` rounded down.
    function sMulWad(int256 x, int256 y) internal pure returns (int256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := mul(x, y)
            // Equivalent to `require((x == 0 || z / x == y) && !(x == -1 && y == type(int256).min))`.
            if iszero(gt(or(iszero(x), eq(sdiv(z, x), y)), lt(not(x), eq(y, shl(255, 1))))) {
                mstore(0x00, 0xedcd4dd4) // `SMulWadFailed()`.
                revert(0x1c, 0x04)
            }
            z := sdiv(z, WAD)
        }
    }

    /// @dev Equivalent to `(x * y) / WAD` rounded down, but without overflow checks.
    function rawMulWad(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := div(mul(x, y), WAD)
        }
    }

    /// @dev Equivalent to `(x * y) / WAD` rounded down, but without overflow checks.
    function rawSMulWad(int256 x, int256 y) internal pure returns (int256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := sdiv(mul(x, y), WAD)
        }
    }

    /// @dev Equivalent to `(x * y) / WAD` rounded up.
    function mulWadUp(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := mul(x, y)
            // Equivalent to `require(y == 0 || x <= type(uint256).max / y)`.
            if iszero(eq(div(z, y), x)) {
                if y {
                    mstore(0x00, 0xbac65e5b) // `MulWadFailed()`.
                    revert(0x1c, 0x04)
                }
            }
            z := add(iszero(iszero(mod(z, WAD))), div(z, WAD))
        }
    }

    /// @dev Equivalent to `(x * y) / WAD` rounded up, but without overflow checks.
    function rawMulWadUp(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := add(iszero(iszero(mod(mul(x, y), WAD))), div(mul(x, y), WAD))
        }
    }

    /// @dev Equivalent to `(x * WAD) / y` rounded down.
    function divWad(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            // Equivalent to `require(y != 0 && x <= type(uint256).max / WAD)`.
            if iszero(mul(y, lt(x, add(1, div(not(0), WAD))))) {
                mstore(0x00, 0x7c5f487d) // `DivWadFailed()`.
                revert(0x1c, 0x04)
            }
            z := div(mul(x, WAD), y)
        }
    }

    /// @dev Equivalent to `(x * WAD) / y` rounded down.
    function sDivWad(int256 x, int256 y) internal pure returns (int256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := mul(x, WAD)
            // Equivalent to `require(y != 0 && ((x * WAD) / WAD == x))`.
            if iszero(mul(y, eq(sdiv(z, WAD), x))) {
                mstore(0x00, 0x5c43740d) // `SDivWadFailed()`.
                revert(0x1c, 0x04)
            }
            z := sdiv(z, y)
        }
    }

    /// @dev Equivalent to `(x * WAD) / y` rounded down, but without overflow and divide by zero checks.
    function rawDivWad(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := div(mul(x, WAD), y)
        }
    }

    /// @dev Equivalent to `(x * WAD) / y` rounded down, but without overflow and divide by zero checks.
    function rawSDivWad(int256 x, int256 y) internal pure returns (int256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := sdiv(mul(x, WAD), y)
        }
    }

    /// @dev Equivalent to `(x * WAD) / y` rounded up.
    function divWadUp(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            // Equivalent to `require(y != 0 && x <= type(uint256).max / WAD)`.
            if iszero(mul(y, lt(x, add(1, div(not(0), WAD))))) {
                mstore(0x00, 0x7c5f487d) // `DivWadFailed()`.
                revert(0x1c, 0x04)
            }
            z := add(iszero(iszero(mod(mul(x, WAD), y))), div(mul(x, WAD), y))
        }
    }

    /// @dev Equivalent to `(x * WAD) / y` rounded up, but without overflow and divide by zero checks.
    function rawDivWadUp(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := add(iszero(iszero(mod(mul(x, WAD), y))), div(mul(x, WAD), y))
        }
    }

    /// @dev Equivalent to `x` to the power of `y`.
    /// because `x ** y = (e ** ln(x)) ** y = e ** (ln(x) * y)`.
    /// Note: This function is an approximation.
    function powWad(int256 x, int256 y) internal pure returns (int256) {
        // Using `ln(x)` means `x` must be greater than 0.
        return expWad((lnWad(x) * y) / int256(WAD));
    }

    /// @dev Returns `exp(x)`, denominated in `WAD`.
    /// Credit to Remco Bloemen under MIT license: https://2π.com/22/exp-ln
    /// Note: This function is an approximation. Monotonically increasing.
    function expWad(int256 x) internal pure returns (int256 r) {
        unchecked {
            // When the result is less than 0.5 we return zero.
            // This happens when `x <= (log(1e-18) * 1e18) ~ -4.15e19`.
            if (x <= -41446531673892822313) return r;

            /// @solidity memory-safe-assembly
            assembly {
                // When the result is greater than `(2**255 - 1) / 1e18` we can not represent it as
                // an int. This happens when `x >= floor(log((2**255 - 1) / 1e18) * 1e18) ≈ 135`.
                if iszero(slt(x, 135305999368893231589)) {
                    mstore(0x00, 0xa37bfec9) // `ExpOverflow()`.
                    revert(0x1c, 0x04)
                }
            }

            // `x` is now in the range `(-42, 136) * 1e18`. Convert to `(-42, 136) * 2**96`
            // for more intermediate precision and a binary basis. This base conversion
            // is a multiplication by 1e18 / 2**96 = 5**18 / 2**78.
            x = (x << 78) / 5 ** 18;

            // Reduce range of x to (-½ ln 2, ½ ln 2) * 2**96 by factoring out powers
            // of two such that exp(x) = exp(x') * 2**k, where k is an integer.
            // Solving this gives k = round(x / log(2)) and x' = x - k * log(2).
            int256 k = ((x << 96) / 54916777467707473351141471128 + 2 ** 95) >> 96;
            x = x - k * 54916777467707473351141471128;

            // `k` is in the range `[-61, 195]`.

            // Evaluate using a (6, 7)-term rational approximation.
            // `p` is made monic, we'll multiply by a scale factor later.
            int256 y = x + 1346386616545796478920950773328;
            y = ((y * x) >> 96) + 57155421227552351082224309758442;
            int256 p = y + x - 94201549194550492254356042504812;
            p = ((p * y) >> 96) + 28719021644029726153956944680412240;
            p = p * x + (4385272521454847904659076985693276 << 96);

            // We leave `p` in `2**192` basis so we don't need to scale it back up for the division.
            int256 q = x - 2855989394907223263936484059900;
            q = ((q * x) >> 96) + 50020603652535783019961831881945;
            q = ((q * x) >> 96) - 533845033583426703283633433725380;
            q = ((q * x) >> 96) + 3604857256930695427073651918091429;
            q = ((q * x) >> 96) - 14423608567350463180887372962807573;
            q = ((q * x) >> 96) + 26449188498355588339934803723976023;

            /// @solidity memory-safe-assembly
            assembly {
                // Div in assembly because solidity adds a zero check despite the unchecked.
                // The q polynomial won't have zeros in the domain as all its roots are complex.
                // No scaling is necessary because p is already `2**96` too large.
                r := sdiv(p, q)
            }

            // r should be in the range `(0.09, 0.25) * 2**96`.

            // We now need to multiply r by:
            // - The scale factor `s ≈ 6.031367120`.
            // - The `2**k` factor from the range reduction.
            // - The `1e18 / 2**96` factor for base conversion.
            // We do this all at once, with an intermediate result in `2**213`
            // basis, so the final right shift is always by a positive amount.
            r = int256(
                (uint256(r) * 3822833074963236453042738258902158003155416615667) >> uint256(195 - k)
            );
        }
    }

    /// @dev Returns `ln(x)`, denominated in `WAD`.
    /// Credit to Remco Bloemen under MIT license: https://2π.com/22/exp-ln
    /// Note: This function is an approximation. Monotonically increasing.
    function lnWad(int256 x) internal pure returns (int256 r) {
        /// @solidity memory-safe-assembly
        assembly {
            // We want to convert `x` from `10**18` fixed point to `2**96` fixed point.
            // We do this by multiplying by `2**96 / 10**18`. But since
            // `ln(x * C) = ln(x) + ln(C)`, we can simply do nothing here
            // and add `ln(2**96 / 10**18)` at the end.

            // Compute `k = log2(x) - 96`, `r = 159 - k = 255 - log2(x) = 255 ^ log2(x)`.
            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))))
            // We place the check here for more optimal stack operations.
            if iszero(sgt(x, 0)) {
                mstore(0x00, 0x1615e638) // `LnWadUndefined()`.
                revert(0x1c, 0x04)
            }
            // forgefmt: disable-next-item
            r := xor(r, byte(and(0x1f, shr(shr(r, x), 0x8421084210842108cc6318c6db6d54be)),
                0xf8f9f9faf9fdfafbf9fdfcfdfafbfcfef9fafdfafcfcfbfefafafcfbffffffff))

            // Reduce range of x to (1, 2) * 2**96
            // ln(2^k * x) = k * ln(2) + ln(x)
            x := shr(159, shl(r, x))

            // Evaluate using a (8, 8)-term rational approximation.
            // `p` is made monic, we will multiply by a scale factor later.
            // forgefmt: disable-next-item
            let p := sub( // This heavily nested expression is to avoid stack-too-deep for via-ir.
                sar(96, mul(add(43456485725739037958740375743393,
                sar(96, mul(add(24828157081833163892658089445524,
                sar(96, mul(add(3273285459638523848632254066296,
                    x), x))), x))), x)), 11111509109440967052023855526967)
            p := sub(sar(96, mul(p, x)), 45023709667254063763336534515857)
            p := sub(sar(96, mul(p, x)), 14706773417378608786704636184526)
            p := sub(mul(p, x), shl(96, 795164235651350426258249787498))
            // We leave `p` in `2**192` basis so we don't need to scale it back up for the division.

            // `q` is monic by convention.
            let q := add(5573035233440673466300451813936, x)
            q := add(71694874799317883764090561454958, sar(96, mul(x, q)))
            q := add(283447036172924575727196451306956, sar(96, mul(x, q)))
            q := add(401686690394027663651624208769553, sar(96, mul(x, q)))
            q := add(204048457590392012362485061816622, sar(96, mul(x, q)))
            q := add(31853899698501571402653359427138, sar(96, mul(x, q)))
            q := add(909429971244387300277376558375, sar(96, mul(x, q)))

            // `p / q` is in the range `(0, 0.125) * 2**96`.

            // Finalization, we need to:
            // - Multiply by the scale factor `s = 5.549…`.
            // - Add `ln(2**96 / 10**18)`.
            // - Add `k * ln(2)`.
            // - Multiply by `10**18 / 2**96 = 5**18 >> 78`.

            // The q polynomial is known not to have zeros in the domain.
            // No scaling required because p is already `2**96` too large.
            p := sdiv(p, q)
            // Multiply by the scaling factor: `s * 5**18 * 2**96`, base is now `5**18 * 2**192`.
            p := mul(1677202110996718588342820967067443963516166, p)
            // Add `ln(2) * k * 5**18 * 2**192`.
            // forgefmt: disable-next-item
            p := add(mul(16597577552685614221487285958193947469193820559219878177908093499208371, sub(159, r)), p)
            // Add `ln(2**96 / 10**18) * 5**18 * 2**192`.
            p := add(600920179829731861736702779321621459595472258049074101567377883020018308, p)
            // Base conversion: mul `2**18 / 2**192`.
            r := sar(174, p)
        }
    }

    /// @dev Returns `W_0(x)`, denominated in `WAD`.
    /// See: https://en.wikipedia.org/wiki/Lambert_W_function
    /// a.k.a. Product log function. This is an approximation of the principal branch.
    /// Note: This function is an approximation. Monotonically increasing.
    function lambertW0Wad(int256 x) internal pure returns (int256 w) {
        // forgefmt: disable-next-item
        unchecked {
            if ((w = x) <= -367879441171442322) revert OutOfDomain(); // `x` less than `-1/e`.
            (int256 wad, int256 p) = (int256(WAD), x);
            uint256 c; // Whether we need to avoid catastrophic cancellation.
            uint256 i = 4; // Number of iterations.
            if (w <= 0x1ffffffffffff) {
                if (-0x4000000000000 <= w) {
                    i = 1; // Inputs near zero only take one step to converge.
                } else if (w <= -0x3ffffffffffffff) {
                    i = 32; // Inputs near `-1/e` take very long to converge.
                }
            } else if (uint256(w >> 63) == uint256(0)) {
                /// @solidity memory-safe-assembly
                assembly {
                    // Inline log2 for more performance, since the range is small.
                    let v := shr(49, w)
                    let l := shl(3, lt(0xff, v))
                    l := add(or(l, byte(and(0x1f, shr(shr(l, v), 0x8421084210842108cc6318c6db6d54be)),
                        0x0706060506020504060203020504030106050205030304010505030400000000)), 49)
                    w := sdiv(shl(l, 7), byte(sub(l, 31), 0x0303030303030303040506080c13))
                    c := gt(l, 60)
                    i := add(2, add(gt(l, 53), c))
                }
            } else {
                int256 ll = lnWad(w = lnWad(w));
                /// @solidity memory-safe-assembly
                assembly {
                    // `w = ln(x) - ln(ln(x)) + b * ln(ln(x)) / ln(x)`.
                    w := add(sdiv(mul(ll, 1023715080943847266), w), sub(w, ll))
                    i := add(3, iszero(shr(68, x)))
                    c := iszero(shr(143, x))
                }
                if (c == uint256(0)) {
                    do { // If `x` is big, use Newton's so that intermediate values won't overflow.
                        int256 e = expWad(w);
                        /// @solidity memory-safe-assembly
                        assembly {
                            let t := mul(w, div(e, wad))
                            w := sub(w, sdiv(sub(t, x), div(add(e, t), wad)))
                        }
                        if (p <= w) break;
                        p = w;
                    } while (--i != uint256(0));
                    /// @solidity memory-safe-assembly
                    assembly {
                        w := sub(w, sgt(w, 2))
                    }
                    return w;
                }
            }
            do { // Otherwise, use Halley's for faster convergence.
                int256 e = expWad(w);
                /// @solidity memory-safe-assembly
                assembly {
                    let t := add(w, wad)
                    let s := sub(mul(w, e), mul(x, wad))
                    w := sub(w, sdiv(mul(s, wad), sub(mul(e, t), sdiv(mul(add(t, wad), s), add(t, t)))))
                }
                if (p <= w) break;
                p = w;
            } while (--i != c);
            /// @solidity memory-safe-assembly
            assembly {
                w := sub(w, sgt(w, 2))
            }
            // For certain ranges of `x`, we'll use the quadratic-rate recursive formula of
            // R. Iacono and J.P. Boyd for the last iteration, to avoid catastrophic cancellation.
            if (c == uint256(0)) return w;
            int256 t = w | 1;
            /// @solidity memory-safe-assembly
            assembly {
                x := sdiv(mul(x, wad), t)
            }
            x = (t * (wad + lnWad(x)));
            /// @solidity memory-safe-assembly
            assembly {
                w := sdiv(x, add(wad, t))
            }
        }
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                  GENERAL NUMBER UTILITIES                  */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Returns `a * b == x * y`, with full precision.
    function fullMulEq(uint256 a, uint256 b, uint256 x, uint256 y)
        internal
        pure
        returns (bool result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            result := and(eq(mul(a, b), mul(x, y)), eq(mulmod(x, y, not(0)), mulmod(a, b, not(0))))
        }
    }

    /// @dev Calculates `floor(x * y / d)` with full precision.
    /// Throws if result overflows a uint256 or when `d` is zero.
    /// Credit to Remco Bloemen under MIT license: https://2π.com/21/muldiv
    function fullMulDiv(uint256 x, uint256 y, uint256 d) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            // 512-bit multiply `[p1 p0] = x * y`.
            // 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 = p1 * 2**256 + p0`.

            // Temporarily use `z` as `p0` to save gas.
            z := mul(x, y) // Lower 256 bits of `x * y`.
            for {} 1 {} {
                // If overflows.
                if iszero(mul(or(iszero(x), eq(div(z, x), y)), d)) {
                    let mm := mulmod(x, y, not(0))
                    let p1 := sub(mm, add(z, lt(mm, z))) // Upper 256 bits of `x * y`.

                    /*------------------- 512 by 256 division --------------------*/

                    // Make division exact by subtracting the remainder from `[p1 p0]`.
                    let r := mulmod(x, y, d) // Compute remainder using mulmod.
                    let t := and(d, sub(0, d)) // The least significant bit of `d`. `t >= 1`.
                    // Make sure `z` is less than `2**256`. Also prevents `d == 0`.
                    // Placing the check here seems to give more optimal stack operations.
                    if iszero(gt(d, p1)) {
                        mstore(0x00, 0xae47f702) // `FullMulDivFailed()`.
                        revert(0x1c, 0x04)
                    }
                    d := div(d, t) // Divide `d` by `t`, which is a power of two.
                    // Invert `d mod 2**256`
                    // Now that `d` is an odd number, it has an inverse
                    // modulo `2**256` such that `d * inv = 1 mod 2**256`.
                    // Compute the inverse by starting with a seed that is correct
                    // correct for four bits. That is, `d * inv = 1 mod 2**4`.
                    let inv := xor(2, mul(3, d))
                    // 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 := mul(inv, sub(2, mul(d, inv))) // inverse mod 2**8
                    inv := mul(inv, sub(2, mul(d, inv))) // inverse mod 2**16
                    inv := mul(inv, sub(2, mul(d, inv))) // inverse mod 2**32
                    inv := mul(inv, sub(2, mul(d, inv))) // inverse mod 2**64
                    inv := mul(inv, sub(2, mul(d, inv))) // inverse mod 2**128
                    z :=
                        mul(
                            // Divide [p1 p0] by the factors of two.
                            // Shift in bits from `p1` into `p0`. For this we need
                            // to flip `t` such that it is `2**256 / t`.
                            or(mul(sub(p1, gt(r, z)), add(div(sub(0, t), t), 1)), div(sub(z, r), t)),
                            mul(sub(2, mul(d, inv)), inv) // inverse mod 2**256
                        )
                    break
                }
                z := div(z, d)
                break
            }
        }
    }

    /// @dev Calculates `floor(x * y / d)` with full precision.
    /// Behavior is undefined if `d` is zero or the final result cannot fit in 256 bits.
    /// Performs the full 512 bit calculation regardless.
    function fullMulDivUnchecked(uint256 x, uint256 y, uint256 d)
        internal
        pure
        returns (uint256 z)
    {
        /// @solidity memory-safe-assembly
        assembly {
            z := mul(x, y)
            let mm := mulmod(x, y, not(0))
            let p1 := sub(mm, add(z, lt(mm, z)))
            let t := and(d, sub(0, d))
            let r := mulmod(x, y, d)
            d := div(d, t)
            let inv := xor(2, mul(3, d))
            inv := mul(inv, sub(2, mul(d, inv)))
            inv := mul(inv, sub(2, mul(d, inv)))
            inv := mul(inv, sub(2, mul(d, inv)))
            inv := mul(inv, sub(2, mul(d, inv)))
            inv := mul(inv, sub(2, mul(d, inv)))
            z :=
                mul(
                    or(mul(sub(p1, gt(r, z)), add(div(sub(0, t), t), 1)), div(sub(z, r), t)),
                    mul(sub(2, mul(d, inv)), inv)
                )
        }
    }

    /// @dev Calculates `floor(x * y / d)` with full precision, rounded up.
    /// Throws if result overflows a uint256 or when `d` is zero.
    /// Credit to Uniswap-v3-core under MIT license:
    /// https://github.com/Uniswap/v3-core/blob/main/contracts/libraries/FullMath.sol
    function fullMulDivUp(uint256 x, uint256 y, uint256 d) internal pure returns (uint256 z) {
        z = fullMulDiv(x, y, d);
        /// @solidity memory-safe-assembly
        assembly {
            if mulmod(x, y, d) {
                z := add(z, 1)
                if iszero(z) {
                    mstore(0x00, 0xae47f702) // `FullMulDivFailed()`.
                    revert(0x1c, 0x04)
                }
            }
        }
    }

    /// @dev Calculates `floor(x * y / 2 ** n)` with full precision.
    /// Throws if result overflows a uint256.
    /// Credit to Philogy under MIT license:
    /// https://github.com/SorellaLabs/angstrom/blob/main/contracts/src/libraries/X128MathLib.sol
    function fullMulDivN(uint256 x, uint256 y, uint8 n) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            // Temporarily use `z` as `p0` to save gas.
            z := mul(x, y) // Lower 256 bits of `x * y`. We'll call this `z`.
            for {} 1 {} {
                if iszero(or(iszero(x), eq(div(z, x), y))) {
                    let k := and(n, 0xff) // `n`, cleaned.
                    let mm := mulmod(x, y, not(0))
                    let p1 := sub(mm, add(z, lt(mm, z))) // Upper 256 bits of `x * y`.
                    //         |      p1     |      z     |
                    // Before: | p1_0 ¦ p1_1 | z_0  ¦ z_1 |
                    // Final:  |   0  ¦ p1_0 | p1_1 ¦ z_0 |
                    // Check that final `z` doesn't overflow by checking that p1_0 = 0.
                    if iszero(shr(k, p1)) {
                        z := add(shl(sub(256, k), p1), shr(k, z))
                        break
                    }
                    mstore(0x00, 0xae47f702) // `FullMulDivFailed()`.
                    revert(0x1c, 0x04)
                }
                z := shr(and(n, 0xff), z)
                break
            }
        }
    }

    /// @dev Returns `floor(x * y / d)`.
    /// Reverts if `x * y` overflows, or `d` is zero.
    function mulDiv(uint256 x, uint256 y, uint256 d) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := mul(x, y)
            // Equivalent to `require(d != 0 && (y == 0 || x <= type(uint256).max / y))`.
            if iszero(mul(or(iszero(x), eq(div(z, x), y)), d)) {
                mstore(0x00, 0xad251c27) // `MulDivFailed()`.
                revert(0x1c, 0x04)
            }
            z := div(z, d)
        }
    }

    /// @dev Returns `ceil(x * y / d)`.
    /// Reverts if `x * y` overflows, or `d` is zero.
    function mulDivUp(uint256 x, uint256 y, uint256 d) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := mul(x, y)
            // Equivalent to `require(d != 0 && (y == 0 || x <= type(uint256).max / y))`.
            if iszero(mul(or(iszero(x), eq(div(z, x), y)), d)) {
                mstore(0x00, 0xad251c27) // `MulDivFailed()`.
                revert(0x1c, 0x04)
            }
            z := add(iszero(iszero(mod(z, d))), div(z, d))
        }
    }

    /// @dev Returns `x`, the modular multiplicative inverse of `a`, such that `(a * x) % n == 1`.
    function invMod(uint256 a, uint256 n) internal pure returns (uint256 x) {
        /// @solidity memory-safe-assembly
        assembly {
            let g := n
            let r := mod(a, n)
            for { let y := 1 } 1 {} {
                let q := div(g, r)
                let t := g
                g := r
                r := sub(t, mul(r, q))
                let u := x
                x := y
                y := sub(u, mul(y, q))
                if iszero(r) { break }
            }
            x := mul(eq(g, 1), add(x, mul(slt(x, 0), n)))
        }
    }

    /// @dev Returns `ceil(x / d)`.
    /// Reverts if `d` is zero.
    function divUp(uint256 x, uint256 d) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            if iszero(d) {
                mstore(0x00, 0x65244e4e) // `DivFailed()`.
                revert(0x1c, 0x04)
            }
            z := add(iszero(iszero(mod(x, d))), div(x, d))
        }
    }

    /// @dev Returns `max(0, x - y)`.
    function zeroFloorSub(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := mul(gt(x, y), sub(x, y))
        }
    }

    /// @dev Returns `condition ? x : y`, without branching.
    function ternary(bool condition, uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := xor(x, mul(xor(x, y), iszero(condition)))
        }
    }

    /// @dev Returns `condition ? x : y`, without branching.
    function ternary(bool condition, bytes32 x, bytes32 y) internal pure returns (bytes32 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := xor(x, mul(xor(x, y), iszero(condition)))
        }
    }

    /// @dev Returns `condition ? x : y`, without branching.
    function ternary(bool condition, address x, address y) internal pure returns (address z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := xor(x, mul(xor(x, y), iszero(condition)))
        }
    }

    /// @dev Exponentiate `x` to `y` by squaring, denominated in base `b`.
    /// Reverts if the computation overflows.
    function rpow(uint256 x, uint256 y, uint256 b) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := mul(b, iszero(y)) // `0 ** 0 = 1`. Otherwise, `0 ** n = 0`.
            if x {
                z := xor(b, mul(xor(b, x), and(y, 1))) // `z = isEven(y) ? scale : x`
                let half := shr(1, b) // Divide `b` by 2.
                // Divide `y` by 2 every iteration.
                for { y := shr(1, y) } y { y := shr(1, y) } {
                    let xx := mul(x, x) // Store x squared.
                    let xxRound := add(xx, half) // Round to the nearest number.
                    // Revert if `xx + half` overflowed, or if `x ** 2` overflows.
                    if or(lt(xxRound, xx), shr(128, x)) {
                        mstore(0x00, 0x49f7642b) // `RPowOverflow()`.
                        revert(0x1c, 0x04)
                    }
                    x := div(xxRound, b) // Set `x` to scaled `xxRound`.
                    // If `y` is odd:
                    if and(y, 1) {
                        let zx := mul(z, x) // Compute `z * x`.
                        let zxRound := add(zx, half) // Round to the nearest number.
                        // If `z * x` overflowed or `zx + half` overflowed:
                        if or(xor(div(zx, x), z), lt(zxRound, zx)) {
                            // Revert if `x` is non-zero.
                            if x {
                                mstore(0x00, 0x49f7642b) // `RPowOverflow()`.
                                revert(0x1c, 0x04)
                            }
                        }
                        z := div(zxRound, b) // Return properly scaled `zxRound`.
                    }
                }
            }
        }
    }

    /// @dev Returns the square root of `x`, rounded down.
    function sqrt(uint256 x) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            // `floor(sqrt(2**15)) = 181`. `sqrt(2**15) - 181 = 2.84`.
            z := 181 // The "correct" value is 1, but this saves a multiplication later.

            // This segment is to get a reasonable initial estimate for the Babylonian method. With a bad
            // start, the correct # of bits increases ~linearly each iteration instead of ~quadratically.

            // Let `y = x / 2**r`. We check `y >= 2**(k + 8)`
            // but shift right by `k` bits to ensure that if `x >= 256`, then `y >= 256`.
            let r := shl(7, lt(0xffffffffffffffffffffffffffffffffff, x))
            r := or(r, shl(6, lt(0xffffffffffffffffff, shr(r, x))))
            r := or(r, shl(5, lt(0xffffffffff, shr(r, x))))
            r := or(r, shl(4, lt(0xffffff, shr(r, x))))
            z := shl(shr(1, r), z)

            // Goal was to get `z*z*y` within a small factor of `x`. More iterations could
            // get y in a tighter range. Currently, we will have y in `[256, 256*(2**16))`.
            // We ensured `y >= 256` so that the relative difference between `y` and `y+1` is small.
            // That's not possible if `x < 256` but we can just verify those cases exhaustively.

            // Now, `z*z*y <= x < z*z*(y+1)`, and `y <= 2**(16+8)`, and either `y >= 256`, or `x < 256`.
            // Correctness can be checked exhaustively for `x < 256`, so we assume `y >= 256`.
            // Then `z*sqrt(y)` is within `sqrt(257)/sqrt(256)` of `sqrt(x)`, or about 20bps.

            // For `s` in the range `[1/256, 256]`, the estimate `f(s) = (181/1024) * (s+1)`
            // is in the range `(1/2.84 * sqrt(s), 2.84 * sqrt(s))`,
            // with largest error when `s = 1` and when `s = 256` or `1/256`.

            // Since `y` is in `[256, 256*(2**16))`, let `a = y/65536`, so that `a` is in `[1/256, 256)`.
            // Then we can estimate `sqrt(y)` using
            // `sqrt(65536) * 181/1024 * (a + 1) = 181/4 * (y + 65536)/65536 = 181 * (y + 65536)/2**18`.

            // There is no overflow risk here since `y < 2**136` after the first branch above.
            z := shr(18, mul(z, add(shr(r, x), 65536))) // A `mul()` is saved from starting `z` at 181.

            // Given the worst case multiplicative error of 2.84 above, 7 iterations should be enough.
            z := shr(1, add(z, div(x, z)))
            z := shr(1, add(z, div(x, z)))
            z := shr(1, add(z, div(x, z)))
            z := shr(1, add(z, div(x, z)))
            z := shr(1, add(z, div(x, z)))
            z := shr(1, add(z, div(x, z)))
            z := shr(1, add(z, div(x, z)))

            // If `x+1` is a perfect square, the Babylonian method cycles between
            // `floor(sqrt(x))` and `ceil(sqrt(x))`. This statement ensures we return floor.
            // See: https://en.wikipedia.org/wiki/Integer_square_root#Using_only_integer_division
            z := sub(z, lt(div(x, z), z))
        }
    }

    /// @dev Returns the cube root of `x`, rounded down.
    /// Credit to bout3fiddy and pcaversaccio under AGPLv3 license:
    /// https://github.com/pcaversaccio/snekmate/blob/main/src/utils/Math.vy
    /// Formally verified by xuwinnie:
    /// https://github.com/vectorized/solady/blob/main/audits/xuwinnie-solady-cbrt-proof.pdf
    function cbrt(uint256 x) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            let 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))))
            // Makeshift lookup table to nudge the approximate log2 result.
            z := div(shl(div(r, 3), shl(lt(0xf, shr(r, x)), 0xf)), xor(7, mod(r, 3)))
            // Newton-Raphson's.
            z := div(add(add(div(x, mul(z, z)), z), z), 3)
            z := div(add(add(div(x, mul(z, z)), z), z), 3)
            z := div(add(add(div(x, mul(z, z)), z), z), 3)
            z := div(add(add(div(x, mul(z, z)), z), z), 3)
            z := div(add(add(div(x, mul(z, z)), z), z), 3)
            z := div(add(add(div(x, mul(z, z)), z), z), 3)
            z := div(add(add(div(x, mul(z, z)), z), z), 3)
            // Round down.
            z := sub(z, lt(div(x, mul(z, z)), z))
        }
    }

    /// @dev Returns the square root of `x`, denominated in `WAD`, rounded down.
    function sqrtWad(uint256 x) internal pure returns (uint256 z) {
        unchecked {
            if (x <= type(uint256).max / 10 ** 18) return sqrt(x * 10 ** 18);
            z = (1 + sqrt(x)) * 10 ** 9;
            z = (fullMulDivUnchecked(x, 10 ** 18, z) + z) >> 1;
        }
        /// @solidity memory-safe-assembly
        assembly {
            z := sub(z, gt(999999999999999999, sub(mulmod(z, z, x), 1))) // Round down.
        }
    }

    /// @dev Returns the cube root of `x`, denominated in `WAD`, rounded down.
    /// Formally verified by xuwinnie:
    /// https://github.com/vectorized/solady/blob/main/audits/xuwinnie-solady-cbrt-proof.pdf
    function cbrtWad(uint256 x) internal pure returns (uint256 z) {
        unchecked {
            if (x <= type(uint256).max / 10 ** 36) return cbrt(x * 10 ** 36);
            z = (1 + cbrt(x)) * 10 ** 12;
            z = (fullMulDivUnchecked(x, 10 ** 36, z * z) + z + z) / 3;
        }
        /// @solidity memory-safe-assembly
        assembly {
            let p := x
            for {} 1 {} {
                if iszero(shr(229, p)) {
                    if iszero(shr(199, p)) {
                        p := mul(p, 100000000000000000) // 10 ** 17.
                        break
                    }
                    p := mul(p, 100000000) // 10 ** 8.
                    break
                }
                if iszero(shr(249, p)) { p := mul(p, 100) }
                break
            }
            let t := mulmod(mul(z, z), z, p)
            z := sub(z, gt(lt(t, shr(1, p)), iszero(t))) // Round down.
        }
    }

    /// @dev Returns the factorial of `x`.
    function factorial(uint256 x) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := 1
            if iszero(lt(x, 58)) {
                mstore(0x00, 0xaba0f2a2) // `FactorialOverflow()`.
                revert(0x1c, 0x04)
            }
            for {} x { x := sub(x, 1) } { z := mul(z, x) }
        }
    }

    /// @dev Returns the log2 of `x`.
    /// Equivalent to computing the index of the most significant bit (MSB) of `x`.
    /// Returns 0 if `x` is zero.
    function log2(uint256 x) internal pure returns (uint256 r) {
        /// @solidity memory-safe-assembly
        assembly {
            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)),
                0x0706060506020504060203020504030106050205030304010505030400000000))
        }
    }

    /// @dev Returns the log2 of `x`, rounded up.
    /// Returns 0 if `x` is zero.
    function log2Up(uint256 x) internal pure returns (uint256 r) {
        r = log2(x);
        /// @solidity memory-safe-assembly
        assembly {
            r := add(r, lt(shl(r, 1), x))
        }
    }

    /// @dev Returns the log10 of `x`.
    /// Returns 0 if `x` is zero.
    function log10(uint256 x) internal pure returns (uint256 r) {
        /// @solidity memory-safe-assembly
        assembly {
            if iszero(lt(x, 100000000000000000000000000000000000000)) {
                x := div(x, 100000000000000000000000000000000000000)
                r := 38
            }
            if iszero(lt(x, 100000000000000000000)) {
                x := div(x, 100000000000000000000)
                r := add(r, 20)
            }
            if iszero(lt(x, 10000000000)) {
                x := div(x, 10000000000)
                r := add(r, 10)
            }
            if iszero(lt(x, 100000)) {
                x := div(x, 100000)
                r := add(r, 5)
            }
            r := add(r, add(gt(x, 9), add(gt(x, 99), add(gt(x, 999), gt(x, 9999)))))
        }
    }

    /// @dev Returns the log10 of `x`, rounded up.
    /// Returns 0 if `x` is zero.
    function log10Up(uint256 x) internal pure returns (uint256 r) {
        r = log10(x);
        /// @solidity memory-safe-assembly
        assembly {
            r := add(r, lt(exp(10, r), x))
        }
    }

    /// @dev Returns the log256 of `x`.
    /// Returns 0 if `x` is zero.
    function log256(uint256 x) internal pure returns (uint256 r) {
        /// @solidity memory-safe-assembly
        assembly {
            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(shr(3, r), lt(0xff, shr(r, x)))
        }
    }

    /// @dev Returns the log256 of `x`, rounded up.
    /// Returns 0 if `x` is zero.
    function log256Up(uint256 x) internal pure returns (uint256 r) {
        r = log256(x);
        /// @solidity memory-safe-assembly
        assembly {
            r := add(r, lt(shl(shl(3, r), 1), x))
        }
    }

    /// @dev Returns the scientific notation format `mantissa * 10 ** exponent` of `x`.
    /// Useful for compressing prices (e.g. using 25 bit mantissa and 7 bit exponent).
    function sci(uint256 x) internal pure returns (uint256 mantissa, uint256 exponent) {
        /// @solidity memory-safe-assembly
        assembly {
            mantissa := x
            if mantissa {
                if iszero(mod(mantissa, 1000000000000000000000000000000000)) {
                    mantissa := div(mantissa, 1000000000000000000000000000000000)
                    exponent := 33
                }
                if iszero(mod(mantissa, 10000000000000000000)) {
                    mantissa := div(mantissa, 10000000000000000000)
                    exponent := add(exponent, 19)
                }
                if iszero(mod(mantissa, 1000000000000)) {
                    mantissa := div(mantissa, 1000000000000)
                    exponent := add(exponent, 12)
                }
                if iszero(mod(mantissa, 1000000)) {
                    mantissa := div(mantissa, 1000000)
                    exponent := add(exponent, 6)
                }
                if iszero(mod(mantissa, 10000)) {
                    mantissa := div(mantissa, 10000)
                    exponent := add(exponent, 4)
                }
                if iszero(mod(mantissa, 100)) {
                    mantissa := div(mantissa, 100)
                    exponent := add(exponent, 2)
                }
                if iszero(mod(mantissa, 10)) {
                    mantissa := div(mantissa, 10)
                    exponent := add(exponent, 1)
                }
            }
        }
    }

    /// @dev Convenience function for packing `x` into a smaller number using `sci`.
    /// The `mantissa` will be in bits [7..255] (the upper 249 bits).
    /// The `exponent` will be in bits [0..6] (the lower 7 bits).
    /// Use `SafeCastLib` to safely ensure that the `packed` number is small
    /// enough to fit in the desired unsigned integer type:
    /// ```
    ///     uint32 packed = SafeCastLib.toUint32(FixedPointMathLib.packSci(777 ether));
    /// ```
    function packSci(uint256 x) internal pure returns (uint256 packed) {
        (x, packed) = sci(x); // Reuse for `mantissa` and `exponent`.
        /// @solidity memory-safe-assembly
        assembly {
            if shr(249, x) {
                mstore(0x00, 0xce30380c) // `MantissaOverflow()`.
                revert(0x1c, 0x04)
            }
            packed := or(shl(7, x), packed)
        }
    }

    /// @dev Convenience function for unpacking a packed number from `packSci`.
    function unpackSci(uint256 packed) internal pure returns (uint256 unpacked) {
        unchecked {
            unpacked = (packed >> 7) * 10 ** (packed & 0x7f);
        }
    }

    /// @dev Returns the average of `x` and `y`. Rounds towards zero.
    function avg(uint256 x, uint256 y) internal pure returns (uint256 z) {
        unchecked {
            z = (x & y) + ((x ^ y) >> 1);
        }
    }

    /// @dev Returns the average of `x` and `y`. Rounds towards negative infinity.
    function avg(int256 x, int256 y) internal pure returns (int256 z) {
        unchecked {
            z = (x >> 1) + (y >> 1) + (x & y & 1);
        }
    }

    /// @dev Returns the absolute value of `x`.
    function abs(int256 x) internal pure returns (uint256 z) {
        unchecked {
            z = (uint256(x) + uint256(x >> 255)) ^ uint256(x >> 255);
        }
    }

    /// @dev Returns the absolute distance between `x` and `y`.
    function dist(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := add(xor(sub(0, gt(x, y)), sub(y, x)), gt(x, y))
        }
    }

    /// @dev Returns the absolute distance between `x` and `y`.
    function dist(int256 x, int256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := add(xor(sub(0, sgt(x, y)), sub(y, x)), sgt(x, y))
        }
    }

    /// @dev Returns the minimum of `x` and `y`.
    function min(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := xor(x, mul(xor(x, y), lt(y, x)))
        }
    }

    /// @dev Returns the minimum of `x` and `y`.
    function min(int256 x, int256 y) internal pure returns (int256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := xor(x, mul(xor(x, y), slt(y, x)))
        }
    }

    /// @dev Returns the maximum of `x` and `y`.
    function max(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := xor(x, mul(xor(x, y), gt(y, x)))
        }
    }

    /// @dev Returns the maximum of `x` and `y`.
    function max(int256 x, int256 y) internal pure returns (int256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := xor(x, mul(xor(x, y), sgt(y, x)))
        }
    }

    /// @dev Returns `x`, bounded to `minValue` and `maxValue`.
    function clamp(uint256 x, uint256 minValue, uint256 maxValue)
        internal
        pure
        returns (uint256 z)
    {
        /// @solidity memory-safe-assembly
        assembly {
            z := xor(x, mul(xor(x, minValue), gt(minValue, x)))
            z := xor(z, mul(xor(z, maxValue), lt(maxValue, z)))
        }
    }

    /// @dev Returns `x`, bounded to `minValue` and `maxValue`.
    function clamp(int256 x, int256 minValue, int256 maxValue) internal pure returns (int256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := xor(x, mul(xor(x, minValue), sgt(minValue, x)))
            z := xor(z, mul(xor(z, maxValue), slt(maxValue, z)))
        }
    }

    /// @dev Returns greatest common divisor of `x` and `y`.
    function gcd(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            for { z := x } y {} {
                let t := y
                y := mod(z, y)
                z := t
            }
        }
    }

    /// @dev Returns `a + (b - a) * (t - begin) / (end - begin)`,
    /// with `t` clamped between `begin` and `end` (inclusive).
    /// Agnostic to the order of (`a`, `b`) and (`end`, `begin`).
    /// If `begins == end`, returns `t <= begin ? a : b`.
    function lerp(uint256 a, uint256 b, uint256 t, uint256 begin, uint256 end)
        internal
        pure
        returns (uint256)
    {
        if (begin > end) (t, begin, end) = (~t, ~begin, ~end);
        if (t <= begin) return a;
        if (t >= end) return b;
        unchecked {
            if (b >= a) return a + fullMulDiv(b - a, t - begin, end - begin);
            return a - fullMulDiv(a - b, t - begin, end - begin);
        }
    }

    /// @dev Returns `a + (b - a) * (t - begin) / (end - begin)`.
    /// with `t` clamped between `begin` and `end` (inclusive).
    /// Agnostic to the order of (`a`, `b`) and (`end`, `begin`).
    /// If `begins == end`, returns `t <= begin ? a : b`.
    function lerp(int256 a, int256 b, int256 t, int256 begin, int256 end)
        internal
        pure
        returns (int256)
    {
        if (begin > end) (t, begin, end) = (~t, ~begin, ~end);
        if (t <= begin) return a;
        if (t >= end) return b;
        // forgefmt: disable-next-item
        unchecked {
            if (b >= a) return int256(uint256(a) + fullMulDiv(uint256(b - a),
                uint256(t - begin), uint256(end - begin)));
            return int256(uint256(a) - fullMulDiv(uint256(a - b),
                uint256(t - begin), uint256(end - begin)));
        }
    }

    /// @dev Returns if `x` is an even number. Some people may need this.
    function isEven(uint256 x) internal pure returns (bool) {
        return x & uint256(1) == uint256(0);
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                   RAW NUMBER OPERATIONS                    */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Returns `x + y`, without checking for overflow.
    function rawAdd(uint256 x, uint256 y) internal pure returns (uint256 z) {
        unchecked {
            z = x + y;
        }
    }

    /// @dev Returns `x + y`, without checking for overflow.
    function rawAdd(int256 x, int256 y) internal pure returns (int256 z) {
        unchecked {
            z = x + y;
        }
    }

    /// @dev Returns `x - y`, without checking for underflow.
    function rawSub(uint256 x, uint256 y) internal pure returns (uint256 z) {
        unchecked {
            z = x - y;
        }
    }

    /// @dev Returns `x - y`, without checking for underflow.
    function rawSub(int256 x, int256 y) internal pure returns (int256 z) {
        unchecked {
            z = x - y;
        }
    }

    /// @dev Returns `x * y`, without checking for overflow.
    function rawMul(uint256 x, uint256 y) internal pure returns (uint256 z) {
        unchecked {
            z = x * y;
        }
    }

    /// @dev Returns `x * y`, without checking for overflow.
    function rawMul(int256 x, int256 y) internal pure returns (int256 z) {
        unchecked {
            z = x * y;
        }
    }

    /// @dev Returns `x / y`, returning 0 if `y` is zero.
    function rawDiv(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := div(x, y)
        }
    }

    /// @dev Returns `x / y`, returning 0 if `y` is zero.
    function rawSDiv(int256 x, int256 y) internal pure returns (int256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := sdiv(x, y)
        }
    }

    /// @dev Returns `x % y`, returning 0 if `y` is zero.
    function rawMod(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := mod(x, y)
        }
    }

    /// @dev Returns `x % y`, returning 0 if `y` is zero.
    function rawSMod(int256 x, int256 y) internal pure returns (int256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := smod(x, y)
        }
    }

    /// @dev Returns `(x + y) % d`, return 0 if `d` if zero.
    function rawAddMod(uint256 x, uint256 y, uint256 d) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := addmod(x, y, d)
        }
    }

    /// @dev Returns `(x * y) % d`, return 0 if `d` if zero.
    function rawMulMod(uint256 x, uint256 y, uint256 d) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := mulmod(x, y, d)
        }
    }
}