// File: @1inch/erc20-pods/contracts/interfaces/IERC20Pods.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

import "@openzeppelin/contracts/token/ERC20/IERC20.sol";

interface IERC20Pods is IERC20 {
    event PodAdded(address account, address pod);
    event PodRemoved(address account, address pod);

    function hasPod(address account, address pod) external view returns(bool);
    function podsCount(address account) external view returns(uint256);
    function podAt(address account, uint256 index) external view returns(address);
    function pods(address account) external view returns(address[] memory);
    function podBalanceOf(address pod, address account) external view returns(uint256);

    function addPod(address pod) external;
    function removePod(address pod) external;
    function removeAllPods() external;
}

// File: @1inch/erc20-pods/contracts/interfaces/IPod.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

interface IPod {
    function updateBalances(address from, address to, uint256 amount) external;
}

// File: @1inch/erc20-pods/contracts/Pod.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

import "./interfaces/IPod.sol";
import "./interfaces/IERC20Pods.sol";

abstract contract Pod is IPod {
    error AccessDenied();

    IERC20Pods public immutable token;

    modifier onlyToken {
        if (msg.sender != address(token)) revert AccessDenied();
        _;
    }

    constructor(IERC20Pods token_) {
        token = token_;
    }

    function updateBalances(address from, address to, uint256 amount) external onlyToken {
        _updateBalances(from, to, amount);
    }

    function _updateBalances(address from, address to, uint256 amount) internal virtual;
}

// File: @1inch/farming/contracts/accounting/FarmAccounting.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

import "@openzeppelin/contracts/utils/math/Math.sol";

library FarmAccounting {
    error ZeroDuration();
    error DurationTooLarge();
    error AmountTooLarge();

    struct Info {
        uint40 finished;
        uint32 duration;
        uint184 reward;
    }

    uint256 internal constant _MAX_REWARD_AMOUNT = 1e32;  // 108 bits
    uint256 internal constant _SCALE = 1e18;  // 60 bits

    /// @dev Requires extra 18 decimals for precision, result fits in 168 bits
    function farmedSinceCheckpointScaled(Info memory info, uint256 checkpoint) internal view returns(uint256 amount) {
        unchecked {
            if (info.duration > 0) {
                uint256 elapsed = Math.min(block.timestamp, info.finished) - Math.min(checkpoint, info.finished);
                // size of (type(uint32).max * _MAX_REWARD_AMOUNT * _SCALE) is less than 200 bits, so there is no overflow
                return elapsed * info.reward * _SCALE / info.duration;
            }
        }
    }

    function startFarming(Info storage info, uint256 amount, uint256 period) internal returns(uint256) {
        if (period == 0) revert ZeroDuration();
        if (period > type(uint32).max) revert DurationTooLarge();
        if (amount > _MAX_REWARD_AMOUNT) revert AmountTooLarge();

        // If something left from prev farming add it to the new farming
        Info memory prev = info;
        if (block.timestamp < prev.finished) {
            amount += prev.reward - farmedSinceCheckpointScaled(prev, prev.finished - prev.duration) / _SCALE;
        }

        (info.finished, info.duration, info.reward) = (uint40(block.timestamp + period), uint32(period), uint184(amount));
        return amount;
    }
}

// File: @1inch/farming/contracts/accounting/UserAccounting.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

import "./FarmAccounting.sol";

library UserAccounting {
    struct Info {
        uint40 checkpoint;
        uint216 farmedPerTokenStored;
        mapping(address => int256) corrections;
    }

    function farmedPerToken(
        Info storage info,
        bytes32 context,
        function(bytes32) internal view returns(uint256) lazyGetSupply,
        function(bytes32, uint256) internal view returns(uint256) lazyGetFarmed
    ) internal view returns(uint256) {
        (uint256 checkpoint, uint256 fpt) = (info.checkpoint, info.farmedPerTokenStored);
        if (block.timestamp != checkpoint) {
            uint256 supply = lazyGetSupply(context);
            if (supply > 0) {
                // fpt increases by 168 bit / supply
                unchecked { fpt += lazyGetFarmed(context, checkpoint) / supply; }
            }
        }
        return fpt;
    }

    function farmed(Info storage info, address account, uint256 balance, uint256 fpt) internal view returns(uint256) {
        // balance * fpt is less than 168 bit
        return uint256(int256(balance * fpt) - info.corrections[account]) / FarmAccounting._SCALE;
    }

    function eraseFarmed(Info storage info, address account, uint256 balance, uint256 fpt) internal {
        // balance * fpt is less than 168 bit
        info.corrections[account] = int256(balance * fpt);
    }

    function updateFarmedPerToken(Info storage info, uint256 fpt) internal {
        (info.checkpoint, info.farmedPerTokenStored) = (uint40(block.timestamp), uint216(fpt));
    }

    function updateBalances(Info storage info, address from, address to, uint256 amount, uint256 fpt) internal {
        bool fromZero = (from == address(0));
        bool toZero = (to == address(0));
        if (amount > 0 && from != to) {
            if (fromZero || toZero) {
                updateFarmedPerToken(info, fpt);
            }

            // fpt is less than 168 bit, so amount should be less 98 bit
            int256 diff = int256(amount * fpt);
            if (!fromZero) {
                info.corrections[from] -= diff;
            }
            if (!toZero) {
                info.corrections[to] += diff;
            }
        }
    }
}

// File: @1inch/farming/contracts/FarmingLib.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

import "./accounting/FarmAccounting.sol";
import "./accounting/UserAccounting.sol";

library FarmingLib {
    using FarmAccounting for FarmAccounting.Info;
    using UserAccounting for UserAccounting.Info;
    using FarmingLib for FarmingLib.Info;

    struct Data {
        FarmAccounting.Info farmInfo;
        UserAccounting.Info userInfo;
    }

    struct Info {
        function() internal view returns(uint256) getTotalSupply;
        bytes32 dataSlot;
    }

    function makeInfo(function() internal view returns(uint256) getTotalSupply, Data storage data) internal pure returns(Info memory info) {
        info.getTotalSupply = getTotalSupply;
        bytes32 dataSlot;
        assembly {  // solhint-disable-line no-inline-assembly
            dataSlot := data.slot
        }
        info.dataSlot = dataSlot;
    }

    function getData(Info memory self) internal pure returns(Data storage data) {
        bytes32 dataSlot = self.dataSlot;
        assembly {  // solhint-disable-line no-inline-assembly
            data.slot := dataSlot
        }
    }

    function startFarming(Info memory self, uint256 amount, uint256 period) internal returns(uint256 reward) {
        Data storage data = self.getData();
        data.userInfo.updateFarmedPerToken(_farmedPerToken(self));
        reward = data.farmInfo.startFarming(amount, period);
    }

    function farmed(Info memory self, address account, uint256 balance) internal view returns(uint256) {
        return self.getData().userInfo.farmed(account, balance, _farmedPerToken(self));
    }

    function claim(Info memory self, address account, uint256 balance) internal returns(uint256 amount) {
        Data storage data = self.getData();
        uint256 fpt = _farmedPerToken(self);
        amount = data.userInfo.farmed(account, balance, fpt);
        if (amount > 0) {
            data.userInfo.eraseFarmed(account, balance, fpt);
        }
    }

    function updateBalances(Info memory self, address from, address to, uint256 amount) internal {
        self.getData().userInfo.updateBalances(from, to, amount, _farmedPerToken(self));
    }

    function _farmedPerToken(Info memory self) private view returns (uint256) {
        return self.getData().userInfo.farmedPerToken(_infoToContext(self), _lazyGetSupply, _lazyGetFarmed);
    }

    // UserAccounting bindings

    function _lazyGetSupply(bytes32 context) private view returns(uint256) {
        Info memory self = _contextToInfo(context);
        return self.getTotalSupply();
    }

    function _lazyGetFarmed(bytes32 context, uint256 checkpoint) private view returns(uint256) {
        Info memory self = _contextToInfo(context);
        return self.getData().farmInfo.farmedSinceCheckpointScaled(checkpoint);
    }

    function _contextToInfo(bytes32 context) private pure returns(Info memory self) {
        assembly {  // solhint-disable-line no-inline-assembly
            self := context
        }
    }

    function _infoToContext(Info memory self) private pure returns(bytes32 context) {
        assembly {  // solhint-disable-line no-inline-assembly
            context := self
        }
    }
}

// File: @1inch/farming/contracts/FarmingPod.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

import "@openzeppelin/contracts/access/Ownable.sol";
import "@openzeppelin/contracts/utils/Address.sol";
import "@1inch/solidity-utils/contracts/libraries/SafeERC20.sol";
import "@1inch/erc20-pods/contracts/Pod.sol";
import "@1inch/erc20-pods/contracts/interfaces/IERC20Pods.sol";

import "./interfaces/IFarmingPod.sol";
import "./FarmingLib.sol";

contract FarmingPod is Pod, IFarmingPod, Ownable {
    using SafeERC20 for IERC20;
    using FarmingLib for FarmingLib.Info;
    using Address for address payable;

    error ZeroFarmableTokenAddress();
    error ZeroRewardsTokenAddress();
    error SameDistributor();

    IERC20 public immutable rewardsToken;

    address private _distributor;
    uint256 private _totalSupply;
    FarmingLib.Data private _farm;

    modifier onlyDistributor {
        if (msg.sender != _distributor) revert AccessDenied();
        _;
    }

    constructor(IERC20Pods farmableToken_, IERC20 rewardsToken_)
        Pod(farmableToken_)
    {
        if (address(farmableToken_) == address(0)) revert ZeroFarmableTokenAddress();
        if (address(rewardsToken_) == address(0)) revert ZeroRewardsTokenAddress();
        rewardsToken = rewardsToken_;
        emit FarmCreated(address(farmableToken_), address(rewardsToken_));
    }

    function farmInfo() public view returns(FarmAccounting.Info memory) {
        return _farm.farmInfo;
    }

    function totalSupply() public view returns(uint256) {
        return _totalSupply;
    }

    function distributor() public view returns(address) {
        return _distributor;
    }

    function setDistributor(address distributor_) public virtual onlyOwner {
        address oldDistributor = _distributor;
        if (distributor_ == oldDistributor) revert SameDistributor();
        emit DistributorChanged(oldDistributor, distributor_);
        _distributor = distributor_;
    }

    function startFarming(uint256 amount, uint256 period) public virtual onlyDistributor {
        uint256 reward = _makeInfo().startFarming(amount, period);
        emit RewardAdded(reward, period);
        rewardsToken.safeTransferFrom(msg.sender, address(this), amount);
    }

    function farmed(address account) public view virtual returns(uint256) {
        uint256 balance = IERC20Pods(token).podBalanceOf(address(this), account);
        return _makeInfo().farmed(account, balance);
    }

    function claim() public virtual {
        uint256 podBalance = IERC20Pods(token).podBalanceOf(address(this), msg.sender);
        uint256 amount = _makeInfo().claim(msg.sender, podBalance);
        if (amount > 0) {
            _transferReward(rewardsToken, msg.sender, amount);
        }
    }

    function _transferReward(IERC20 reward, address to, uint256 amount) internal virtual {
        reward.safeTransfer(to, amount);
    }

    function _updateBalances(address from, address to, uint256 amount) internal virtual override {
        _makeInfo().updateBalances(from, to, amount);
        if (from == address(0)) {
            _totalSupply += amount;
        }
        if (to == address(0)) {
            _totalSupply -= amount;
        }
    }

    function rescueFunds(IERC20 token, uint256 amount) public virtual onlyDistributor {
        if(token == IERC20(address(0))) {
            payable(_distributor).sendValue(amount);
        } else {
            token.safeTransfer(_distributor, amount);
        }
    }

    function _makeInfo() private view returns(FarmingLib.Info memory) {
        return FarmingLib.makeInfo(totalSupply, _farm);
    }
}

// File: @1inch/farming/contracts/interfaces/IFarmingPod.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

import "@openzeppelin/contracts/token/ERC20/IERC20.sol";
import "@1inch/erc20-pods/contracts/interfaces/IPod.sol";
import "../accounting/FarmAccounting.sol";

interface IFarmingPod is IPod {
    event FarmCreated(address token, address reward);
    event DistributorChanged(address oldDistributor, address newDistributor);
    event RewardAdded(uint256 reward, uint256 duration);

    // View functions
    function totalSupply() external view returns(uint256);
    function distributor() external view returns(address);
    function farmInfo() external view returns(FarmAccounting.Info memory);
    function farmed(address account) external view returns(uint256);

    // User functions
    function claim() external;

    // Owner functions
    function setDistributor(address distributor_) external;

    // Distributor functions
    function startFarming(uint256 amount, uint256 period) external;
    function rescueFunds(IERC20 token, uint256 amount) external;
}

// File: @1inch/solidity-utils/contracts/interfaces/IDaiLikePermit.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;
pragma abicoder v1;

interface IDaiLikePermit {
    function permit(
        address holder,
        address spender,
        uint256 nonce,
        uint256 expiry,
        bool allowed,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) external;
}

// File: @1inch/solidity-utils/contracts/libraries/RevertReasonForwarder.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;
pragma abicoder v1;

/// @title Revert reason forwarder.
library RevertReasonForwarder {
    /// @dev Forwards latest externall call revert.
    function reRevert() internal pure {
        // bubble up revert reason from latest external call
        /// @solidity memory-safe-assembly
        assembly { // solhint-disable-line no-inline-assembly
            let ptr := mload(0x40)
            returndatacopy(ptr, 0, returndatasize())
            revert(ptr, returndatasize())
        }
    }
}

// File: @1inch/solidity-utils/contracts/libraries/SafeERC20.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;
pragma abicoder v1;

import "@openzeppelin/contracts/token/ERC20/IERC20.sol";
import "@openzeppelin/contracts/token/ERC20/extensions/draft-IERC20Permit.sol";
import "../interfaces/IDaiLikePermit.sol";
import "../libraries/RevertReasonForwarder.sol";

/// @title Implements efficient safe methods for ERC20 interface.
library SafeERC20 {
    error SafeTransferFailed();
    error SafeTransferFromFailed();
    error ForceApproveFailed();
    error SafeIncreaseAllowanceFailed();
    error SafeDecreaseAllowanceFailed();
    error SafePermitBadLength();

    /// @dev Ensures method do not revert or return boolean `true`, admits call to non-smart-contract.
    function safeTransferFrom(
        IERC20 token,
        address from,
        address to,
        uint256 amount
    ) internal {
        bytes4 selector = token.transferFrom.selector;
        bool success;
        /// @solidity memory-safe-assembly
        assembly { // solhint-disable-line no-inline-assembly
            let data := mload(0x40)

            mstore(data, selector)
            mstore(add(data, 0x04), from)
            mstore(add(data, 0x24), to)
            mstore(add(data, 0x44), amount)
            success := call(gas(), token, 0, data, 100, 0x0, 0x20)
            if success {
                switch returndatasize()
                case 0 {
                    success := gt(extcodesize(token), 0)
                }
                default {
                    success := and(gt(returndatasize(), 31), eq(mload(0), 1))
                }
            }
        }
        if (!success) revert SafeTransferFromFailed();
    }

    /// @dev Ensures method do not revert or return boolean `true`, admits call to non-smart-contract.
    function safeTransfer(
        IERC20 token,
        address to,
        uint256 value
    ) internal {
        if (!_makeCall(token, token.transfer.selector, to, value)) {
            revert SafeTransferFailed();
        }
    }

    /// @dev If `approve(from, to, amount)` fails, try to `approve(from, to, 0)` before retry.
    function forceApprove(
        IERC20 token,
        address spender,
        uint256 value
    ) internal {
        if (!_makeCall(token, token.approve.selector, spender, value)) {
            if (
                !_makeCall(token, token.approve.selector, spender, 0) ||
                !_makeCall(token, token.approve.selector, spender, value)
            ) {
                revert ForceApproveFailed();
            }
        }
    }

    /// @dev Allowance increase with safe math check.
    function safeIncreaseAllowance(
        IERC20 token,
        address spender,
        uint256 value
    ) internal {
        uint256 allowance = token.allowance(address(this), spender);
        if (value > type(uint256).max - allowance) revert SafeIncreaseAllowanceFailed();
        forceApprove(token, spender, allowance + value);
    }

    /// @dev Allowance decrease with safe math check.
    function safeDecreaseAllowance(
        IERC20 token,
        address spender,
        uint256 value
    ) internal {
        uint256 allowance = token.allowance(address(this), spender);
        if (value > allowance) revert SafeDecreaseAllowanceFailed();
        forceApprove(token, spender, allowance - value);
    }

    /// @dev Calls either ERC20 or Dai `permit` for `token`, if unsuccessful forwards revert from external call.
    function safePermit(IERC20 token, bytes calldata permit) internal {
        if (!tryPermit(token, permit)) RevertReasonForwarder.reRevert();
    }

    function tryPermit(IERC20 token, bytes calldata permit) internal returns(bool) {
        if (permit.length == 32 * 7) {
            return _makeCalldataCall(token, IERC20Permit.permit.selector, permit);
        }
        if (permit.length == 32 * 8) {
            return _makeCalldataCall(token, IDaiLikePermit.permit.selector, permit);
        }
        revert SafePermitBadLength();
    }

    function _makeCall(
        IERC20 token,
        bytes4 selector,
        address to,
        uint256 amount
    ) private returns (bool success) {
        /// @solidity memory-safe-assembly
        assembly { // solhint-disable-line no-inline-assembly
            let data := mload(0x40)

            mstore(data, selector)
            mstore(add(data, 0x04), to)
            mstore(add(data, 0x24), amount)
            success := call(gas(), token, 0, data, 0x44, 0x0, 0x20)
            if success {
                switch returndatasize()
                case 0 {
                    success := gt(extcodesize(token), 0)
                }
                default {
                    success := and(gt(returndatasize(), 31), eq(mload(0), 1))
                }
            }
        }
    }

    function _makeCalldataCall(
        IERC20 token,
        bytes4 selector,
        bytes calldata args
    ) private returns (bool success) {
        /// @solidity memory-safe-assembly
        assembly { // solhint-disable-line no-inline-assembly
            let len := add(4, args.length)
            let data := mload(0x40)

            mstore(data, selector)
            calldatacopy(add(data, 0x04), args.offset, args.length)
            success := call(gas(), token, 0, data, len, 0x0, 0x20)
            if success {
                switch returndatasize()
                case 0 {
                    success := gt(extcodesize(token), 0)
                }
                default {
                    success := and(gt(returndatasize(), 31), eq(mload(0), 1))
                }
            }
        }
    }
}

// File: @openzeppelin/contracts/access/Ownable.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (access/Ownable.sol)

pragma solidity ^0.8.0;

import "../utils/Context.sol";

/**
 * @dev Contract module which provides a basic access control mechanism, where
 * there is an account (an owner) that can be granted exclusive access to
 * specific functions.
 *
 * By default, the owner account will be the one that deploys the contract. This
 * can later be changed with {transferOwnership}.
 *
 * This module is used through inheritance. It will make available the modifier
 * `onlyOwner`, which can be applied to your functions to restrict their use to
 * the owner.
 */
abstract contract Ownable is Context {
    address private _owner;

    event OwnershipTransferred(address indexed previousOwner, address indexed newOwner);

    /**
     * @dev Initializes the contract setting the deployer as the initial owner.
     */
    constructor() {
        _transferOwnership(_msgSender());
    }

    /**
     * @dev Throws if called by any account other than the owner.
     */
    modifier onlyOwner() {
        _checkOwner();
        _;
    }

    /**
     * @dev Returns the address of the current owner.
     */
    function owner() public view virtual returns (address) {
        return _owner;
    }

    /**
     * @dev Throws if the sender is not the owner.
     */
    function _checkOwner() internal view virtual {
        require(owner() == _msgSender(), "Ownable: caller is not the owner");
    }

    /**
     * @dev Leaves the contract without owner. It will not be possible to call
     * `onlyOwner` functions anymore. Can only be called by the current owner.
     *
     * NOTE: Renouncing ownership will leave the contract without an owner,
     * thereby removing any functionality that is only available to the owner.
     */
    function renounceOwnership() public virtual onlyOwner {
        _transferOwnership(address(0));
    }

    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`).
     * Can only be called by the current owner.
     */
    function transferOwnership(address newOwner) public virtual onlyOwner {
        require(newOwner != address(0), "Ownable: new owner is the zero address");
        _transferOwnership(newOwner);
    }

    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`).
     * Internal function without access restriction.
     */
    function _transferOwnership(address newOwner) internal virtual {
        address oldOwner = _owner;
        _owner = newOwner;
        emit OwnershipTransferred(oldOwner, newOwner);
    }
}

// File: @openzeppelin/contracts/token/ERC20/extensions/draft-IERC20Permit.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (token/ERC20/extensions/draft-IERC20Permit.sol)

pragma solidity ^0.8.0;

/**
 * @dev Interface of the ERC20 Permit extension allowing approvals to be made via signatures, as defined in
 * https://eips.ethereum.org/EIPS/eip-2612[EIP-2612].
 *
 * Adds the {permit} method, which can be used to change an account's ERC20 allowance (see {IERC20-allowance}) by
 * presenting a message signed by the account. By not relying on {IERC20-approve}, the token holder account doesn't
 * need to send a transaction, and thus is not required to hold Ether at all.
 */
interface IERC20Permit {
    /**
     * @dev Sets `value` as the allowance of `spender` over ``owner``'s tokens,
     * given ``owner``'s signed approval.
     *
     * IMPORTANT: The same issues {IERC20-approve} has related to transaction
     * ordering also apply here.
     *
     * Emits an {Approval} event.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     * - `deadline` must be a timestamp in the future.
     * - `v`, `r` and `s` must be a valid `secp256k1` signature from `owner`
     * over the EIP712-formatted function arguments.
     * - the signature must use ``owner``'s current nonce (see {nonces}).
     *
     * For more information on the signature format, see the
     * https://eips.ethereum.org/EIPS/eip-2612#specification[relevant EIP
     * section].
     */
    function permit(
        address owner,
        address spender,
        uint256 value,
        uint256 deadline,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) external;

    /**
     * @dev Returns the current nonce for `owner`. This value must be
     * included whenever a signature is generated for {permit}.
     *
     * Every successful call to {permit} increases ``owner``'s nonce by one. This
     * prevents a signature from being used multiple times.
     */
    function nonces(address owner) external view returns (uint256);

    /**
     * @dev Returns the domain separator used in the encoding of the signature for {permit}, as defined by {EIP712}.
     */
    // solhint-disable-next-line func-name-mixedcase
    function DOMAIN_SEPARATOR() external view returns (bytes32);
}

// File: @openzeppelin/contracts/token/ERC20/IERC20.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.6.0) (token/ERC20/IERC20.sol)

pragma solidity ^0.8.0;

/**
 * @dev Interface of the ERC20 standard as defined in the EIP.
 */
interface IERC20 {
    /**
     * @dev Emitted when `value` tokens are moved from one account (`from`) to
     * another (`to`).
     *
     * Note that `value` may be zero.
     */
    event Transfer(address indexed from, address indexed to, uint256 value);

    /**
     * @dev Emitted when the allowance of a `spender` for an `owner` is set by
     * a call to {approve}. `value` is the new allowance.
     */
    event Approval(address indexed owner, address indexed spender, uint256 value);

    /**
     * @dev Returns the amount of tokens in existence.
     */
    function totalSupply() external view returns (uint256);

    /**
     * @dev Returns the amount of tokens owned by `account`.
     */
    function balanceOf(address account) external view returns (uint256);

    /**
     * @dev Moves `amount` tokens from the caller's account to `to`.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * Emits a {Transfer} event.
     */
    function transfer(address to, uint256 amount) external returns (bool);

    /**
     * @dev Returns the remaining number of tokens that `spender` will be
     * allowed to spend on behalf of `owner` through {transferFrom}. This is
     * zero by default.
     *
     * This value changes when {approve} or {transferFrom} are called.
     */
    function allowance(address owner, address spender) external view returns (uint256);

    /**
     * @dev Sets `amount` as the allowance of `spender` over the caller's tokens.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * IMPORTANT: Beware that changing an allowance with this method brings the risk
     * that someone may use both the old and the new allowance by unfortunate
     * transaction ordering. One possible solution to mitigate this race
     * condition is to first reduce the spender's allowance to 0 and set the
     * desired value afterwards:
     * https://github.com/ethereum/EIPs/issues/20#issuecomment-263524729
     *
     * Emits an {Approval} event.
     */
    function approve(address spender, uint256 amount) external returns (bool);

    /**
     * @dev Moves `amount` tokens from `from` to `to` using the
     * allowance mechanism. `amount` is then deducted from the caller's
     * allowance.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * Emits a {Transfer} event.
     */
    function transferFrom(
        address from,
        address to,
        uint256 amount
    ) external returns (bool);
}

// File: @openzeppelin/contracts/utils/Address.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (utils/Address.sol)

pragma solidity ^0.8.1;

/**
 * @dev Collection of functions related to the address type
 */
library Address {
    /**
     * @dev Returns true if `account` is a contract.
     *
     * [IMPORTANT]
     * ====
     * It is unsafe to assume that an address for which this function returns
     * false is an externally-owned account (EOA) and not a contract.
     *
     * Among others, `isContract` will return false for the following
     * types of addresses:
     *
     *  - an externally-owned account
     *  - a contract in construction
     *  - an address where a contract will be created
     *  - an address where a contract lived, but was destroyed
     * ====
     *
     * [IMPORTANT]
     * ====
     * You shouldn't rely on `isContract` to protect against flash loan attacks!
     *
     * Preventing calls from contracts is highly discouraged. It breaks composability, breaks support for smart wallets
     * like Gnosis Safe, and does not provide security since it can be circumvented by calling from a contract
     * constructor.
     * ====
     */
    function isContract(address account) internal view returns (bool) {
        // This method relies on extcodesize/address.code.length, which returns 0
        // for contracts in construction, since the code is only stored at the end
        // of the constructor execution.

        return account.code.length > 0;
    }

    /**
     * @dev Replacement for Solidity's `transfer`: sends `amount` wei to
     * `recipient`, forwarding all available gas and reverting on errors.
     *
     * https://eips.ethereum.org/EIPS/eip-1884[EIP1884] increases the gas cost
     * of certain opcodes, possibly making contracts go over the 2300 gas limit
     * imposed by `transfer`, making them unable to receive funds via
     * `transfer`. {sendValue} removes this limitation.
     *
     * https://diligence.consensys.net/posts/2019/09/stop-using-soliditys-transfer-now/[Learn more].
     *
     * IMPORTANT: because control is transferred to `recipient`, care must be
     * taken to not create reentrancy vulnerabilities. Consider using
     * {ReentrancyGuard} or the
     * https://solidity.readthedocs.io/en/v0.5.11/security-considerations.html#use-the-checks-effects-interactions-pattern[checks-effects-interactions pattern].
     */
    function sendValue(address payable recipient, uint256 amount) internal {
        require(address(this).balance >= amount, "Address: insufficient balance");

        (bool success, ) = recipient.call{value: amount}("");
        require(success, "Address: unable to send value, recipient may have reverted");
    }

    /**
     * @dev Performs a Solidity function call using a low level `call`. A
     * plain `call` is an unsafe replacement for a function call: use this
     * function instead.
     *
     * If `target` reverts with a revert reason, it is bubbled up by this
     * function (like regular Solidity function calls).
     *
     * Returns the raw returned data. To convert to the expected return value,
     * use https://solidity.readthedocs.io/en/latest/units-and-global-variables.html?highlight=abi.decode#abi-encoding-and-decoding-functions[`abi.decode`].
     *
     * Requirements:
     *
     * - `target` must be a contract.
     * - calling `target` with `data` must not revert.
     *
     * _Available since v3.1._
     */
    function functionCall(address target, bytes memory data) internal returns (bytes memory) {
        return functionCallWithValue(target, data, 0, "Address: low-level call failed");
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`], but with
     * `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal returns (bytes memory) {
        return functionCallWithValue(target, data, 0, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but also transferring `value` wei to `target`.
     *
     * Requirements:
     *
     * - the calling contract must have an ETH balance of at least `value`.
     * - the called Solidity function must be `payable`.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(
        address target,
        bytes memory data,
        uint256 value
    ) internal returns (bytes memory) {
        return functionCallWithValue(target, data, value, "Address: low-level call with value failed");
    }

    /**
     * @dev Same as {xref-Address-functionCallWithValue-address-bytes-uint256-}[`functionCallWithValue`], but
     * with `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(
        address target,
        bytes memory data,
        uint256 value,
        string memory errorMessage
    ) internal returns (bytes memory) {
        require(address(this).balance >= value, "Address: insufficient balance for call");
        (bool success, bytes memory returndata) = target.call{value: value}(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(address target, bytes memory data) internal view returns (bytes memory) {
        return functionStaticCall(target, data, "Address: low-level static call failed");
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal view returns (bytes memory) {
        (bool success, bytes memory returndata) = target.staticcall(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a delegate call.
     *
     * _Available since v3.4._
     */
    function functionDelegateCall(address target, bytes memory data) internal returns (bytes memory) {
        return functionDelegateCall(target, data, "Address: low-level delegate call failed");
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a delegate call.
     *
     * _Available since v3.4._
     */
    function functionDelegateCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal returns (bytes memory) {
        (bool success, bytes memory returndata) = target.delegatecall(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }

    /**
     * @dev Tool to verify that a low level call to smart-contract was successful, and revert (either by bubbling
     * the revert reason or using the provided one) in case of unsuccessful call or if target was not a contract.
     *
     * _Available since v4.8._
     */
    function verifyCallResultFromTarget(
        address target,
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) internal view returns (bytes memory) {
        if (success) {
            if (returndata.length == 0) {
                // only check isContract if the call was successful and the return data is empty
                // otherwise we already know that it was a contract
                require(isContract(target), "Address: call to non-contract");
            }
            return returndata;
        } else {
            _revert(returndata, errorMessage);
        }
    }

    /**
     * @dev Tool to verify that a low level call was successful, and revert if it wasn't, either by bubbling the
     * revert reason or using the provided one.
     *
     * _Available since v4.3._
     */
    function verifyCallResult(
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) internal pure returns (bytes memory) {
        if (success) {
            return returndata;
        } else {
            _revert(returndata, errorMessage);
        }
    }

    function _revert(bytes memory returndata, string memory errorMessage) private pure {
        // Look for revert reason and bubble it up if present
        if (returndata.length > 0) {
            // The easiest way to bubble the revert reason is using memory via assembly
            /// @solidity memory-safe-assembly
            assembly {
                let returndata_size := mload(returndata)
                revert(add(32, returndata), returndata_size)
            }
        } else {
            revert(errorMessage);
        }
    }
}

// File: @openzeppelin/contracts/utils/Context.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/Context.sol)

pragma solidity ^0.8.0;

/**
 * @dev Provides information about the current execution context, including the
 * sender of the transaction and its data. While these are generally available
 * via msg.sender and msg.data, they should not be accessed in such a direct
 * manner, since when dealing with meta-transactions the account sending and
 * paying for execution may not be the actual sender (as far as an application
 * is concerned).
 *
 * This contract is only required for intermediate, library-like contracts.
 */
abstract contract Context {
    function _msgSender() internal view virtual returns (address) {
        return msg.sender;
    }

    function _msgData() internal view virtual returns (bytes calldata) {
        return msg.data;
    }
}

// File: @openzeppelin/contracts/utils/math/Math.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (utils/math/Math.sol)

pragma solidity ^0.8.0;

/**
 * @dev Standard math utilities missing in the Solidity language.
 */
library Math {
    enum Rounding {
        Down, // Toward negative infinity
        Up, // Toward infinity
        Zero // Toward zero
    }

    /**
     * @dev Returns the largest of two numbers.
     */
    function max(uint256 a, uint256 b) internal pure returns (uint256) {
        return a > b ? a : b;
    }

    /**
     * @dev Returns the smallest of two numbers.
     */
    function min(uint256 a, uint256 b) internal pure returns (uint256) {
        return a < b ? a : b;
    }

    /**
     * @dev Returns the average of two numbers. The result is rounded towards
     * zero.
     */
    function average(uint256 a, uint256 b) internal pure returns (uint256) {
        // (a + b) / 2 can overflow.
        return (a & b) + (a ^ b) / 2;
    }

    /**
     * @dev Returns the ceiling of the division of two numbers.
     *
     * This differs from standard division with `/` in that it rounds up instead
     * of rounding down.
     */
    function ceilDiv(uint256 a, uint256 b) internal pure returns (uint256) {
        // (a + b - 1) / b can overflow on addition, so we distribute.
        return a == 0 ? 0 : (a - 1) / b + 1;
    }

    /**
     * @notice Calculates floor(x * y / denominator) with full precision. Throws if result overflows a uint256 or denominator == 0
     * @dev Original credit to Remco Bloemen under MIT license (https://xn--2-umb.com/21/muldiv)
     * with further edits by Uniswap Labs also under MIT license.
     */
    function mulDiv(
        uint256 x,
        uint256 y,
        uint256 denominator
    ) internal pure returns (uint256 result) {
        unchecked {
            // 512-bit multiply [prod1 prod0] = x * y. Compute the product mod 2^256 and mod 2^256 - 1, then use
            // use the Chinese Remainder Theorem to reconstruct the 512 bit result. The result is stored in two 256
            // variables such that product = prod1 * 2^256 + prod0.
            uint256 prod0; // Least significant 256 bits of the product
            uint256 prod1; // Most significant 256 bits of the product
            assembly {
                let mm := mulmod(x, y, not(0))
                prod0 := mul(x, y)
                prod1 := sub(sub(mm, prod0), lt(mm, prod0))
            }

            // Handle non-overflow cases, 256 by 256 division.
            if (prod1 == 0) {
                return prod0 / denominator;
            }

            // Make sure the result is less than 2^256. Also prevents denominator == 0.
            require(denominator > prod1);

            ///////////////////////////////////////////////
            // 512 by 256 division.
            ///////////////////////////////////////////////

            // Make division exact by subtracting the remainder from [prod1 prod0].
            uint256 remainder;
            assembly {
                // Compute remainder using mulmod.
                remainder := mulmod(x, y, denominator)

                // Subtract 256 bit number from 512 bit number.
                prod1 := sub(prod1, gt(remainder, prod0))
                prod0 := sub(prod0, remainder)
            }

            // Factor powers of two out of denominator and compute largest power of two divisor of denominator. Always >= 1.
            // See https://cs.stackexchange.com/q/138556/92363.

            // Does not overflow because the denominator cannot be zero at this stage in the function.
            uint256 twos = denominator & (~denominator + 1);
            assembly {
                // Divide denominator by twos.
                denominator := div(denominator, twos)

                // Divide [prod1 prod0] by twos.
                prod0 := div(prod0, twos)

                // Flip twos such that it is 2^256 / twos. If twos is zero, then it becomes one.
                twos := add(div(sub(0, twos), twos), 1)
            }

            // Shift in bits from prod1 into prod0.
            prod0 |= prod1 * twos;

            // Invert denominator mod 2^256. Now that denominator is an odd number, it has an inverse modulo 2^256 such
            // that denominator * inv = 1 mod 2^256. Compute the inverse by starting with a seed that is correct for
            // four bits. That is, denominator * inv = 1 mod 2^4.
            uint256 inverse = (3 * denominator) ^ 2;

            // Use the 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.
            inverse *= 2 - denominator * inverse; // inverse mod 2^8
            inverse *= 2 - denominator * inverse; // inverse mod 2^16
            inverse *= 2 - denominator * inverse; // inverse mod 2^32
            inverse *= 2 - denominator * inverse; // inverse mod 2^64
            inverse *= 2 - denominator * inverse; // inverse mod 2^128
            inverse *= 2 - denominator * inverse; // inverse mod 2^256

            // Because the division is now exact we can divide by multiplying with the modular inverse of denominator.
            // This will give us the correct result modulo 2^256. Since the preconditions guarantee that the outcome is
            // less than 2^256, this is the final result. We don't need to compute the high bits of the result and prod1
            // is no longer required.
            result = prod0 * inverse;
            return result;
        }
    }

    /**
     * @notice Calculates x * y / denominator with full precision, following the selected rounding direction.
     */
    function mulDiv(
        uint256 x,
        uint256 y,
        uint256 denominator,
        Rounding rounding
    ) internal pure returns (uint256) {
        uint256 result = mulDiv(x, y, denominator);
        if (rounding == Rounding.Up && mulmod(x, y, denominator) > 0) {
            result += 1;
        }
        return result;
    }

    /**
     * @dev Returns the square root of a number. If the number is not a perfect square, the value is rounded down.
     *
     * Inspired by Henry S. Warren, Jr.'s "Hacker's Delight" (Chapter 11).
     */
    function sqrt(uint256 a) internal pure returns (uint256) {
        if (a == 0) {
            return 0;
        }

        // For our first guess, we get the biggest power of 2 which is smaller than the square root of the target.
        //
        // We know that the "msb" (most significant bit) of our target number `a` is a power of 2 such that we have
        // `msb(a) <= a < 2*msb(a)`. This value can be written `msb(a)=2**k` with `k=log2(a)`.
        //
        // This can be rewritten `2**log2(a) <= a < 2**(log2(a) + 1)`
        // → `sqrt(2**k) <= sqrt(a) < sqrt(2**(k+1))`
        // → `2**(k/2) <= sqrt(a) < 2**((k+1)/2) <= 2**(k/2 + 1)`
        //
        // Consequently, `2**(log2(a) / 2)` is a good first approximation of `sqrt(a)` with at least 1 correct bit.
        uint256 result = 1 << (log2(a) >> 1);

        // At this point `result` is an estimation with one bit of precision. We know the true value is a uint128,
        // since it is the square root of a uint256. Newton's method converges quadratically (precision doubles at
        // every iteration). We thus need at most 7 iteration to turn our partial result with one bit of precision
        // into the expected uint128 result.
        unchecked {
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            return min(result, a / result);
        }
    }

    /**
     * @notice Calculates sqrt(a), following the selected rounding direction.
     */
    function sqrt(uint256 a, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = sqrt(a);
            return result + (rounding == Rounding.Up && result * result < a ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 2, rounded down, of a positive value.
     * Returns 0 if given 0.
     */
    function log2(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >> 128 > 0) {
                value >>= 128;
                result += 128;
            }
            if (value >> 64 > 0) {
                value >>= 64;
                result += 64;
            }
            if (value >> 32 > 0) {
                value >>= 32;
                result += 32;
            }
            if (value >> 16 > 0) {
                value >>= 16;
                result += 16;
            }
            if (value >> 8 > 0) {
                value >>= 8;
                result += 8;
            }
            if (value >> 4 > 0) {
                value >>= 4;
                result += 4;
            }
            if (value >> 2 > 0) {
                value >>= 2;
                result += 2;
            }
            if (value >> 1 > 0) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 2, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log2(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log2(value);
            return result + (rounding == Rounding.Up && 1 << result < value ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 10, rounded down, of a positive value.
     * Returns 0 if given 0.
     */
    function log10(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >= 10**64) {
                value /= 10**64;
                result += 64;
            }
            if (value >= 10**32) {
                value /= 10**32;
                result += 32;
            }
            if (value >= 10**16) {
                value /= 10**16;
                result += 16;
            }
            if (value >= 10**8) {
                value /= 10**8;
                result += 8;
            }
            if (value >= 10**4) {
                value /= 10**4;
                result += 4;
            }
            if (value >= 10**2) {
                value /= 10**2;
                result += 2;
            }
            if (value >= 10**1) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 10, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log10(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log10(value);
            return result + (rounding == Rounding.Up && 10**result < value ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 256, rounded down, of a positive value.
     * Returns 0 if given 0.
     *
     * Adding one to the result gives the number of pairs of hex symbols needed to represent `value` as a hex string.
     */
    function log256(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >> 128 > 0) {
                value >>= 128;
                result += 16;
            }
            if (value >> 64 > 0) {
                value >>= 64;
                result += 8;
            }
            if (value >> 32 > 0) {
                value >>= 32;
                result += 4;
            }
            if (value >> 16 > 0) {
                value >>= 16;
                result += 2;
            }
            if (value >> 8 > 0) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 10, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log256(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log256(value);
            return result + (rounding == Rounding.Up && 1 << (result * 8) < value ? 1 : 0);
        }
    }
}