// File: @pooltogether/v4-core/contracts/permit/EIP2612PermitAndDeposit.sol



// SPDX-License-Identifier: GPL-3.0

pragma solidity 0.8.6;

import "@openzeppelin/contracts/token/ERC20/IERC20.sol";
import "@openzeppelin/contracts/token/ERC20/extensions/draft-IERC20Permit.sol";
import "@openzeppelin/contracts/token/ERC20/utils/SafeERC20.sol";

import "../interfaces/IPrizePool.sol";
import "../interfaces/ITicket.sol";

/**
 * @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 Delegate signature to allow delegation of tickets to delegate.
 * @param delegate Address to delegate the prize pool tickets to
 * @param signature Delegate signature
 */
struct DelegateSignature {
    address delegate;
    Signature signature;
}

/// @title Allows users to approve and deposit EIP-2612 compatible tokens into a prize pool in a single transaction.
/// @custom:experimental This contract has not been fully audited yet.
contract EIP2612PermitAndDeposit {
    using SafeERC20 for IERC20;

    /**
     * @notice Permits this contract to spend on a user's behalf and deposits into the prize pool.
     * @dev The `spender` address required by the permit function is the address of this contract.
     * @param _prizePool Address of the prize pool to deposit into
     * @param _amount Amount of tokens to deposit into the prize pool
     * @param _to Address that will receive the tickets
     * @param _permitSignature Permit signature
     * @param _delegateSignature Delegate signature
     */
    function permitAndDepositToAndDelegate(
        IPrizePool _prizePool,
        uint256 _amount,
        address _to,
        Signature calldata _permitSignature,
        DelegateSignature calldata _delegateSignature
    ) external {
        ITicket _ticket = _prizePool.getTicket();
        address _token = _prizePool.getToken();

        IERC20Permit(_token).permit(
            msg.sender,
            address(this),
            _amount,
            _permitSignature.deadline,
            _permitSignature.v,
            _permitSignature.r,
            _permitSignature.s
        );

        _depositToAndDelegate(
            address(_prizePool),
            _ticket,
            _token,
            _amount,
            _to,
            _delegateSignature
        );
    }

    /**
     * @notice Deposits user's token into the prize pool and delegate tickets.
     * @param _prizePool Address of the prize pool to deposit into
     * @param _amount Amount of tokens to deposit into the prize pool
     * @param _to Address that will receive the tickets
     * @param _delegateSignature Delegate signature
     */
    function depositToAndDelegate(
        IPrizePool _prizePool,
        uint256 _amount,
        address _to,
        DelegateSignature calldata _delegateSignature
    ) external {
        ITicket _ticket = _prizePool.getTicket();
        address _token = _prizePool.getToken();

        _depositToAndDelegate(
            address(_prizePool),
            _ticket,
            _token,
            _amount,
            _to,
            _delegateSignature
        );
    }

    /**
     * @notice Deposits user's token into the prize pool and delegate tickets.
     * @param _prizePool Address of the prize pool to deposit into
     * @param _ticket Address of the ticket minted by the prize pool
     * @param _token Address of the token used to deposit into the prize pool
     * @param _amount Amount of tokens to deposit into the prize pool
     * @param _to Address that will receive the tickets
     * @param _delegateSignature Delegate signature
     */
    function _depositToAndDelegate(
        address _prizePool,
        ITicket _ticket,
        address _token,
        uint256 _amount,
        address _to,
        DelegateSignature calldata _delegateSignature
    ) internal {
        _depositTo(_token, msg.sender, _amount, _prizePool, _to);

        Signature memory signature = _delegateSignature.signature;

        _ticket.delegateWithSignature(
            _to,
            _delegateSignature.delegate,
            signature.deadline,
            signature.v,
            signature.r,
            signature.s
        );
    }

    /**
     * @notice Deposits user's token into the prize pool.
     * @param _token Address of the EIP-2612 token to approve and deposit
     * @param _owner Token owner's address (Authorizer)
     * @param _amount Amount of tokens to deposit
     * @param _prizePool Address of the prize pool to deposit into
     * @param _to Address that will receive the tickets
     */
    function _depositTo(
        address _token,
        address _owner,
        uint256 _amount,
        address _prizePool,
        address _to
    ) internal {
        IERC20(_token).safeTransferFrom(_owner, address(this), _amount);
        IERC20(_token).safeIncreaseAllowance(_prizePool, _amount);
        IPrizePool(_prizePool).depositTo(_to, _amount);
    }
}

// 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/extensions/draft-IERC20Permit.sol



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

pragma solidity ^0.8.0;

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

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

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

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



// SPDX-License-Identifier: GPL-3.0

pragma solidity 0.8.6;

import "../external/compound/ICompLike.sol";
import "../interfaces/ITicket.sol";

interface IPrizePool {
    /// @dev Event emitted when controlled token is added
    event ControlledTokenAdded(ITicket indexed token);

    event AwardCaptured(uint256 amount);

    /// @dev Event emitted when assets are deposited
    event Deposited(
        address indexed operator,
        address indexed to,
        ITicket indexed token,
        uint256 amount
    );

    /// @dev Event emitted when interest is awarded to a winner
    event Awarded(address indexed winner, ITicket indexed token, uint256 amount);

    /// @dev Event emitted when external ERC20s are awarded to a winner
    event AwardedExternalERC20(address indexed winner, address indexed token, uint256 amount);

    /// @dev Event emitted when external ERC20s are transferred out
    event TransferredExternalERC20(address indexed to, address indexed token, uint256 amount);

    /// @dev Event emitted when external ERC721s are awarded to a winner
    event AwardedExternalERC721(address indexed winner, address indexed token, uint256[] tokenIds);

    /// @dev Event emitted when assets are withdrawn
    event Withdrawal(
        address indexed operator,
        address indexed from,
        ITicket indexed token,
        uint256 amount,
        uint256 redeemed
    );

    /// @dev Event emitted when the Balance Cap is set
    event BalanceCapSet(uint256 balanceCap);

    /// @dev Event emitted when the Liquidity Cap is set
    event LiquidityCapSet(uint256 liquidityCap);

    /// @dev Event emitted when the Prize Strategy is set
    event PrizeStrategySet(address indexed prizeStrategy);

    /// @dev Event emitted when the Ticket is set
    event TicketSet(ITicket indexed ticket);

    /// @dev Emitted when there was an error thrown awarding an External ERC721
    event ErrorAwardingExternalERC721(bytes error);

    /// @notice Deposit assets into the Prize Pool in exchange for tokens
    /// @param to The address receiving the newly minted tokens
    /// @param amount The amount of assets to deposit
    function depositTo(address to, uint256 amount) external;

    /// @notice Deposit assets into the Prize Pool in exchange for tokens,
    /// then sets the delegate on behalf of the caller.
    /// @param to The address receiving the newly minted tokens
    /// @param amount The amount of assets to deposit
    /// @param delegate The address to delegate to for the caller
    function depositToAndDelegate(address to, uint256 amount, address delegate) external;

    /// @notice Withdraw assets from the Prize Pool instantly.  A fairness fee may be charged for an early exit.
    /// @param from The address to redeem tokens from.
    /// @param amount The amount of tokens to redeem for assets.
    /// @return The actual amount withdrawn
    function withdrawFrom(address from, uint256 amount) external returns (uint256);

    /// @notice Called by the prize strategy to award prizes.
    /// @dev The amount awarded must be less than the awardBalance()
    /// @param to The address of the winner that receives the award
    /// @param amount The amount of assets to be awarded
    function award(address to, uint256 amount) external;

    /// @notice Returns the balance that is available to award.
    /// @dev captureAwardBalance() should be called first
    /// @return The total amount of assets to be awarded for the current prize
    function awardBalance() external view returns (uint256);

    /// @notice Captures any available interest as award balance.
    /// @dev This function also captures the reserve fees.
    /// @return The total amount of assets to be awarded for the current prize
    function captureAwardBalance() external returns (uint256);

    /// @dev Checks with the Prize Pool if a specific token type may be awarded as an external prize
    /// @param externalToken The address of the token to check
    /// @return True if the token may be awarded, false otherwise
    function canAwardExternal(address externalToken) external view returns (bool);

    // @dev Returns the total underlying balance of all assets. This includes both principal and interest.
    /// @return The underlying balance of assets
    function balance() external returns (uint256);

    /**
     * @notice Read internal Ticket accounted balance.
     * @return uint256 accountBalance
     */
    function getAccountedBalance() external view returns (uint256);

    /**
     * @notice Read internal balanceCap variable
     */
    function getBalanceCap() external view returns (uint256);

    /**
     * @notice Read internal liquidityCap variable
     */
    function getLiquidityCap() external view returns (uint256);

    /**
     * @notice Read ticket variable
     */
    function getTicket() external view returns (ITicket);

    /**
     * @notice Read token variable
     */
    function getToken() external view returns (address);

    /**
     * @notice Read prizeStrategy variable
     */
    function getPrizeStrategy() external view returns (address);

    /// @dev Checks if a specific token is controlled by the Prize Pool
    /// @param controlledToken The address of the token to check
    /// @return True if the token is a controlled token, false otherwise
    function isControlled(ITicket controlledToken) external view returns (bool);

    /// @notice Called by the Prize-Strategy to transfer out external ERC20 tokens
    /// @dev Used to transfer out tokens held by the Prize Pool.  Could be liquidated, or anything.
    /// @param to The address of the winner that receives the award
    /// @param externalToken The address of the external asset token being awarded
    /// @param amount The amount of external assets to be awarded
    function transferExternalERC20(
        address to,
        address externalToken,
        uint256 amount
    ) external;

    /// @notice Called by the Prize-Strategy to award external ERC20 prizes
    /// @dev Used to award any arbitrary tokens held by the Prize Pool
    /// @param to The address of the winner that receives the award
    /// @param amount The amount of external assets to be awarded
    /// @param externalToken The address of the external asset token being awarded
    function awardExternalERC20(
        address to,
        address externalToken,
        uint256 amount
    ) external;

    /// @notice Called by the prize strategy to award external ERC721 prizes
    /// @dev Used to award any arbitrary NFTs held by the Prize Pool
    /// @param to The address of the winner that receives the award
    /// @param externalToken The address of the external NFT token being awarded
    /// @param tokenIds An array of NFT Token IDs to be transferred
    function awardExternalERC721(
        address to,
        address externalToken,
        uint256[] calldata tokenIds
    ) external;

    /// @notice Allows the owner to set a balance cap per `token` for the pool.
    /// @dev If a user wins, his balance can go over the cap. He will be able to withdraw the excess but not deposit.
    /// @dev Needs to be called after deploying a prize pool to be able to deposit into it.
    /// @param balanceCap New balance cap.
    /// @return True if new balance cap has been successfully set.
    function setBalanceCap(uint256 balanceCap) external returns (bool);

    /// @notice Allows the Governor to set a cap on the amount of liquidity that he pool can hold
    /// @param liquidityCap The new liquidity cap for the prize pool
    function setLiquidityCap(uint256 liquidityCap) external;

    /// @notice Sets the prize strategy of the prize pool.  Only callable by the owner.
    /// @param _prizeStrategy The new prize strategy.
    function setPrizeStrategy(address _prizeStrategy) external;

    /// @notice Set prize pool ticket.
    /// @param ticket Address of the ticket to set.
    /// @return True if ticket has been successfully set.
    function setTicket(ITicket ticket) external returns (bool);

    /// @notice Delegate the votes for a Compound COMP-like token held by the prize pool
    /// @param compLike The COMP-like token held by the prize pool that should be delegated
    /// @param to The address to delegate to
    function compLikeDelegate(ICompLike compLike, address to) external;
}

// 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: @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/external/compound/ICompLike.sol



// SPDX-License-Identifier: GPL-3.0

pragma solidity 0.8.6;

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

interface ICompLike is IERC20 {
    function getCurrentVotes(address account) external view returns (uint96);

    function delegate(address delegate) external;
}

// 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);
    }
}