// File: @pooltogether/v4-twab-delegator/contracts/TWABDelegator.sol



// SPDX-License-Identifier: GPL-3.0

pragma solidity 0.8.6;

import "@openzeppelin/contracts/proxy/Clones.sol";
import "@openzeppelin/contracts/token/ERC20/IERC20.sol";
import "@openzeppelin/contracts/token/ERC20/ERC20.sol";
import "@openzeppelin/contracts/token/ERC20/utils/SafeERC20.sol";
import "@pooltogether/v4-core/contracts/interfaces/ITicket.sol";

import "./Delegation.sol";
import "./LowLevelDelegator.sol";
import "./PermitAndMulticall.sol";

/**
 * @title Delegate chances to win to multiple accounts.
 * @notice This contract allows accounts to easily delegate a portion of their tickets to multiple delegatees.
  The delegatees chance of winning prizes is increased by the delegated amount.
  If a delegator doesn't want to actively manage the delegations, then they can stake on the contract and appoint representatives.
 */
contract TWABDelegator is ERC20, LowLevelDelegator, PermitAndMulticall {
  using Address for address;
  using Clones for address;
  using SafeERC20 for IERC20;

  /* ============ Events ============ */

  /**
   * @notice Emitted when ticket associated with this contract has been set.
   * @param ticket Address of the ticket
   */
  event TicketSet(ITicket indexed ticket);

  /**
   * @notice Emitted when tickets have been staked.
   * @param delegator Address of the delegator
   * @param amount Amount of tickets staked
   */
  event TicketsStaked(address indexed delegator, uint256 amount);

  /**
   * @notice Emitted when tickets have been unstaked.
   * @param delegator Address of the delegator
   * @param recipient Address of the recipient that will receive the tickets
   * @param amount Amount of tickets unstaked
   */
  event TicketsUnstaked(address indexed delegator, address indexed recipient, uint256 amount);

  /**
   * @notice Emitted when a new delegation is created.
   * @param delegator Delegator of the delegation
   * @param slot Slot of the delegation
   * @param lockUntil Timestamp until which the delegation is locked
   * @param delegatee Address of the delegatee
   * @param delegation Address of the delegation that was created
   * @param user Address of the user who created the delegation
   */
  event DelegationCreated(
    address indexed delegator,
    uint256 indexed slot,
    uint96 lockUntil,
    address indexed delegatee,
    Delegation delegation,
    address user
  );

  /**
   * @notice Emitted when a delegatee is updated.
   * @param delegator Address of the delegator
   * @param slot Slot of the delegation
   * @param delegatee Address of the delegatee
   * @param lockUntil Timestamp until which the delegation is locked
   * @param user Address of the user who updated the delegatee
   */
  event DelegateeUpdated(
    address indexed delegator,
    uint256 indexed slot,
    address indexed delegatee,
    uint96 lockUntil,
    address user
  );

  /**
   * @notice Emitted when a delegation is funded.
   * @param delegator Address of the delegator
   * @param slot Slot of the delegation
   * @param amount Amount of tickets that were sent to the delegation
   * @param user Address of the user who funded the delegation
   */
  event DelegationFunded(
    address indexed delegator,
    uint256 indexed slot,
    uint256 amount,
    address indexed user
  );

  /**
   * @notice Emitted when a delegation is funded from the staked amount.
   * @param delegator Address of the delegator
   * @param slot Slot of the delegation
   * @param amount Amount of tickets that were sent to the delegation
   * @param user Address of the user who pulled funds from the delegator stake to the delegation
   */
  event DelegationFundedFromStake(
    address indexed delegator,
    uint256 indexed slot,
    uint256 amount,
    address indexed user
  );

  /**
   * @notice Emitted when an amount of tickets has been withdrawn from a delegation. The tickets are held by this contract and the delegator stake is increased.
   * @param delegator Address of the delegator
   * @param slot Slot of the delegation
   * @param amount Amount of tickets withdrawn
   * @param user Address of the user who withdrew the tickets
   */
  event WithdrewDelegationToStake(
    address indexed delegator,
    uint256 indexed slot,
    uint256 amount,
    address indexed user
  );

  /**
   * @notice Emitted when a delegator withdraws an amount of tickets from a delegation to a specified wallet.
   * @param delegator Address of the delegator
   * @param slot  Slot of the delegation
   * @param amount Amount of tickets withdrawn
   * @param to Recipient address of withdrawn tickets
   */
  event TransferredDelegation(
    address indexed delegator,
    uint256 indexed slot,
    uint256 amount,
    address indexed to
  );

  /**
   * @notice Emitted when a representative is set.
   * @param delegator Address of the delegator
   * @param representative Address of the representative
   * @param set Boolean indicating if the representative was set or unset
   */
  event RepresentativeSet(address indexed delegator, address indexed representative, bool set);

  /* ============ Variables ============ */

  /// @notice Prize pool ticket to which this contract is tied to.
  ITicket public immutable ticket;

  /// @notice Max lock time during which a delegation cannot be updated.
  uint256 public constant MAX_LOCK = 180 days;

  /**
   * @notice Representative elected by the delegator to handle delegation.
   * @dev Representative can only handle delegation and cannot withdraw tickets to their wallet.
   * @dev delegator => representative => bool allowing representative to represent the delegator
   */
  mapping(address => mapping(address => bool)) internal representatives;

  /* ============ Constructor ============ */

  /**
   * @notice Creates a new TWAB Delegator that is bound to the given ticket contract.
   * @param name_ The name for the staked ticket token
   * @param symbol_ The symbol for the staked ticket token
   * @param _ticket Address of the ticket contract
   */
  constructor(
    string memory name_,
    string memory symbol_,
    ITicket _ticket
  ) LowLevelDelegator() ERC20(name_, symbol_) {
    require(address(_ticket) != address(0), "TWABDelegator/tick-not-zero-addr");
    ticket = _ticket;

    emit TicketSet(_ticket);
  }

  /* ============ External Functions ============ */

  /**
   * @notice Stake `_amount` of tickets in this contract.
   * @dev Tickets can be staked on behalf of a `_to` user.
   * @param _to Address to which the stake will be attributed
   * @param _amount Amount of tickets to stake
   */
  function stake(address _to, uint256 _amount) external {
    _requireAmountGtZero(_amount);

    IERC20(ticket).safeTransferFrom(msg.sender, address(this), _amount);
    _mint(_to, _amount);

    emit TicketsStaked(_to, _amount);
  }

  /**
   * @notice Unstake `_amount` of tickets from this contract. Transfers ticket to the passed `_to` address.
   * @dev If delegator has delegated his whole stake, he will first have to withdraw from a delegation to be able to unstake.
   * @param _to Address of the recipient that will receive the tickets
   * @param _amount Amount of tickets to unstake
   */
  function unstake(address _to, uint256 _amount) external {
    _requireRecipientNotZeroAddress(_to);
    _requireAmountGtZero(_amount);

    _burn(msg.sender, _amount);

    IERC20(ticket).safeTransfer(_to, _amount);

    emit TicketsUnstaked(msg.sender, _to, _amount);
  }

  /**
   * @notice Creates a new delegation.
   This will create a new Delegation contract for the given slot and have it delegate its tickets to the given delegatee.
   If a non-zero lock duration is passed, then the delegatee cannot be changed, nor funding withdrawn, until the lock has expired.
   * @dev The `_delegator` and `_slot` params are used to compute the salt of the delegation
   * @param _delegator Address of the delegator that will be able to handle the delegation
   * @param _slot Slot of the delegation
   * @param _delegatee Address of the delegatee
   * @param _lockDuration Duration of time for which the delegation is locked. Must be less than the max duration.
   * @return Returns the address of the Delegation contract that will hold the tickets
   */
  function createDelegation(
    address _delegator,
    uint256 _slot,
    address _delegatee,
    uint96 _lockDuration
  ) external returns (Delegation) {
    _requireDelegatorOrRepresentative(_delegator);
    _requireDelegateeNotZeroAddress(_delegatee);
    _requireLockDuration(_lockDuration);

    uint96 _lockUntil = _computeLockUntil(_lockDuration);

    Delegation _delegation = _createDelegation(
      _computeSalt(_delegator, bytes32(_slot)),
      _lockUntil
    );

    _setDelegateeCall(_delegation, _delegatee);

    emit DelegationCreated(_delegator, _slot, _lockUntil, _delegatee, _delegation, msg.sender);

    return _delegation;
  }

  /**
   * @notice Updates the delegatee and lock duration for a delegation slot.
   * @dev Only callable by the `_delegator` or their representative.
   * @dev Will revert if delegation is still locked.
   * @param _delegator Address of the delegator
   * @param _slot Slot of the delegation
   * @param _delegatee Address of the delegatee
   * @param _lockDuration Duration of time during which the delegatee cannot be changed nor withdrawn
   * @return The address of the Delegation
   */
  function updateDelegatee(
    address _delegator,
    uint256 _slot,
    address _delegatee,
    uint96 _lockDuration
  ) external returns (Delegation) {
    _requireDelegatorOrRepresentative(_delegator);
    _requireDelegateeNotZeroAddress(_delegatee);
    _requireLockDuration(_lockDuration);

    Delegation _delegation = Delegation(_computeAddress(_delegator, _slot));
    _requireDelegationUnlocked(_delegation);

    uint96 _lockUntil = _computeLockUntil(_lockDuration);

    if (_lockDuration > 0) {
      _delegation.setLockUntil(_lockUntil);
    }

    _setDelegateeCall(_delegation, _delegatee);

    emit DelegateeUpdated(_delegator, _slot, _delegatee, _lockUntil, msg.sender);

    return _delegation;
  }

  /**
   * @notice Fund a delegation by transferring tickets from the caller to the delegation.
   * @dev Callable by anyone.
   * @dev Will revert if delegation does not exist.
   * @param _delegator Address of the delegator
   * @param _slot Slot of the delegation
   * @param _amount Amount of tickets to transfer
   * @return The address of the Delegation
   */
  function fundDelegation(
    address _delegator,
    uint256 _slot,
    uint256 _amount
  ) external returns (Delegation) {
    require(_delegator != address(0), "TWABDelegator/dlgtr-not-zero-adr");
    _requireAmountGtZero(_amount);

    Delegation _delegation = Delegation(_computeAddress(_delegator, _slot));
    IERC20(ticket).safeTransferFrom(msg.sender, address(_delegation), _amount);

    emit DelegationFunded(_delegator, _slot, _amount, msg.sender);

    return _delegation;
  }

  /**
   * @notice Fund a delegation using the `_delegator` stake.
   * @dev Callable only by the `_delegator` or a representative.
   * @dev Will revert if delegation does not exist.
   * @dev Will revert if `_amount` is greater than the staked amount.
   * @param _delegator Address of the delegator
   * @param _slot Slot of the delegation
   * @param _amount Amount of tickets to send to the delegation from the staked amount
   * @return The address of the Delegation
   */
  function fundDelegationFromStake(
    address _delegator,
    uint256 _slot,
    uint256 _amount
  ) external returns (Delegation) {
    _requireDelegatorOrRepresentative(_delegator);
    _requireAmountGtZero(_amount);

    Delegation _delegation = Delegation(_computeAddress(_delegator, _slot));

    _burn(_delegator, _amount);

    IERC20(ticket).safeTransfer(address(_delegation), _amount);

    emit DelegationFundedFromStake(_delegator, _slot, _amount, msg.sender);

    return _delegation;
  }

  /**
   * @notice Withdraw tickets from a delegation. The tickets will be held by this contract and the delegator's stake will increase.
   * @dev Only callable by the `_delegator` or a representative.
   * @dev Will send the tickets to this contract and increase the `_delegator` staked amount.
   * @dev Will revert if delegation is still locked.
   * @param _delegator Address of the delegator
   * @param _slot Slot of the delegation
   * @param _amount Amount of tickets to withdraw
   * @return The address of the Delegation
   */
  function withdrawDelegationToStake(
    address _delegator,
    uint256 _slot,
    uint256 _amount
  ) external returns (Delegation) {
    _requireDelegatorOrRepresentative(_delegator);

    Delegation _delegation = Delegation(_computeAddress(_delegator, _slot));

    _transfer(_delegation, address(this), _amount);

    _mint(_delegator, _amount);

    emit WithdrewDelegationToStake(_delegator, _slot, _amount, msg.sender);

    return _delegation;
  }

  /**
   * @notice Withdraw an `_amount` of tickets from a delegation. The delegator is assumed to be the caller.
   * @dev Tickets are sent directly to the passed `_to` address.
   * @dev Will revert if delegation is still locked.
   * @param _slot Slot of the delegation
   * @param _amount Amount to withdraw
   * @param _to Account to transfer the withdrawn tickets to
   * @return The address of the Delegation
   */
  function transferDelegationTo(
    uint256 _slot,
    uint256 _amount,
    address _to
  ) external returns (Delegation) {
    _requireRecipientNotZeroAddress(_to);

    Delegation _delegation = Delegation(_computeAddress(msg.sender, _slot));
    _transfer(_delegation, _to, _amount);

    emit TransferredDelegation(msg.sender, _slot, _amount, _to);

    return _delegation;
  }

  /**
   * @notice Allow an account to set or unset a `_representative` to handle delegation.
   * @dev If `_set` is `true`, `_representative` will be set as representative of `msg.sender`.
   * @dev If `_set` is `false`, `_representative` will be unset as representative of `msg.sender`.
   * @param _representative Address of the representative
   * @param _set Set or unset the representative
   */
  function setRepresentative(address _representative, bool _set) external {
    require(_representative != address(0), "TWABDelegator/rep-not-zero-addr");

    representatives[msg.sender][_representative] = _set;

    emit RepresentativeSet(msg.sender, _representative, _set);
  }

  /**
   * @notice Returns whether or not the given rep is a representative of the delegator.
   * @param _delegator The delegator
   * @param _representative The representative to check for
   * @return True if the rep is a rep, false otherwise
   */
  function isRepresentativeOf(address _delegator, address _representative)
    external
    view
    returns (bool)
  {
    return representatives[_delegator][_representative];
  }

  /**
   * @notice Allows a user to call multiple functions on the same contract.  Useful for EOA who wants to batch transactions.
   * @param _data An array of encoded function calls.  The calls must be abi-encoded calls to this contract.
   * @return The results from each function call
   */
  function multicall(bytes[] calldata _data) external returns (bytes[] memory) {
    return _multicall(_data);
  }

  /**
   * @notice Alow a user to approve ticket and run various calls in one transaction.
   * @param _amount Amount of tickets to approve
   * @param _permitSignature Permit signature
   * @param _data Datas to call with `functionDelegateCall`
   */
  function permitAndMulticall(
    uint256 _amount,
    Signature calldata _permitSignature,
    bytes[] calldata _data
  ) external {
    _permitAndMulticall(IERC20Permit(address(ticket)), _amount, _permitSignature, _data);
  }

  /**
   * @notice Allows the caller to easily get the details for a delegation.
   * @param _delegator The delegator address
   * @param _slot The delegation slot they are using
   * @return delegation The address that holds tickets for the delegation
   * @return delegatee The address that tickets are being delegated to
   * @return balance The balance of tickets in the delegation
   * @return lockUntil The timestamp at which the delegation unlocks
   * @return wasCreated Whether or not the delegation has been created
   */
  function getDelegation(address _delegator, uint256 _slot)
    external
    view
    returns (
      Delegation delegation,
      address delegatee,
      uint256 balance,
      uint256 lockUntil,
      bool wasCreated
    )
  {
    delegation = Delegation(_computeAddress(_delegator, _slot));
    wasCreated = address(delegation).isContract();
    delegatee = ticket.delegateOf(address(delegation));
    balance = ticket.balanceOf(address(delegation));

    if (wasCreated) {
      lockUntil = delegation.lockUntil();
    }
  }

  /**
   * @notice Computes the address of the delegation for the delegator + slot combination.
   * @param _delegator The user who is delegating tickets
   * @param _slot The delegation slot
   * @return The address of the delegation.  This is the address that holds the balance of tickets.
   */
  function computeDelegationAddress(address _delegator, uint256 _slot)
    external
    view
    returns (address)
  {
    return _computeAddress(_delegator, _slot);
  }

  /**
   * @notice Returns the ERC20 token decimals.
   * @dev This value is equal to the decimals of the ticket being delegated.
   * @return ERC20 token decimals
   */
  function decimals() public view virtual override returns (uint8) {
    return ERC20(address(ticket)).decimals();
  }

  /* ============ Internal Functions ============ */

  /**
   * @notice Computes the address of a delegation contract using the delegator and slot as a salt.
   The contract is a clone, also known as minimal proxy contract.
   * @param _delegator Address of the delegator
   * @param _slot Slot of the delegation
   * @return Address at which the delegation contract will be deployed
   */
  function _computeAddress(address _delegator, uint256 _slot) internal view returns (address) {
    return _computeAddress(_computeSalt(_delegator, bytes32(_slot)));
  }

  /**
   * @notice Computes the timestamp at which the delegation unlocks, after which the delegatee can be changed and tickets withdrawn.
   * @param _lockDuration The duration of the lock
   * @return The lock expiration timestamp
   */
  function _computeLockUntil(uint96 _lockDuration) internal view returns (uint96) {
    unchecked {
      return uint96(block.timestamp) + _lockDuration;
    }
  }

  /**
   * @notice Delegates tickets from the `_delegation` contract to the `_delegatee` address.
   * @param _delegation Address of the delegation contract
   * @param _delegatee Address of the delegatee
   */
  function _setDelegateeCall(Delegation _delegation, address _delegatee) internal {
    bytes4 _selector = ticket.delegate.selector;
    bytes memory _data = abi.encodeWithSelector(_selector, _delegatee);

    _executeCall(_delegation, _data);
  }

  /**
   * @notice Tranfers tickets from the Delegation contract to the `_to` address.
   * @param _delegation Address of the delegation contract
   * @param _to Address of the recipient
   * @param _amount Amount of tickets to transfer
   */
  function _transferCall(
    Delegation _delegation,
    address _to,
    uint256 _amount
  ) internal {
    bytes4 _selector = ticket.transfer.selector;
    bytes memory _data = abi.encodeWithSelector(_selector, _to, _amount);

    _executeCall(_delegation, _data);
  }

  /**
   * @notice Execute a function call on the delegation contract.
   * @param _delegation Address of the delegation contract
   * @param _data The call data that will be executed
   * @return The return datas from the calls
   */
  function _executeCall(Delegation _delegation, bytes memory _data)
    internal
    returns (bytes[] memory)
  {
    Delegation.Call[] memory _calls = new Delegation.Call[](1);
    _calls[0] = Delegation.Call({ to: address(ticket), data: _data });

    return _delegation.executeCalls(_calls);
  }

  /**
   * @notice Transfers tickets from a delegation contract to `_to`.
   * @param _delegation Address of the delegation contract
   * @param _to Address of the recipient
   * @param _amount Amount of tickets to transfer
   */
  function _transfer(
    Delegation _delegation,
    address _to,
    uint256 _amount
  ) internal {
    _requireAmountGtZero(_amount);
    _requireDelegationUnlocked(_delegation);

    _transferCall(_delegation, _to, _amount);
  }

  /* ============ Modifier/Require Functions ============ */

  /**
   * @notice Require to only allow the delegator or representative to call a function.
   * @param _delegator Address of the delegator
   */
  function _requireDelegatorOrRepresentative(address _delegator) internal view {
    require(
      _delegator == msg.sender || representatives[_delegator][msg.sender],
      "TWABDelegator/not-dlgtr-or-rep"
    );
  }

  /**
   * @notice Require to verify that `_delegatee` is not address zero.
   * @param _delegatee Address of the delegatee
   */
  function _requireDelegateeNotZeroAddress(address _delegatee) internal pure {
    require(_delegatee != address(0), "TWABDelegator/dlgt-not-zero-addr");
  }

  /**
   * @notice Require to verify that `_amount` is greater than 0.
   * @param _amount Amount to check
   */
  function _requireAmountGtZero(uint256 _amount) internal pure {
    require(_amount > 0, "TWABDelegator/amount-gt-zero");
  }

  /**
   * @notice Require to verify that `_to` is not address zero.
   * @param _to Address to check
   */
  function _requireRecipientNotZeroAddress(address _to) internal pure {
    require(_to != address(0), "TWABDelegator/to-not-zero-addr");
  }

  /**
   * @notice Require to verify if a `_delegation` is locked.
   * @param _delegation Delegation to check
   */
  function _requireDelegationUnlocked(Delegation _delegation) internal view {
    require(block.timestamp >= _delegation.lockUntil(), "TWABDelegator/delegation-locked");
  }

  /**
   * @notice Require to verify that a `_lockDuration` does not exceed the maximum lock duration.
   * @param _lockDuration Lock duration to check
   */
  function _requireLockDuration(uint256 _lockDuration) internal pure {
    require(_lockDuration <= MAX_LOCK, "TWABDelegator/lock-too-long");
  }
}

// File: @openzeppelin/contracts/proxy/Clones.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (proxy/Clones.sol)

pragma solidity ^0.8.0;

/**
 * @dev https://eips.ethereum.org/EIPS/eip-1167[EIP 1167] is a standard for
 * deploying minimal proxy contracts, also known as "clones".
 *
 * > To simply and cheaply clone contract functionality in an immutable way, this standard specifies
 * > a minimal bytecode implementation that delegates all calls to a known, fixed address.
 *
 * The library includes functions to deploy a proxy using either `create` (traditional deployment) or `create2`
 * (salted deterministic deployment). It also includes functions to predict the addresses of clones deployed using the
 * deterministic method.
 *
 * _Available since v3.4._
 */
library Clones {
    /**
     * @dev Deploys and returns the address of a clone that mimics the behaviour of `implementation`.
     *
     * This function uses the create opcode, which should never revert.
     */
    function clone(address implementation) internal returns (address instance) {
        assembly {
            let ptr := mload(0x40)
            mstore(ptr, 0x3d602d80600a3d3981f3363d3d373d3d3d363d73000000000000000000000000)
            mstore(add(ptr, 0x14), shl(0x60, implementation))
            mstore(add(ptr, 0x28), 0x5af43d82803e903d91602b57fd5bf30000000000000000000000000000000000)
            instance := create(0, ptr, 0x37)
        }
        require(instance != address(0), "ERC1167: create failed");
    }

    /**
     * @dev Deploys and returns the address of a clone that mimics the behaviour of `implementation`.
     *
     * This function uses the create2 opcode and a `salt` to deterministically deploy
     * the clone. Using the same `implementation` and `salt` multiple time will revert, since
     * the clones cannot be deployed twice at the same address.
     */
    function cloneDeterministic(address implementation, bytes32 salt) internal returns (address instance) {
        assembly {
            let ptr := mload(0x40)
            mstore(ptr, 0x3d602d80600a3d3981f3363d3d373d3d3d363d73000000000000000000000000)
            mstore(add(ptr, 0x14), shl(0x60, implementation))
            mstore(add(ptr, 0x28), 0x5af43d82803e903d91602b57fd5bf30000000000000000000000000000000000)
            instance := create2(0, ptr, 0x37, salt)
        }
        require(instance != address(0), "ERC1167: create2 failed");
    }

    /**
     * @dev Computes the address of a clone deployed using {Clones-cloneDeterministic}.
     */
    function predictDeterministicAddress(
        address implementation,
        bytes32 salt,
        address deployer
    ) internal pure returns (address predicted) {
        assembly {
            let ptr := mload(0x40)
            mstore(ptr, 0x3d602d80600a3d3981f3363d3d373d3d3d363d73000000000000000000000000)
            mstore(add(ptr, 0x14), shl(0x60, implementation))
            mstore(add(ptr, 0x28), 0x5af43d82803e903d91602b57fd5bf3ff00000000000000000000000000000000)
            mstore(add(ptr, 0x38), shl(0x60, deployer))
            mstore(add(ptr, 0x4c), salt)
            mstore(add(ptr, 0x6c), keccak256(ptr, 0x37))
            predicted := keccak256(add(ptr, 0x37), 0x55)
        }
    }

    /**
     * @dev Computes the address of a clone deployed using {Clones-cloneDeterministic}.
     */
    function predictDeterministicAddress(address implementation, bytes32 salt)
        internal
        view
        returns (address predicted)
    {
        return predictDeterministicAddress(implementation, salt, address(this));
    }
}

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



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (token/ERC20/IERC20.sol)

pragma solidity ^0.8.0;

/**
 * @dev Interface of the ERC20 standard as defined in the EIP.
 */
interface IERC20 {
    /**
     * @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 `recipient`.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * Emits a {Transfer} event.
     */
    function transfer(address recipient, 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 `sender` to `recipient` 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 sender,
        address recipient,
        uint256 amount
    ) external returns (bool);

    /**
     * @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);
}

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



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

pragma solidity ^0.8.0;

import "./IERC20.sol";
import "./extensions/IERC20Metadata.sol";
import "../../utils/Context.sol";

/**
 * @dev Implementation of the {IERC20} interface.
 *
 * This implementation is agnostic to the way tokens are created. This means
 * that a supply mechanism has to be added in a derived contract using {_mint}.
 * For a generic mechanism see {ERC20PresetMinterPauser}.
 *
 * TIP: For a detailed writeup see our guide
 * https://forum.zeppelin.solutions/t/how-to-implement-erc20-supply-mechanisms/226[How
 * to implement supply mechanisms].
 *
 * We have followed general OpenZeppelin Contracts guidelines: functions revert
 * instead returning `false` on failure. This behavior is nonetheless
 * conventional and does not conflict with the expectations of ERC20
 * applications.
 *
 * Additionally, an {Approval} event is emitted on calls to {transferFrom}.
 * This allows applications to reconstruct the allowance for all accounts just
 * by listening to said events. Other implementations of the EIP may not emit
 * these events, as it isn't required by the specification.
 *
 * Finally, the non-standard {decreaseAllowance} and {increaseAllowance}
 * functions have been added to mitigate the well-known issues around setting
 * allowances. See {IERC20-approve}.
 */
contract ERC20 is Context, IERC20, IERC20Metadata {
    mapping(address => uint256) private _balances;

    mapping(address => mapping(address => uint256)) private _allowances;

    uint256 private _totalSupply;

    string private _name;
    string private _symbol;

    /**
     * @dev Sets the values for {name} and {symbol}.
     *
     * The default value of {decimals} is 18. To select a different value for
     * {decimals} you should overload it.
     *
     * All two of these values are immutable: they can only be set once during
     * construction.
     */
    constructor(string memory name_, string memory symbol_) {
        _name = name_;
        _symbol = symbol_;
    }

    /**
     * @dev Returns the name of the token.
     */
    function name() public view virtual override returns (string memory) {
        return _name;
    }

    /**
     * @dev Returns the symbol of the token, usually a shorter version of the
     * name.
     */
    function symbol() public view virtual override returns (string memory) {
        return _symbol;
    }

    /**
     * @dev Returns the number of decimals used to get its user representation.
     * For example, if `decimals` equals `2`, a balance of `505` tokens should
     * be displayed to a user as `5.05` (`505 / 10 ** 2`).
     *
     * Tokens usually opt for a value of 18, imitating the relationship between
     * Ether and Wei. This is the value {ERC20} uses, unless this function is
     * overridden;
     *
     * NOTE: This information is only used for _display_ purposes: it in
     * no way affects any of the arithmetic of the contract, including
     * {IERC20-balanceOf} and {IERC20-transfer}.
     */
    function decimals() public view virtual override returns (uint8) {
        return 18;
    }

    /**
     * @dev See {IERC20-totalSupply}.
     */
    function totalSupply() public view virtual override returns (uint256) {
        return _totalSupply;
    }

    /**
     * @dev See {IERC20-balanceOf}.
     */
    function balanceOf(address account) public view virtual override returns (uint256) {
        return _balances[account];
    }

    /**
     * @dev See {IERC20-transfer}.
     *
     * Requirements:
     *
     * - `recipient` cannot be the zero address.
     * - the caller must have a balance of at least `amount`.
     */
    function transfer(address recipient, uint256 amount) public virtual override returns (bool) {
        _transfer(_msgSender(), recipient, amount);
        return true;
    }

    /**
     * @dev See {IERC20-allowance}.
     */
    function allowance(address owner, address spender) public view virtual override returns (uint256) {
        return _allowances[owner][spender];
    }

    /**
     * @dev See {IERC20-approve}.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     */
    function approve(address spender, uint256 amount) public virtual override returns (bool) {
        _approve(_msgSender(), spender, amount);
        return true;
    }

    /**
     * @dev See {IERC20-transferFrom}.
     *
     * Emits an {Approval} event indicating the updated allowance. This is not
     * required by the EIP. See the note at the beginning of {ERC20}.
     *
     * Requirements:
     *
     * - `sender` and `recipient` cannot be the zero address.
     * - `sender` must have a balance of at least `amount`.
     * - the caller must have allowance for ``sender``'s tokens of at least
     * `amount`.
     */
    function transferFrom(
        address sender,
        address recipient,
        uint256 amount
    ) public virtual override returns (bool) {
        _transfer(sender, recipient, amount);

        uint256 currentAllowance = _allowances[sender][_msgSender()];
        require(currentAllowance >= amount, "ERC20: transfer amount exceeds allowance");
        unchecked {
            _approve(sender, _msgSender(), currentAllowance - amount);
        }

        return true;
    }

    /**
     * @dev Atomically increases the allowance granted to `spender` by the caller.
     *
     * This is an alternative to {approve} that can be used as a mitigation for
     * problems described in {IERC20-approve}.
     *
     * Emits an {Approval} event indicating the updated allowance.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     */
    function increaseAllowance(address spender, uint256 addedValue) public virtual returns (bool) {
        _approve(_msgSender(), spender, _allowances[_msgSender()][spender] + addedValue);
        return true;
    }

    /**
     * @dev Atomically decreases the allowance granted to `spender` by the caller.
     *
     * This is an alternative to {approve} that can be used as a mitigation for
     * problems described in {IERC20-approve}.
     *
     * Emits an {Approval} event indicating the updated allowance.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     * - `spender` must have allowance for the caller of at least
     * `subtractedValue`.
     */
    function decreaseAllowance(address spender, uint256 subtractedValue) public virtual returns (bool) {
        uint256 currentAllowance = _allowances[_msgSender()][spender];
        require(currentAllowance >= subtractedValue, "ERC20: decreased allowance below zero");
        unchecked {
            _approve(_msgSender(), spender, currentAllowance - subtractedValue);
        }

        return true;
    }

    /**
     * @dev Moves `amount` of tokens from `sender` to `recipient`.
     *
     * This internal function is equivalent to {transfer}, and can be used to
     * e.g. implement automatic token fees, slashing mechanisms, etc.
     *
     * Emits a {Transfer} event.
     *
     * Requirements:
     *
     * - `sender` cannot be the zero address.
     * - `recipient` cannot be the zero address.
     * - `sender` must have a balance of at least `amount`.
     */
    function _transfer(
        address sender,
        address recipient,
        uint256 amount
    ) internal virtual {
        require(sender != address(0), "ERC20: transfer from the zero address");
        require(recipient != address(0), "ERC20: transfer to the zero address");

        _beforeTokenTransfer(sender, recipient, amount);

        uint256 senderBalance = _balances[sender];
        require(senderBalance >= amount, "ERC20: transfer amount exceeds balance");
        unchecked {
            _balances[sender] = senderBalance - amount;
        }
        _balances[recipient] += amount;

        emit Transfer(sender, recipient, amount);

        _afterTokenTransfer(sender, recipient, amount);
    }

    /** @dev Creates `amount` tokens and assigns them to `account`, increasing
     * the total supply.
     *
     * Emits a {Transfer} event with `from` set to the zero address.
     *
     * Requirements:
     *
     * - `account` cannot be the zero address.
     */
    function _mint(address account, uint256 amount) internal virtual {
        require(account != address(0), "ERC20: mint to the zero address");

        _beforeTokenTransfer(address(0), account, amount);

        _totalSupply += amount;
        _balances[account] += amount;
        emit Transfer(address(0), account, amount);

        _afterTokenTransfer(address(0), account, amount);
    }

    /**
     * @dev Destroys `amount` tokens from `account`, reducing the
     * total supply.
     *
     * Emits a {Transfer} event with `to` set to the zero address.
     *
     * Requirements:
     *
     * - `account` cannot be the zero address.
     * - `account` must have at least `amount` tokens.
     */
    function _burn(address account, uint256 amount) internal virtual {
        require(account != address(0), "ERC20: burn from the zero address");

        _beforeTokenTransfer(account, address(0), amount);

        uint256 accountBalance = _balances[account];
        require(accountBalance >= amount, "ERC20: burn amount exceeds balance");
        unchecked {
            _balances[account] = accountBalance - amount;
        }
        _totalSupply -= amount;

        emit Transfer(account, address(0), amount);

        _afterTokenTransfer(account, address(0), amount);
    }

    /**
     * @dev Sets `amount` as the allowance of `spender` over the `owner` s tokens.
     *
     * This internal function is equivalent to `approve`, and can be used to
     * e.g. set automatic allowances for certain subsystems, etc.
     *
     * Emits an {Approval} event.
     *
     * Requirements:
     *
     * - `owner` cannot be the zero address.
     * - `spender` cannot be the zero address.
     */
    function _approve(
        address owner,
        address spender,
        uint256 amount
    ) internal virtual {
        require(owner != address(0), "ERC20: approve from the zero address");
        require(spender != address(0), "ERC20: approve to the zero address");

        _allowances[owner][spender] = amount;
        emit Approval(owner, spender, amount);
    }

    /**
     * @dev Hook that is called before any transfer of tokens. This includes
     * minting and burning.
     *
     * Calling conditions:
     *
     * - when `from` and `to` are both non-zero, `amount` of ``from``'s tokens
     * will be transferred to `to`.
     * - when `from` is zero, `amount` tokens will be minted for `to`.
     * - when `to` is zero, `amount` of ``from``'s tokens will be burned.
     * - `from` and `to` are never both zero.
     *
     * To learn more about hooks, head to xref:ROOT:extending-contracts.adoc#using-hooks[Using Hooks].
     */
    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.
     *
     * Calling conditions:
     *
     * - when `from` and `to` are both non-zero, `amount` of ``from``'s tokens
     * has been transferred to `to`.
     * - when `from` is zero, `amount` tokens have been minted for `to`.
     * - when `to` is zero, `amount` of ``from``'s tokens have been burned.
     * - `from` and `to` are never both zero.
     *
     * To learn more about hooks, head to xref:ROOT:extending-contracts.adoc#using-hooks[Using Hooks].
     */
    function _afterTokenTransfer(
        address from,
        address to,
        uint256 amount
    ) internal virtual {}
}

// File: @openzeppelin/contracts/token/ERC20/utils/SafeERC20.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (token/ERC20/utils/SafeERC20.sol)

pragma solidity ^0.8.0;

import "../IERC20.sol";
import "../../../utils/Address.sol";

/**
 * @title SafeERC20
 * @dev Wrappers around ERC20 operations that throw on failure (when the token
 * contract returns false). Tokens that return no value (and instead revert or
 * throw on failure) are also supported, non-reverting calls are assumed to be
 * successful.
 * To use this library you can add a `using SafeERC20 for IERC20;` statement to your contract,
 * which allows you to call the safe operations as `token.safeTransfer(...)`, etc.
 */
library SafeERC20 {
    using Address for address;

    function safeTransfer(
        IERC20 token,
        address to,
        uint256 value
    ) internal {
        _callOptionalReturn(token, abi.encodeWithSelector(token.transfer.selector, to, value));
    }

    function safeTransferFrom(
        IERC20 token,
        address from,
        address to,
        uint256 value
    ) internal {
        _callOptionalReturn(token, abi.encodeWithSelector(token.transferFrom.selector, from, to, value));
    }

    /**
     * @dev Deprecated. This function has issues similar to the ones found in
     * {IERC20-approve}, and its usage is discouraged.
     *
     * Whenever possible, use {safeIncreaseAllowance} and
     * {safeDecreaseAllowance} instead.
     */
    function safeApprove(
        IERC20 token,
        address spender,
        uint256 value
    ) internal {
        // safeApprove should only be called when setting an initial allowance,
        // or when resetting it to zero. To increase and decrease it, use
        // 'safeIncreaseAllowance' and 'safeDecreaseAllowance'
        require(
            (value == 0) || (token.allowance(address(this), spender) == 0),
            "SafeERC20: approve from non-zero to non-zero allowance"
        );
        _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, value));
    }

    function safeIncreaseAllowance(
        IERC20 token,
        address spender,
        uint256 value
    ) internal {
        uint256 newAllowance = token.allowance(address(this), spender) + value;
        _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, newAllowance));
    }

    function safeDecreaseAllowance(
        IERC20 token,
        address spender,
        uint256 value
    ) internal {
        unchecked {
            uint256 oldAllowance = token.allowance(address(this), spender);
            require(oldAllowance >= value, "SafeERC20: decreased allowance below zero");
            uint256 newAllowance = oldAllowance - value;
            _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, newAllowance));
        }
    }

    /**
     * @dev Imitates a Solidity high-level call (i.e. a regular function call to a contract), relaxing the requirement
     * on the return value: the return value is optional (but if data is returned, it must not be false).
     * @param token The token targeted by the call.
     * @param data The call data (encoded using abi.encode or one of its variants).
     */
    function _callOptionalReturn(IERC20 token, bytes memory data) private {
        // We need to perform a low level call here, to bypass Solidity's return data size checking mechanism, since
        // we're implementing it ourselves. We use {Address.functionCall} to perform this call, which verifies that
        // the target address contains contract code and also asserts for success in the low-level call.

        bytes memory returndata = address(token).functionCall(data, "SafeERC20: low-level call failed");
        if (returndata.length > 0) {
            // Return data is optional
            require(abi.decode(returndata, (bool)), "SafeERC20: ERC20 operation did not succeed");
        }
    }
}

// File: @pooltogether/v4-core/contracts/interfaces/ITicket.sol



// SPDX-License-Identifier: GPL-3.0

pragma solidity 0.8.6;

import "../libraries/TwabLib.sol";
import "./IControlledToken.sol";

interface ITicket is IControlledToken {
    /**
     * @notice A struct containing details for an Account.
     * @param balance The current balance for an Account.
     * @param nextTwabIndex The next available index to store a new twab.
     * @param cardinality The number of recorded twabs (plus one!).
     */
    struct AccountDetails {
        uint224 balance;
        uint16 nextTwabIndex;
        uint16 cardinality;
    }

    /**
     * @notice Combines account details with their twab history.
     * @param details The account details.
     * @param twabs The history of twabs for this account.
     */
    struct Account {
        AccountDetails details;
        ObservationLib.Observation[65535] twabs;
    }

    /**
     * @notice Emitted when TWAB balance has been delegated to another user.
     * @param delegator Address of the delegator.
     * @param delegate Address of the delegate.
     */
    event Delegated(address indexed delegator, address indexed delegate);

    /**
     * @notice Emitted when ticket is initialized.
     * @param name Ticket name (eg: PoolTogether Dai Ticket (Compound)).
     * @param symbol Ticket symbol (eg: PcDAI).
     * @param decimals Ticket decimals.
     * @param controller Token controller address.
     */
    event TicketInitialized(string name, string symbol, uint8 decimals, address indexed controller);

    /**
     * @notice Emitted when a new TWAB has been recorded.
     * @param delegate The recipient of the ticket power (may be the same as the user).
     * @param newTwab Updated TWAB of a ticket holder after a successful TWAB recording.
     */
    event NewUserTwab(
        address indexed delegate,
        ObservationLib.Observation newTwab
    );

    /**
     * @notice Emitted when a new total supply TWAB has been recorded.
     * @param newTotalSupplyTwab Updated TWAB of tickets total supply after a successful total supply TWAB recording.
     */
    event NewTotalSupplyTwab(ObservationLib.Observation newTotalSupplyTwab);

    /**
     * @notice Retrieves the address of the delegate to whom `user` has delegated their tickets.
     * @dev Address of the delegate will be the zero address if `user` has not delegated their tickets.
     * @param user Address of the delegator.
     * @return Address of the delegate.
     */
    function delegateOf(address user) external view returns (address);

    /**
    * @notice Delegate time-weighted average balances to an alternative address.
    * @dev    Transfers (including mints) trigger the storage of a TWAB in delegate(s) account, instead of the
              targetted sender and/or recipient address(s).
    * @dev    To reset the delegate, pass the zero address (0x000.000) as `to` parameter.
    * @dev Current delegate address should be different from the new delegate address `to`.
    * @param  to Recipient of delegated TWAB.
    */
    function delegate(address to) external;

    /**
     * @notice Allows the controller to delegate on a users behalf.
     * @param user The user for whom to delegate
     * @param delegate The new delegate
     */
    function controllerDelegateFor(address user, address delegate) external;

    /**
     * @notice Allows a user to delegate via signature
     * @param user The user who is delegating
     * @param delegate The new delegate
     * @param deadline The timestamp by which this must be submitted
     * @param v The v portion of the ECDSA sig
     * @param r The r portion of the ECDSA sig
     * @param s The s portion of the ECDSA sig
     */
    function delegateWithSignature(
        address user,
        address delegate,
        uint256 deadline,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) external;

    /**
     * @notice Gets a users twab context.  This is a struct with their balance, next twab index, and cardinality.
     * @param user The user for whom to fetch the TWAB context.
     * @return The TWAB context, which includes { balance, nextTwabIndex, cardinality }
     */
    function getAccountDetails(address user) external view returns (TwabLib.AccountDetails memory);

    /**
     * @notice Gets the TWAB at a specific index for a user.
     * @param user The user for whom to fetch the TWAB.
     * @param index The index of the TWAB to fetch.
     * @return The TWAB, which includes the twab amount and the timestamp.
     */
    function getTwab(address user, uint16 index)
        external
        view
        returns (ObservationLib.Observation memory);

    /**
     * @notice Retrieves `user` TWAB balance.
     * @param user Address of the user whose TWAB is being fetched.
     * @param timestamp Timestamp at which we want to retrieve the TWAB balance.
     * @return The TWAB balance at the given timestamp.
     */
    function getBalanceAt(address user, uint64 timestamp) external view returns (uint256);

    /**
     * @notice Retrieves `user` TWAB balances.
     * @param user Address of the user whose TWABs are being fetched.
     * @param timestamps Timestamps range at which we want to retrieve the TWAB balances.
     * @return `user` TWAB balances.
     */
    function getBalancesAt(address user, uint64[] calldata timestamps)
        external
        view
        returns (uint256[] memory);

    /**
     * @notice Retrieves the average balance held by a user for a given time frame.
     * @param user The user whose balance is checked.
     * @param startTime The start time of the time frame.
     * @param endTime The end time of the time frame.
     * @return The average balance that the user held during the time frame.
     */
    function getAverageBalanceBetween(
        address user,
        uint64 startTime,
        uint64 endTime
    ) external view returns (uint256);

    /**
     * @notice Retrieves the average balances held by a user for a given time frame.
     * @param user The user whose balance is checked.
     * @param startTimes The start time of the time frame.
     * @param endTimes The end time of the time frame.
     * @return The average balance that the user held during the time frame.
     */
    function getAverageBalancesBetween(
        address user,
        uint64[] calldata startTimes,
        uint64[] calldata endTimes
    ) external view returns (uint256[] memory);

    /**
     * @notice Retrieves the total supply TWAB balance at the given timestamp.
     * @param timestamp Timestamp at which we want to retrieve the total supply TWAB balance.
     * @return The total supply TWAB balance at the given timestamp.
     */
    function getTotalSupplyAt(uint64 timestamp) external view returns (uint256);

    /**
     * @notice Retrieves the total supply TWAB balance between the given timestamps range.
     * @param timestamps Timestamps range at which we want to retrieve the total supply TWAB balance.
     * @return Total supply TWAB balances.
     */
    function getTotalSuppliesAt(uint64[] calldata timestamps)
        external
        view
        returns (uint256[] memory);

    /**
     * @notice Retrieves the average total supply balance for a set of given time frames.
     * @param startTimes Array of start times.
     * @param endTimes Array of end times.
     * @return The average total supplies held during the time frame.
     */
    function getAverageTotalSuppliesBetween(
        uint64[] calldata startTimes,
        uint64[] calldata endTimes
    ) external view returns (uint256[] memory);
}

// File: @pooltogether/v4-twab-delegator/contracts/Delegation.sol



// SPDX-License-Identifier: GPL-3.0

pragma solidity 0.8.6;

/**
 * @title Contract instantiated via CREATE2 to handle a Delegation by a delegator to a delegatee.
 * @notice A Delegation allows his owner to execute calls on behalf of the contract.
 * @dev This contract is intended to be counterfactually instantiated via CREATE2 through the LowLevelDelegator contract.
 * @dev This contract will hold tickets that will be delegated to a chosen delegatee.
 */
contract Delegation {
  /**
   * @notice A structure to define arbitrary contract calls.
   * @param to The address to call
   * @param data The call data
   */
  struct Call {
    address to;
    bytes data;
  }

  /// @notice Contract owner.
  address private _owner;

  /// @notice Timestamp until which the delegation is locked.
  uint96 public lockUntil;

  /**
   * @notice Initializes the delegation.
   * @param _lockUntil Timestamp until which the delegation is locked
   */
  function initialize(uint96 _lockUntil) external {
    require(_owner == address(0), "Delegation/already-init");
    _owner = msg.sender;
    lockUntil = _lockUntil;
  }

  /**
   * @notice Executes calls on behalf of this contract.
   * @param calls The array of calls to be executed
   * @return An array of the return values for each of the calls
   */
  function executeCalls(Call[] calldata calls) external onlyOwner returns (bytes[] memory) {
    uint256 _callsLength = calls.length;
    bytes[] memory response = new bytes[](_callsLength);
    Call memory call;

    for (uint256 i; i < _callsLength; i++) {
      call = calls[i];
      response[i] = _executeCall(call.to, call.data);
    }

    return response;
  }

  /**
   * @notice Set the timestamp until which the delegation is locked.
   * @param _lockUntil The timestamp until which the delegation is locked
   */
  function setLockUntil(uint96 _lockUntil) external onlyOwner {
    lockUntil = _lockUntil;
  }

  /**
   * @notice Executes a call to another contract.
   * @param to The address to call
   * @param data The call data
   * @return The return data from the call
   */
  function _executeCall(address to, bytes memory data) internal returns (bytes memory) {
    (bool succeeded, bytes memory returnValue) = to.call{ value: 0 }(data);
    require(succeeded, string(returnValue));
    return returnValue;
  }

  /// @notice Modifier to only allow the contract owner to call a function
  modifier onlyOwner() {
    require(msg.sender == _owner, "Delegation/only-owner");
    _;
  }
}

// File: @pooltogether/v4-twab-delegator/contracts/LowLevelDelegator.sol



// SPDX-License-Identifier: GPL-3.0

pragma solidity 0.8.6;

import "@openzeppelin/contracts/proxy/Clones.sol";

import "./Delegation.sol";

/// @title The LowLevelDelegator allows users to create delegations very cheaply.
contract LowLevelDelegator {
  using Clones for address;

  /// @notice The instance to which all proxies will point.
  Delegation public delegationInstance;

  /// @notice Contract constructor.
  constructor() {
    delegationInstance = new Delegation();
    delegationInstance.initialize(uint96(0));
  }

  /**
   * @notice Creates a clone of the delegation.
   * @param _salt Random number used to deterministically deploy the clone
   * @param _lockUntil Timestamp until which the delegation is locked
   * @return The newly created delegation
   */
  function _createDelegation(bytes32 _salt, uint96 _lockUntil) internal returns (Delegation) {
    Delegation _delegation = Delegation(address(delegationInstance).cloneDeterministic(_salt));
    _delegation.initialize(_lockUntil);
    return _delegation;
  }

  /**
   * @notice Computes the address of a clone, also known as minimal proxy contract.
   * @param _salt Random number used to compute the address
   * @return Address at which the clone will be deployed
   */
  function _computeAddress(bytes32 _salt) internal view returns (address) {
    return address(delegationInstance).predictDeterministicAddress(_salt, address(this));
  }

  /**
   * @notice Computes salt used to deterministically deploy a clone.
   * @param _delegator Address of the delegator
   * @param _slot Slot of the delegation
   * @return Salt used to deterministically deploy a clone.
   */
  function _computeSalt(address _delegator, bytes32 _slot) internal pure returns (bytes32) {
    return keccak256(abi.encodePacked(_delegator, _slot));
  }
}

// File: @pooltogether/v4-twab-delegator/contracts/PermitAndMulticall.sol



// SPDX-License-Identifier: GPL-3.0

pragma solidity 0.8.6;

import "@openzeppelin/contracts/token/ERC20/extensions/draft-IERC20Permit.sol";
import "@openzeppelin/contracts/utils/Address.sol";

/**
 * @notice Allows a user to permit token spend and then call multiple functions on a contract.
 */
contract PermitAndMulticall {
  /**
   * @notice Secp256k1 signature values.
   * @param deadline Timestamp at which the signature expires
   * @param v `v` portion of the signature
   * @param r `r` portion of the signature
   * @param s `s` portion of the signature
   */
  struct Signature {
    uint256 deadline;
    uint8 v;
    bytes32 r;
    bytes32 s;
  }

  /**
   * @notice Allows a user to call multiple functions on the same contract.  Useful for EOA who want to batch transactions.
   * @param _data An array of encoded function calls.  The calls must be abi-encoded calls to this contract.
   * @return The results from each function call
   */
  function _multicall(bytes[] calldata _data) internal virtual returns (bytes[] memory) {
    uint256 _dataLength = _data.length;
    bytes[] memory results = new bytes[](_dataLength);

    for (uint256 i; i < _dataLength; i++) {
      results[i] = Address.functionDelegateCall(address(this), _data[i]);
    }

    return results;
  }

  /**
   * @notice Allow a user to approve an ERC20 token and run various calls in one transaction.
   * @param _permitToken Address of the ERC20 token
   * @param _amount Amount of tickets to approve
   * @param _permitSignature Permit signature
   * @param _data Datas to call with `functionDelegateCall`
   */
  function _permitAndMulticall(
    IERC20Permit _permitToken,
    uint256 _amount,
    Signature calldata _permitSignature,
    bytes[] calldata _data
  ) internal {
    _permitToken.permit(
      msg.sender,
      address(this),
      _amount,
      _permitSignature.deadline,
      _permitSignature.v,
      _permitSignature.r,
      _permitSignature.s
    );

    _multicall(_data);
  }
}

// File: @openzeppelin/contracts/token/ERC20/extensions/IERC20Metadata.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (token/ERC20/extensions/IERC20Metadata.sol)

pragma solidity ^0.8.0;

import "../IERC20.sol";

/**
 * @dev Interface for the optional metadata functions from the ERC20 standard.
 *
 * _Available since v4.1._
 */
interface IERC20Metadata is IERC20 {
    /**
     * @dev Returns the name of the token.
     */
    function name() external view returns (string memory);

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

    /**
     * @dev Returns the decimals places of the token.
     */
    function decimals() external view returns (uint8);
}

// 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/Address.sol



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

pragma solidity ^0.8.0;

/**
 * @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
     * ====
     */
    function isContract(address account) internal view returns (bool) {
        // This method relies on extcodesize, which returns 0 for contracts in
        // construction, since the code is only stored at the end of the
        // constructor execution.

        uint256 size;
        assembly {
            size := extcodesize(account)
        }
        return size > 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 functionCall(target, data, "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");
        require(isContract(target), "Address: call to non-contract");

        (bool success, bytes memory returndata) = target.call{value: value}(data);
        return verifyCallResult(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) {
        require(isContract(target), "Address: static call to non-contract");

        (bool success, bytes memory returndata) = target.staticcall(data);
        return verifyCallResult(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) {
        require(isContract(target), "Address: delegate call to non-contract");

        (bool success, bytes memory returndata) = target.delegatecall(data);
        return verifyCallResult(success, returndata, errorMessage);
    }

    /**
     * @dev Tool to verifies that a low level call was successful, and revert if it wasn't, either by bubbling the
     * revert reason 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 {
            // 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

                assembly {
                    let returndata_size := mload(returndata)
                    revert(add(32, returndata), returndata_size)
                }
            } else {
                revert(errorMessage);
            }
        }
    }
}

// File: @pooltogether/v4-core/contracts/libraries/TwabLib.sol



// SPDX-License-Identifier: GPL-3.0

pragma solidity 0.8.6;

import "./ExtendedSafeCastLib.sol";
import "./OverflowSafeComparatorLib.sol";
import "./RingBufferLib.sol";
import "./ObservationLib.sol";

/**
  * @title  PoolTogether V4 TwabLib (Library)
  * @author PoolTogether Inc Team
  * @dev    Time-Weighted Average Balance Library for ERC20 tokens.
  * @notice This TwabLib adds on-chain historical lookups to a user(s) time-weighted average balance.
            Each user is mapped to an Account struct containing the TWAB history (ring bufffer) and
            ring buffer parameters. Every token.transfer() creates a new TWAB checkpoint. The new TWAB
            checkpoint is stored in the circular ring buffer, as either a new checkpoint or rewriting
            a previous checkpoint with new parameters. The TwabLib (using existing blocktimes 1block/15sec)
            guarantees minimum 7.4 years of search history.
 */
library TwabLib {
    using OverflowSafeComparatorLib for uint32;
    using ExtendedSafeCastLib for uint256;

    /**
      * @notice Sets max ring buffer length in the Account.twabs Observation list.
                As users transfer/mint/burn tickets new Observation checkpoints are
                recorded. The current max cardinality guarantees a six month minimum,
                of historical accurate lookups with current estimates of 1 new block
                every 15 seconds - the of course contain a transfer to trigger an
                observation write to storage.
      * @dev    The user Account.AccountDetails.cardinality parameter can NOT exceed
                the max cardinality variable. Preventing "corrupted" ring buffer lookup
                pointers and new observation checkpoints.

                The MAX_CARDINALITY in fact guarantees at least 7.4 years of records:
                If 14 = block time in seconds
                (2**24) * 14 = 234881024 seconds of history
                234881024 / (365 * 24 * 60 * 60) ~= 7.44 years
    */
    uint24 public constant MAX_CARDINALITY = 16777215; // 2**24

    /** @notice Struct ring buffer parameters for single user Account
      * @param balance       Current balance for an Account
      * @param nextTwabIndex Next uninitialized or updatable ring buffer checkpoint storage slot
      * @param cardinality   Current total "initialized" ring buffer checkpoints for single user AccountDetails.
                             Used to set initial boundary conditions for an efficient binary search.
    */
    struct AccountDetails {
        uint208 balance;
        uint24 nextTwabIndex;
        uint24 cardinality;
    }

    /// @notice Combines account details with their twab history
    /// @param details The account details
    /// @param twabs The history of twabs for this account
    struct Account {
        AccountDetails details;
        ObservationLib.Observation[MAX_CARDINALITY] twabs;
    }

    /// @notice Increases an account's balance and records a new twab.
    /// @param _account The account whose balance will be increased
    /// @param _amount The amount to increase the balance by
    /// @param _currentTime The current time
    /// @return accountDetails The new AccountDetails
    /// @return twab The user's latest TWAB
    /// @return isNew Whether the TWAB is new
    function increaseBalance(
        Account storage _account,
        uint208 _amount,
        uint32 _currentTime
    )
        internal
        returns (
            AccountDetails memory accountDetails,
            ObservationLib.Observation memory twab,
            bool isNew
        )
    {
        AccountDetails memory _accountDetails = _account.details;
        (accountDetails, twab, isNew) = _nextTwab(_account.twabs, _accountDetails, _currentTime);
        accountDetails.balance = _accountDetails.balance + _amount;
    }

    /** @notice Calculates the next TWAB checkpoint for an account with a decreasing balance.
     * @dev    With Account struct and amount decreasing calculates the next TWAB observable checkpoint.
     * @param _account        Account whose balance will be decreased
     * @param _amount         Amount to decrease the balance by
     * @param _revertMessage  Revert message for insufficient balance
     * @return accountDetails Updated Account.details struct
     * @return twab           TWAB observation (with decreasing average)
     * @return isNew          Whether TWAB is new or calling twice in the same block
     */
    function decreaseBalance(
        Account storage _account,
        uint208 _amount,
        string memory _revertMessage,
        uint32 _currentTime
    )
        internal
        returns (
            AccountDetails memory accountDetails,
            ObservationLib.Observation memory twab,
            bool isNew
        )
    {
        AccountDetails memory _accountDetails = _account.details;

        require(_accountDetails.balance >= _amount, _revertMessage);

        (accountDetails, twab, isNew) = _nextTwab(_account.twabs, _accountDetails, _currentTime);
        unchecked {
            accountDetails.balance -= _amount;
        }
    }

    /** @notice Calculates the average balance held by a user for a given time frame.
      * @dev    Finds the average balance between start and end timestamp epochs.
                Validates the supplied end time is within the range of elapsed time i.e. less then timestamp of now.
      * @param _twabs          Individual user Observation recorded checkpoints passed as storage pointer
      * @param _accountDetails User AccountDetails struct loaded in memory
      * @param _startTime      Start of timestamp range as an epoch
      * @param _endTime        End of timestamp range as an epoch
      * @param _currentTime    Block.timestamp
      * @return Average balance of user held between epoch timestamps start and end
    */
    function getAverageBalanceBetween(
        ObservationLib.Observation[MAX_CARDINALITY] storage _twabs,
        AccountDetails memory _accountDetails,
        uint32 _startTime,
        uint32 _endTime,
        uint32 _currentTime
    ) internal view returns (uint256) {
        uint32 endTime = _endTime > _currentTime ? _currentTime : _endTime;

        return
            _getAverageBalanceBetween(_twabs, _accountDetails, _startTime, endTime, _currentTime);
    }

    /// @notice Retrieves the oldest TWAB
    /// @param _twabs The storage array of twabs
    /// @param _accountDetails The TWAB account details
    /// @return index The index of the oldest TWAB in the twabs array
    /// @return twab The oldest TWAB
    function oldestTwab(
        ObservationLib.Observation[MAX_CARDINALITY] storage _twabs,
        AccountDetails memory _accountDetails
    ) internal view returns (uint24 index, ObservationLib.Observation memory twab) {
        index = _accountDetails.nextTwabIndex;
        twab = _twabs[index];

        // If the TWAB is not initialized we go to the beginning of the TWAB circular buffer at index 0
        if (twab.timestamp == 0) {
            index = 0;
            twab = _twabs[0];
        }
    }

    /// @notice Retrieves the newest TWAB
    /// @param _twabs The storage array of twabs
    /// @param _accountDetails The TWAB account details
    /// @return index The index of the newest TWAB in the twabs array
    /// @return twab The newest TWAB
    function newestTwab(
        ObservationLib.Observation[MAX_CARDINALITY] storage _twabs,
        AccountDetails memory _accountDetails
    ) internal view returns (uint24 index, ObservationLib.Observation memory twab) {
        index = uint24(RingBufferLib.newestIndex(_accountDetails.nextTwabIndex, MAX_CARDINALITY));
        twab = _twabs[index];
    }

    /// @notice Retrieves amount at `_targetTime` timestamp
    /// @param _twabs List of TWABs to search through.
    /// @param _accountDetails Accounts details
    /// @param _targetTime Timestamp at which the reserved TWAB should be for.
    /// @return uint256 TWAB amount at `_targetTime`.
    function getBalanceAt(
        ObservationLib.Observation[MAX_CARDINALITY] storage _twabs,
        AccountDetails memory _accountDetails,
        uint32 _targetTime,
        uint32 _currentTime
    ) internal view returns (uint256) {
        uint32 timeToTarget = _targetTime > _currentTime ? _currentTime : _targetTime;
        return _getBalanceAt(_twabs, _accountDetails, timeToTarget, _currentTime);
    }

    /// @notice Calculates the average balance held by a user for a given time frame.
    /// @param _startTime The start time of the time frame.
    /// @param _endTime The end time of the time frame.
    /// @return The average balance that the user held during the time frame.
    function _getAverageBalanceBetween(
        ObservationLib.Observation[MAX_CARDINALITY] storage _twabs,
        AccountDetails memory _accountDetails,
        uint32 _startTime,
        uint32 _endTime,
        uint32 _currentTime
    ) private view returns (uint256) {
        (uint24 oldestTwabIndex, ObservationLib.Observation memory oldTwab) = oldestTwab(
            _twabs,
            _accountDetails
        );

        (uint24 newestTwabIndex, ObservationLib.Observation memory newTwab) = newestTwab(
            _twabs,
            _accountDetails
        );

        ObservationLib.Observation memory startTwab = _calculateTwab(
            _twabs,
            _accountDetails,
            newTwab,
            oldTwab,
            newestTwabIndex,
            oldestTwabIndex,
            _startTime,
            _currentTime
        );

        ObservationLib.Observation memory endTwab = _calculateTwab(
            _twabs,
            _accountDetails,
            newTwab,
            oldTwab,
            newestTwabIndex,
            oldestTwabIndex,
            _endTime,
            _currentTime
        );

        // Difference in amount / time
        return (endTwab.amount - startTwab.amount) / OverflowSafeComparatorLib.checkedSub(endTwab.timestamp, startTwab.timestamp, _currentTime);
    }

    /** @notice Searches TWAB history and calculate the difference between amount(s)/timestamp(s) to return average balance
                between the Observations closes to the supplied targetTime.
      * @param _twabs          Individual user Observation recorded checkpoints passed as storage pointer
      * @param _accountDetails User AccountDetails struct loaded in memory
      * @param _targetTime     Target timestamp to filter Observations in the ring buffer binary search
      * @param _currentTime    Block.timestamp
      * @return uint256 Time-weighted average amount between two closest observations.
    */
    function _getBalanceAt(
        ObservationLib.Observation[MAX_CARDINALITY] storage _twabs,
        AccountDetails memory _accountDetails,
        uint32 _targetTime,
        uint32 _currentTime
    ) private view returns (uint256) {
        uint24 newestTwabIndex;
        ObservationLib.Observation memory afterOrAt;
        ObservationLib.Observation memory beforeOrAt;
        (newestTwabIndex, beforeOrAt) = newestTwab(_twabs, _accountDetails);

        // If `_targetTime` is chronologically after the newest TWAB, we can simply return the current balance
        if (beforeOrAt.timestamp.lte(_targetTime, _currentTime)) {
            return _accountDetails.balance;
        }

        uint24 oldestTwabIndex;
        // Now, set before to the oldest TWAB
        (oldestTwabIndex, beforeOrAt) = oldestTwab(_twabs, _accountDetails);

        // If `_targetTime` is chronologically before the oldest TWAB, we can early return
        if (_targetTime.lt(beforeOrAt.timestamp, _currentTime)) {
            return 0;
        }

        // Otherwise, we perform the `binarySearch`
        (beforeOrAt, afterOrAt) = ObservationLib.binarySearch(
            _twabs,
            newestTwabIndex,
            oldestTwabIndex,
            _targetTime,
            _accountDetails.cardinality,
            _currentTime
        );

        // Sum the difference in amounts and divide by the difference in timestamps.
        // The time-weighted average balance uses time measured between two epoch timestamps as
        // a constaint on the measurement when calculating the time weighted average balance.
        return
            (afterOrAt.amount - beforeOrAt.amount) / OverflowSafeComparatorLib.checkedSub(afterOrAt.timestamp, beforeOrAt.timestamp, _currentTime);
    }

    /** @notice Calculates a user TWAB for a target timestamp using the historical TWAB records.
                The balance is linearly interpolated: amount differences / timestamp differences
                using the simple (after.amount - before.amount / end.timestamp - start.timestamp) formula.
    /** @dev    Binary search in _calculateTwab fails when searching out of bounds. Thus, before
                searching we exclude target timestamps out of range of newest/oldest TWAB(s).
                IF a search is before or after the range we "extrapolate" a Observation from the expected state.
      * @param _twabs           Individual user Observation recorded checkpoints passed as storage pointer
      * @param _accountDetails  User AccountDetails struct loaded in memory
      * @param _newestTwab      Newest TWAB in history (end of ring buffer)
      * @param _oldestTwab      Olderst TWAB in history (end of ring buffer)
      * @param _newestTwabIndex Pointer in ring buffer to newest TWAB
      * @param _oldestTwabIndex Pointer in ring buffer to oldest TWAB
      * @param _targetTimestamp Epoch timestamp to calculate for time (T) in the TWAB
      * @param _time            Block.timestamp
      * @return accountDetails Updated Account.details struct
    */
    function _calculateTwab(
        ObservationLib.Observation[MAX_CARDINALITY] storage _twabs,
        AccountDetails memory _accountDetails,
        ObservationLib.Observation memory _newestTwab,
        ObservationLib.Observation memory _oldestTwab,
        uint24 _newestTwabIndex,
        uint24 _oldestTwabIndex,
        uint32 _targetTimestamp,
        uint32 _time
    ) private view returns (ObservationLib.Observation memory) {
        // If `_targetTimestamp` is chronologically after the newest TWAB, we extrapolate a new one
        if (_newestTwab.timestamp.lt(_targetTimestamp, _time)) {
            return _computeNextTwab(_newestTwab, _accountDetails.balance, _targetTimestamp);
        }

        if (_newestTwab.timestamp == _targetTimestamp) {
            return _newestTwab;
        }

        if (_oldestTwab.timestamp == _targetTimestamp) {
            return _oldestTwab;
        }

        // If `_targetTimestamp` is chronologically before the oldest TWAB, we create a zero twab
        if (_targetTimestamp.lt(_oldestTwab.timestamp, _time)) {
            return ObservationLib.Observation({ amount: 0, timestamp: _targetTimestamp });
        }

        // Otherwise, both timestamps must be surrounded by twabs.
        (
            ObservationLib.Observation memory beforeOrAtStart,
            ObservationLib.Observation memory afterOrAtStart
        ) = ObservationLib.binarySearch(
                _twabs,
                _newestTwabIndex,
                _oldestTwabIndex,
                _targetTimestamp,
                _accountDetails.cardinality,
                _time
            );

        uint224 heldBalance = (afterOrAtStart.amount - beforeOrAtStart.amount) /
            OverflowSafeComparatorLib.checkedSub(afterOrAtStart.timestamp, beforeOrAtStart.timestamp, _time);

        return _computeNextTwab(beforeOrAtStart, heldBalance, _targetTimestamp);
    }

    /**
     * @notice Calculates the next TWAB using the newestTwab and updated balance.
     * @dev    Storage of the TWAB obersation is managed by the calling function and not _computeNextTwab.
     * @param _currentTwab    Newest Observation in the Account.twabs list
     * @param _currentBalance User balance at time of most recent (newest) checkpoint write
     * @param _time           Current block.timestamp
     * @return TWAB Observation
     */
    function _computeNextTwab(
        ObservationLib.Observation memory _currentTwab,
        uint224 _currentBalance,
        uint32 _time
    ) private pure returns (ObservationLib.Observation memory) {
        // New twab amount = last twab amount (or zero) + (current amount * elapsed seconds)
        return
            ObservationLib.Observation({
                amount: _currentTwab.amount +
                    _currentBalance *
                    (_time.checkedSub(_currentTwab.timestamp, _time)),
                timestamp: _time
            });
    }

    /// @notice Sets a new TWAB Observation at the next available index and returns the new account details.
    /// @dev Note that if _currentTime is before the last observation timestamp, it appears as an overflow
    /// @param _twabs The twabs array to insert into
    /// @param _accountDetails The current account details
    /// @param _currentTime The current time
    /// @return accountDetails The new account details
    /// @return twab The newest twab (may or may not be brand-new)
    /// @return isNew Whether the newest twab was created by this call
    function _nextTwab(
        ObservationLib.Observation[MAX_CARDINALITY] storage _twabs,
        AccountDetails memory _accountDetails,
        uint32 _currentTime
    )
        private
        returns (
            AccountDetails memory accountDetails,
            ObservationLib.Observation memory twab,
            bool isNew
        )
    {
        (, ObservationLib.Observation memory _newestTwab) = newestTwab(_twabs, _accountDetails);

        // if we're in the same block, return
        if (_newestTwab.timestamp == _currentTime) {
            return (_accountDetails, _newestTwab, false);
        }

        ObservationLib.Observation memory newTwab = _computeNextTwab(
            _newestTwab,
            _accountDetails.balance,
            _currentTime
        );

        _twabs[_accountDetails.nextTwabIndex] = newTwab;

        AccountDetails memory nextAccountDetails = push(_accountDetails);

        return (nextAccountDetails, newTwab, true);
    }

    /// @notice "Pushes" a new element on the AccountDetails ring buffer, and returns the new AccountDetails
    /// @param _accountDetails The account details from which to pull the cardinality and next index
    /// @return The new AccountDetails
    function push(AccountDetails memory _accountDetails)
        internal
        pure
        returns (AccountDetails memory)
    {
        _accountDetails.nextTwabIndex = uint24(
            RingBufferLib.nextIndex(_accountDetails.nextTwabIndex, MAX_CARDINALITY)
        );

        // Prevent the Account specific cardinality from exceeding the MAX_CARDINALITY.
        // The ring buffer length is limited by MAX_CARDINALITY. IF the account.cardinality
        // exceeds the max cardinality, new observations would be incorrectly set or the
        // observation would be out of "bounds" of the ring buffer. Once reached the
        // AccountDetails.cardinality will continue to be equal to max cardinality.
        if (_accountDetails.cardinality < MAX_CARDINALITY) {
            _accountDetails.cardinality += 1;
        }

        return _accountDetails;
    }
}

// File: @pooltogether/v4-core/contracts/interfaces/IControlledToken.sol



// SPDX-License-Identifier: GPL-3.0

pragma solidity 0.8.6;

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

/** @title IControlledToken
  * @author PoolTogether Inc Team
  * @notice ERC20 Tokens with a controller for minting & burning.
*/
interface IControlledToken is IERC20 {

    /** 
        @notice Interface to the contract responsible for controlling mint/burn
    */
    function controller() external view returns (address);

    /** 
      * @notice Allows the controller to mint tokens for a user account
      * @dev May be overridden to provide more granular control over minting
      * @param user Address of the receiver of the minted tokens
      * @param amount Amount of tokens to mint
    */
    function controllerMint(address user, uint256 amount) external;

    /** 
      * @notice Allows the controller to burn tokens from a user account
      * @dev May be overridden to provide more granular control over burning
      * @param user Address of the holder account to burn tokens from
      * @param amount Amount of tokens to burn
    */
    function controllerBurn(address user, uint256 amount) external;

    /** 
      * @notice Allows an operator via the controller to burn tokens on behalf of a user account
      * @dev May be overridden to provide more granular control over operator-burning
      * @param operator Address of the operator performing the burn action via the controller contract
      * @param user Address of the holder account to burn tokens from
      * @param amount Amount of tokens to burn
    */
    function controllerBurnFrom(
        address operator,
        address user,
        uint256 amount
    ) external;
}

// File: @pooltogether/v4-core/contracts/libraries/ExtendedSafeCastLib.sol



// SPDX-License-Identifier: GPL-3.0

pragma solidity 0.8.6;

/**
 * @dev Wrappers over Solidity's uintXX/intXX casting operators with added overflow
 * checks.
 *
 * Downcasting from uint256/int256 in Solidity does not revert on overflow. This can
 * easily result in undesired exploitation or bugs, since developers usually
 * assume that overflows raise errors. `SafeCast` restores this intuition by
 * reverting the transaction when such an operation overflows.
 *
 * Using this library instead of the unchecked operations eliminates an entire
 * class of bugs, so it's recommended to use it always.
 *
 * Can be combined with {SafeMath} and {SignedSafeMath} to extend it to smaller types, by performing
 * all math on `uint256` and `int256` and then downcasting.
 */
library ExtendedSafeCastLib {

    /**
     * @dev Returns the downcasted uint104 from uint256, reverting on
     * overflow (when the input is greater than largest uint104).
     *
     * Counterpart to Solidity's `uint104` operator.
     *
     * Requirements:
     *
     * - input must fit into 104 bits
     */
    function toUint104(uint256 _value) internal pure returns (uint104) {
        require(_value <= type(uint104).max, "SafeCast: value doesn't fit in 104 bits");
        return uint104(_value);
    }

    /**
     * @dev Returns the downcasted uint208 from uint256, reverting on
     * overflow (when the input is greater than largest uint208).
     *
     * Counterpart to Solidity's `uint208` operator.
     *
     * Requirements:
     *
     * - input must fit into 208 bits
     */
    function toUint208(uint256 _value) internal pure returns (uint208) {
        require(_value <= type(uint208).max, "SafeCast: value doesn't fit in 208 bits");
        return uint208(_value);
    }

    /**
     * @dev Returns the downcasted uint224 from uint256, reverting on
     * overflow (when the input is greater than largest uint224).
     *
     * Counterpart to Solidity's `uint224` operator.
     *
     * Requirements:
     *
     * - input must fit into 224 bits
     */
    function toUint224(uint256 _value) internal pure returns (uint224) {
        require(_value <= type(uint224).max, "SafeCast: value doesn't fit in 224 bits");
        return uint224(_value);
    }
}

// File: @pooltogether/v4-core/contracts/libraries/OverflowSafeComparatorLib.sol



// SPDX-License-Identifier: GPL-3.0

pragma solidity 0.8.6;

/// @title OverflowSafeComparatorLib library to share comparator functions between contracts
/// @dev Code taken from Uniswap V3 Oracle.sol: https://github.com/Uniswap/v3-core/blob/3e88af408132fc957e3e406f65a0ce2b1ca06c3d/contracts/libraries/Oracle.sol
/// @author PoolTogether Inc.
library OverflowSafeComparatorLib {
    /// @notice 32-bit timestamps comparator.
    /// @dev safe for 0 or 1 overflows, `_a` and `_b` must be chronologically before or equal to time.
    /// @param _a A comparison timestamp from which to determine the relative position of `_timestamp`.
    /// @param _b Timestamp to compare against `_a`.
    /// @param _timestamp A timestamp truncated to 32 bits.
    /// @return bool Whether `_a` is chronologically < `_b`.
    function lt(
        uint32 _a,
        uint32 _b,
        uint32 _timestamp
    ) internal pure returns (bool) {
        // No need to adjust if there hasn't been an overflow
        if (_a <= _timestamp && _b <= _timestamp) return _a < _b;

        uint256 aAdjusted = _a > _timestamp ? _a : _a + 2**32;
        uint256 bAdjusted = _b > _timestamp ? _b : _b + 2**32;

        return aAdjusted < bAdjusted;
    }

    /// @notice 32-bit timestamps comparator.
    /// @dev safe for 0 or 1 overflows, `_a` and `_b` must be chronologically before or equal to time.
    /// @param _a A comparison timestamp from which to determine the relative position of `_timestamp`.
    /// @param _b Timestamp to compare against `_a`.
    /// @param _timestamp A timestamp truncated to 32 bits.
    /// @return bool Whether `_a` is chronologically <= `_b`.
    function lte(
        uint32 _a,
        uint32 _b,
        uint32 _timestamp
    ) internal pure returns (bool) {

        // No need to adjust if there hasn't been an overflow
        if (_a <= _timestamp && _b <= _timestamp) return _a <= _b;

        uint256 aAdjusted = _a > _timestamp ? _a : _a + 2**32;
        uint256 bAdjusted = _b > _timestamp ? _b : _b + 2**32;

        return aAdjusted <= bAdjusted;
    }

    /// @notice 32-bit timestamp subtractor
    /// @dev safe for 0 or 1 overflows, where `_a` and `_b` must be chronologically before or equal to time
    /// @param _a The subtraction left operand
    /// @param _b The subtraction right operand
    /// @param _timestamp The current time.  Expected to be chronologically after both.
    /// @return The difference between a and b, adjusted for overflow
    function checkedSub(
        uint32 _a,
        uint32 _b,
        uint32 _timestamp
    ) internal pure returns (uint32) {
        // No need to adjust if there hasn't been an overflow

        if (_a <= _timestamp && _b <= _timestamp) return _a - _b;

        uint256 aAdjusted = _a > _timestamp ? _a : _a + 2**32;
        uint256 bAdjusted = _b > _timestamp ? _b : _b + 2**32;

        return uint32(aAdjusted - bAdjusted);
    }
}

// File: @pooltogether/v4-core/contracts/libraries/RingBufferLib.sol



// SPDX-License-Identifier: GPL-3.0

pragma solidity 0.8.6;

library RingBufferLib {
    /**
    * @notice Returns wrapped TWAB index.
    * @dev  In order to navigate the TWAB circular buffer, we need to use the modulo operator.
    * @dev  For example, if `_index` is equal to 32 and the TWAB circular buffer is of `_cardinality` 32,
    *       it will return 0 and will point to the first element of the array.
    * @param _index Index used to navigate through the TWAB circular buffer.
    * @param _cardinality TWAB buffer cardinality.
    * @return TWAB index.
    */
    function wrap(uint256 _index, uint256 _cardinality) internal pure returns (uint256) {
        return _index % _cardinality;
    }

    /**
    * @notice Computes the negative offset from the given index, wrapped by the cardinality.
    * @dev  We add `_cardinality` to `_index` to be able to offset even if `_amount` is superior to `_cardinality`.
    * @param _index The index from which to offset
    * @param _amount The number of indices to offset.  This is subtracted from the given index.
    * @param _cardinality The number of elements in the ring buffer
    * @return Offsetted index.
     */
    function offset(
        uint256 _index,
        uint256 _amount,
        uint256 _cardinality
    ) internal pure returns (uint256) {
        return wrap(_index + _cardinality - _amount, _cardinality);
    }

    /// @notice Returns the index of the last recorded TWAB
    /// @param _nextIndex The next available twab index.  This will be recorded to next.
    /// @param _cardinality The cardinality of the TWAB history.
    /// @return The index of the last recorded TWAB
    function newestIndex(uint256 _nextIndex, uint256 _cardinality)
        internal
        pure
        returns (uint256)
    {
        if (_cardinality == 0) {
            return 0;
        }

        return wrap(_nextIndex + _cardinality - 1, _cardinality);
    }

    /// @notice Computes the ring buffer index that follows the given one, wrapped by cardinality
    /// @param _index The index to increment
    /// @param _cardinality The number of elements in the Ring Buffer
    /// @return The next index relative to the given index.  Will wrap around to 0 if the next index == cardinality
    function nextIndex(uint256 _index, uint256 _cardinality)
        internal
        pure
        returns (uint256)
    {
        return wrap(_index + 1, _cardinality);
    }
}

// File: @pooltogether/v4-core/contracts/libraries/ObservationLib.sol



// SPDX-License-Identifier: GPL-3.0

pragma solidity 0.8.6;

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

import "./OverflowSafeComparatorLib.sol";
import "./RingBufferLib.sol";

/**
* @title Observation Library
* @notice This library allows one to store an array of timestamped values and efficiently binary search them.
* @dev Largely pulled from Uniswap V3 Oracle.sol: https://github.com/Uniswap/v3-core/blob/c05a0e2c8c08c460fb4d05cfdda30b3ad8deeaac/contracts/libraries/Oracle.sol
* @author PoolTogether Inc.
*/
library ObservationLib {
    using OverflowSafeComparatorLib for uint32;
    using SafeCast for uint256;

    /// @notice The maximum number of observations
    uint24 public constant MAX_CARDINALITY = 16777215; // 2**24

    /**
    * @notice Observation, which includes an amount and timestamp.
    * @param amount `amount` at `timestamp`.
    * @param timestamp Recorded `timestamp`.
    */
    struct Observation {
        uint224 amount;
        uint32 timestamp;
    }

    /**
    * @notice Fetches Observations `beforeOrAt` and `atOrAfter` a `_target`, eg: where [`beforeOrAt`, `atOrAfter`] is satisfied.
    * The result may be the same Observation, or adjacent Observations.
    * @dev The answer must be contained in the array used when the target is located within the stored Observation.
    * boundaries: older than the most recent Observation and younger, or the same age as, the oldest Observation.
    * @dev  If `_newestObservationIndex` is less than `_oldestObservationIndex`, it means that we've wrapped around the circular buffer.
    *       So the most recent observation will be at `_oldestObservationIndex + _cardinality - 1`, at the beginning of the circular buffer.
    * @param _observations List of Observations to search through.
    * @param _newestObservationIndex Index of the newest Observation. Right side of the circular buffer.
    * @param _oldestObservationIndex Index of the oldest Observation. Left side of the circular buffer.
    * @param _target Timestamp at which we are searching the Observation.
    * @param _cardinality Cardinality of the circular buffer we are searching through.
    * @param _time Timestamp at which we perform the binary search.
    * @return beforeOrAt Observation recorded before, or at, the target.
    * @return atOrAfter Observation recorded at, or after, the target.
    */
    function binarySearch(
        Observation[MAX_CARDINALITY] storage _observations,
        uint24 _newestObservationIndex,
        uint24 _oldestObservationIndex,
        uint32 _target,
        uint24 _cardinality,
        uint32 _time
    ) internal view returns (Observation memory beforeOrAt, Observation memory atOrAfter) {
        uint256 leftSide = _oldestObservationIndex;
        uint256 rightSide = _newestObservationIndex < leftSide
            ? leftSide + _cardinality - 1
            : _newestObservationIndex;
        uint256 currentIndex;

        while (true) {
            // We start our search in the middle of the `leftSide` and `rightSide`.
            // After each iteration, we narrow down the search to the left or the right side while still starting our search in the middle.
            currentIndex = (leftSide + rightSide) / 2;

            beforeOrAt = _observations[uint24(RingBufferLib.wrap(currentIndex, _cardinality))];
            uint32 beforeOrAtTimestamp = beforeOrAt.timestamp;

            // We've landed on an uninitialized timestamp, keep searching higher (more recently).
            if (beforeOrAtTimestamp == 0) {
                leftSide = currentIndex + 1;
                continue;
            }

            atOrAfter = _observations[uint24(RingBufferLib.nextIndex(currentIndex, _cardinality))];

            bool targetAtOrAfter = beforeOrAtTimestamp.lte(_target, _time);

            // Check if we've found the corresponding Observation.
            if (targetAtOrAfter && _target.lte(atOrAfter.timestamp, _time)) {
                break;
            }

            // If `beforeOrAtTimestamp` is greater than `_target`, then we keep searching lower. To the left of the current index.
            if (!targetAtOrAfter) {
                rightSide = currentIndex - 1;
            } else {
                // Otherwise, we keep searching higher. To the left of the current index.
                leftSide = currentIndex + 1;
            }
        }
    }
}

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



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

pragma solidity ^0.8.0;

/**
 * @dev Wrappers over Solidity's uintXX/intXX casting operators with added overflow
 * checks.
 *
 * Downcasting from uint256/int256 in Solidity does not revert on overflow. This can
 * easily result in undesired exploitation or bugs, since developers usually
 * assume that overflows raise errors. `SafeCast` restores this intuition by
 * reverting the transaction when such an operation overflows.
 *
 * Using this library instead of the unchecked operations eliminates an entire
 * class of bugs, so it's recommended to use it always.
 *
 * Can be combined with {SafeMath} and {SignedSafeMath} to extend it to smaller types, by performing
 * all math on `uint256` and `int256` and then downcasting.
 */
library SafeCast {
    /**
     * @dev Returns the downcasted uint224 from uint256, reverting on
     * overflow (when the input is greater than largest uint224).
     *
     * Counterpart to Solidity's `uint224` operator.
     *
     * Requirements:
     *
     * - input must fit into 224 bits
     */
    function toUint224(uint256 value) internal pure returns (uint224) {
        require(value <= type(uint224).max, "SafeCast: value doesn't fit in 224 bits");
        return uint224(value);
    }

    /**
     * @dev Returns the downcasted uint128 from uint256, reverting on
     * overflow (when the input is greater than largest uint128).
     *
     * Counterpart to Solidity's `uint128` operator.
     *
     * Requirements:
     *
     * - input must fit into 128 bits
     */
    function toUint128(uint256 value) internal pure returns (uint128) {
        require(value <= type(uint128).max, "SafeCast: value doesn't fit in 128 bits");
        return uint128(value);
    }

    /**
     * @dev Returns the downcasted uint96 from uint256, reverting on
     * overflow (when the input is greater than largest uint96).
     *
     * Counterpart to Solidity's `uint96` operator.
     *
     * Requirements:
     *
     * - input must fit into 96 bits
     */
    function toUint96(uint256 value) internal pure returns (uint96) {
        require(value <= type(uint96).max, "SafeCast: value doesn't fit in 96 bits");
        return uint96(value);
    }

    /**
     * @dev Returns the downcasted uint64 from uint256, reverting on
     * overflow (when the input is greater than largest uint64).
     *
     * Counterpart to Solidity's `uint64` operator.
     *
     * Requirements:
     *
     * - input must fit into 64 bits
     */
    function toUint64(uint256 value) internal pure returns (uint64) {
        require(value <= type(uint64).max, "SafeCast: value doesn't fit in 64 bits");
        return uint64(value);
    }

    /**
     * @dev Returns the downcasted uint32 from uint256, reverting on
     * overflow (when the input is greater than largest uint32).
     *
     * Counterpart to Solidity's `uint32` operator.
     *
     * Requirements:
     *
     * - input must fit into 32 bits
     */
    function toUint32(uint256 value) internal pure returns (uint32) {
        require(value <= type(uint32).max, "SafeCast: value doesn't fit in 32 bits");
        return uint32(value);
    }

    /**
     * @dev Returns the downcasted uint16 from uint256, reverting on
     * overflow (when the input is greater than largest uint16).
     *
     * Counterpart to Solidity's `uint16` operator.
     *
     * Requirements:
     *
     * - input must fit into 16 bits
     */
    function toUint16(uint256 value) internal pure returns (uint16) {
        require(value <= type(uint16).max, "SafeCast: value doesn't fit in 16 bits");
        return uint16(value);
    }

    /**
     * @dev Returns the downcasted uint8 from uint256, reverting on
     * overflow (when the input is greater than largest uint8).
     *
     * Counterpart to Solidity's `uint8` operator.
     *
     * Requirements:
     *
     * - input must fit into 8 bits.
     */
    function toUint8(uint256 value) internal pure returns (uint8) {
        require(value <= type(uint8).max, "SafeCast: value doesn't fit in 8 bits");
        return uint8(value);
    }

    /**
     * @dev Converts a signed int256 into an unsigned uint256.
     *
     * Requirements:
     *
     * - input must be greater than or equal to 0.
     */
    function toUint256(int256 value) internal pure returns (uint256) {
        require(value >= 0, "SafeCast: value must be positive");
        return uint256(value);
    }

    /**
     * @dev Returns the downcasted int128 from int256, reverting on
     * overflow (when the input is less than smallest int128 or
     * greater than largest int128).
     *
     * Counterpart to Solidity's `int128` operator.
     *
     * Requirements:
     *
     * - input must fit into 128 bits
     *
     * _Available since v3.1._
     */
    function toInt128(int256 value) internal pure returns (int128) {
        require(value >= type(int128).min && value <= type(int128).max, "SafeCast: value doesn't fit in 128 bits");
        return int128(value);
    }

    /**
     * @dev Returns the downcasted int64 from int256, reverting on
     * overflow (when the input is less than smallest int64 or
     * greater than largest int64).
     *
     * Counterpart to Solidity's `int64` operator.
     *
     * Requirements:
     *
     * - input must fit into 64 bits
     *
     * _Available since v3.1._
     */
    function toInt64(int256 value) internal pure returns (int64) {
        require(value >= type(int64).min && value <= type(int64).max, "SafeCast: value doesn't fit in 64 bits");
        return int64(value);
    }

    /**
     * @dev Returns the downcasted int32 from int256, reverting on
     * overflow (when the input is less than smallest int32 or
     * greater than largest int32).
     *
     * Counterpart to Solidity's `int32` operator.
     *
     * Requirements:
     *
     * - input must fit into 32 bits
     *
     * _Available since v3.1._
     */
    function toInt32(int256 value) internal pure returns (int32) {
        require(value >= type(int32).min && value <= type(int32).max, "SafeCast: value doesn't fit in 32 bits");
        return int32(value);
    }

    /**
     * @dev Returns the downcasted int16 from int256, reverting on
     * overflow (when the input is less than smallest int16 or
     * greater than largest int16).
     *
     * Counterpart to Solidity's `int16` operator.
     *
     * Requirements:
     *
     * - input must fit into 16 bits
     *
     * _Available since v3.1._
     */
    function toInt16(int256 value) internal pure returns (int16) {
        require(value >= type(int16).min && value <= type(int16).max, "SafeCast: value doesn't fit in 16 bits");
        return int16(value);
    }

    /**
     * @dev Returns the downcasted int8 from int256, reverting on
     * overflow (when the input is less than smallest int8 or
     * greater than largest int8).
     *
     * Counterpart to Solidity's `int8` operator.
     *
     * Requirements:
     *
     * - input must fit into 8 bits.
     *
     * _Available since v3.1._
     */
    function toInt8(int256 value) internal pure returns (int8) {
        require(value >= type(int8).min && value <= type(int8).max, "SafeCast: value doesn't fit in 8 bits");
        return int8(value);
    }

    /**
     * @dev Converts an unsigned uint256 into a signed int256.
     *
     * Requirements:
     *
     * - input must be less than or equal to maxInt256.
     */
    function toInt256(uint256 value) internal pure returns (int256) {
        // Note: Unsafe cast below is okay because `type(int256).max` is guaranteed to be positive
        require(value <= uint256(type(int256).max), "SafeCast: value doesn't fit in an int256");
        return int256(value);
    }
}

// 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);
}