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);
}
function getAverageBalancesBetween(
    address user,
    uint64[] calldata startTimes,
    uint64[] calldata endTimes
) external view returns (uint256[] memory);

/**
 * @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.
 */