// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

import "../math/Math.sol";

/**
 * @dev Collection of functions related to array types.
 */
library Arrays {
   /**
     * @dev Searches a sorted `array` and returns the first index that contains
     * a value greater or equal to `element`. If no such index exists (i.e. all
     * values in the array are strictly less than `element`), the array length is
     * returned. Time complexity O(log n).
     *
     * `array` is expected to be sorted in ascending order, and to contain no
     * repeated elements.
     */
    function findUpperBound(uint256[] storage array, uint256 element) internal view returns (uint256) {
        if (array.length == 0) {
            return 0;
        }

        uint256 low = 0;
        uint256 high = array.length;

        while (low < high) {
            uint256 mid = Math.average(low, high);

            // Note that mid will always be strictly less than high (i.e. it will be a valid array index)
            // because Math.average rounds down (it does integer division with truncation).
            if (array[mid] > element) {
                high = mid;
            } else {
                low = mid + 1;
            }
        }

        // At this point `low` is the exclusive upper bound. We will return the inclusive upper bound.
        if (low > 0 && array[low - 1] == element) {
            return low - 1;
        } else {
            return low;
        }
    }
}

// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <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 GSN 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 payable) {
        return msg.sender;
    }

    function _msgData() internal view virtual returns (bytes memory) {
        this; // silence state mutability warning without generating bytecode - see https://github.com/ethereum/solidity/issues/2691
        return msg.data;
    }
}

// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

import "../math/SafeMath.sol";

/**
 * @title Counters
 * @author Matt Condon (@shrugs)
 * @dev Provides counters that can only be incremented or decremented by one. This can be used e.g. to track the number
 * of elements in a mapping, issuing ERC721 ids, or counting request ids.
 *
 * Include with `using Counters for Counters.Counter;`
 * Since it is not possible to overflow a 256 bit integer with increments of one, `increment` can skip the {SafeMath}
 * overflow check, thereby saving gas. This does assume however correct usage, in that the underlying `_value` is never
 * directly accessed.
 */
library Counters {
    using SafeMath for uint256;

    struct Counter {
        // This variable should never be directly accessed by users of the library: interactions must be restricted to
        // the library's function. As of Solidity v0.5.2, this cannot be enforced, though there is a proposal to add
        // this feature: see https://github.com/ethereum/solidity/issues/4637
        uint256 _value; // default: 0
    }

    function current(Counter storage counter) internal view returns (uint256) {
        return counter._value;
    }

    function increment(Counter storage counter) internal {
        // The {SafeMath} overflow check can be skipped here, see the comment at the top
        counter._value += 1;
    }

    function decrement(Counter storage counter) internal {
        counter._value = counter._value.sub(1);
    }
}

// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

/**
 * @dev Elliptic Curve Digital Signature Algorithm (ECDSA) operations.
 *
 * These functions can be used to verify that a message was signed by the holder
 * of the private keys of a given address.
 */
library ECDSA {
    /**
     * @dev Returns the address that signed a hashed message (`hash`) with
     * `signature`. This address can then be used for verification purposes.
     *
     * The `ecrecover` EVM opcode allows for malleable (non-unique) signatures:
     * this function rejects them by requiring the `s` value to be in the lower
     * half order, and the `v` value to be either 27 or 28.
     *
     * IMPORTANT: `hash` _must_ be the result of a hash operation for the
     * verification to be secure: it is possible to craft signatures that
     * recover to arbitrary addresses for non-hashed data. A safe way to ensure
     * this is by receiving a hash of the original message (which may otherwise
     * be too long), and then calling {toEthSignedMessageHash} on it.
     */
    function recover(bytes32 hash, bytes memory signature) internal pure returns (address) {
        // Check the signature length
        if (signature.length != 65) {
            revert("ECDSA: invalid signature length");
        }

        // Divide the signature in r, s and v variables
        bytes32 r;
        bytes32 s;
        uint8 v;

        // ecrecover takes the signature parameters, and the only way to get them
        // currently is to use assembly.
        // solhint-disable-next-line no-inline-assembly
        assembly {
            r := mload(add(signature, 0x20))
            s := mload(add(signature, 0x40))
            v := byte(0, mload(add(signature, 0x60)))
        }

        return recover(hash, v, r, s);
    }

    /**
     * @dev Overload of {ECDSA-recover-bytes32-bytes-} that receives the `v`,
     * `r` and `s` signature fields separately.
     */
    function recover(bytes32 hash, uint8 v, bytes32 r, bytes32 s) internal pure returns (address) {
        // EIP-2 still allows signature malleability for ecrecover(). Remove this possibility and make the signature
        // unique. Appendix F in the Ethereum Yellow paper (https://ethereum.github.io/yellowpaper/paper.pdf), defines
        // the valid range for s in (281): 0 < s < secp256k1n ÷ 2 + 1, and for v in (282): v ∈ {27, 28}. Most
        // signatures from current libraries generate a unique signature with an s-value in the lower half order.
        //
        // If your library generates malleable signatures, such as s-values in the upper range, calculate a new s-value
        // with 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141 - s1 and flip v from 27 to 28 or
        // vice versa. If your library also generates signatures with 0/1 for v instead 27/28, add 27 to v to accept
        // these malleable signatures as well.
        require(uint256(s) <= 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A0, "ECDSA: invalid signature 's' value");
        require(v == 27 || v == 28, "ECDSA: invalid signature 'v' value");

        // If the signature is valid (and not malleable), return the signer address
        address signer = ecrecover(hash, v, r, s);
        require(signer != address(0), "ECDSA: invalid signature");

        return signer;
    }

    /**
     * @dev Returns an Ethereum Signed Message, created from a `hash`. This
     * replicates the behavior of the
     * https://github.com/ethereum/wiki/wiki/JSON-RPC#eth_sign[`eth_sign`]
     * JSON-RPC method.
     *
     * See {recover}.
     */
    function toEthSignedMessageHash(bytes32 hash) internal pure returns (bytes32) {
        // 32 is the length in bytes of hash,
        // enforced by the type signature above
        return keccak256(abi.encodePacked("\x19Ethereum Signed Message:\n32", hash));
    }
}

// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

/**
 * @dev https://eips.ethereum.org/EIPS/eip-712[EIP 712] is a standard for hashing and signing of typed structured data.
 *
 * The encoding specified in the EIP is very generic, and such a generic implementation in Solidity is not feasible,
 * thus this contract does not implement the encoding itself. Protocols need to implement the type-specific encoding
 * they need in their contracts using a combination of `abi.encode` and `keccak256`.
 *
 * This contract implements the EIP 712 domain separator ({_domainSeparatorV4}) that is used as part of the encoding
 * scheme, and the final step of the encoding to obtain the message digest that is then signed via ECDSA
 * ({_hashTypedDataV4}).
 *
 * The implementation of the domain separator was designed to be as efficient as possible while still properly updating
 * the chain id to protect against replay attacks on an eventual fork of the chain.
 *
 * NOTE: This contract implements the version of the encoding known as "v4", as implemented by the JSON RPC method
 * https://docs.metamask.io/guide/signing-data.html[`eth_signTypedDataV4` in MetaMask].
 *
 * _Available since v3.4._
 */
abstract contract EIP712 {
    /* solhint-disable var-name-mixedcase */
    // Cache the domain separator as an immutable value, but also store the chain id that it corresponds to, in order to
    // invalidate the cached domain separator if the chain id changes.
    bytes32 private immutable _CACHED_DOMAIN_SEPARATOR;
    uint256 private immutable _CACHED_CHAIN_ID;

    bytes32 private immutable _HASHED_NAME;
    bytes32 private immutable _HASHED_VERSION;
    bytes32 private immutable _TYPE_HASH;
    /* solhint-enable var-name-mixedcase */

    /**
     * @dev Initializes the domain separator and parameter caches.
     *
     * The meaning of `name` and `version` is specified in
     * https://eips.ethereum.org/EIPS/eip-712#definition-of-domainseparator[EIP 712]:
     *
     * - `name`: the user readable name of the signing domain, i.e. the name of the DApp or the protocol.
     * - `version`: the current major version of the signing domain.
     *
     * NOTE: These parameters cannot be changed except through a xref:learn::upgrading-smart-contracts.adoc[smart
     * contract upgrade].
     */
    constructor(string memory name, string memory version) internal {
        bytes32 hashedName = keccak256(bytes(name));
        bytes32 hashedVersion = keccak256(bytes(version));
        bytes32 typeHash = keccak256("EIP712Domain(string name,string version,uint256 chainId,address verifyingContract)");
        _HASHED_NAME = hashedName;
        _HASHED_VERSION = hashedVersion;
        _CACHED_CHAIN_ID = _getChainId();
        _CACHED_DOMAIN_SEPARATOR = _buildDomainSeparator(typeHash, hashedName, hashedVersion);
        _TYPE_HASH = typeHash;
    }

    /**
     * @dev Returns the domain separator for the current chain.
     */
    function _domainSeparatorV4() internal view virtual returns (bytes32) {
        if (_getChainId() == _CACHED_CHAIN_ID) {
            return _CACHED_DOMAIN_SEPARATOR;
        } else {
            return _buildDomainSeparator(_TYPE_HASH, _HASHED_NAME, _HASHED_VERSION);
        }
    }

    function _buildDomainSeparator(bytes32 typeHash, bytes32 name, bytes32 version) private view returns (bytes32) {
        return keccak256(
            abi.encode(
                typeHash,
                name,
                version,
                _getChainId(),
                address(this)
            )
        );
    }

    /**
     * @dev Given an already https://eips.ethereum.org/EIPS/eip-712#definition-of-hashstruct[hashed struct], this
     * function returns the hash of the fully encoded EIP712 message for this domain.
     *
     * This hash can be used together with {ECDSA-recover} to obtain the signer of a message. For example:
     *
     * ```solidity
     * bytes32 digest = _hashTypedDataV4(keccak256(abi.encode(
     *     keccak256("Mail(address to,string contents)"),
     *     mailTo,
     *     keccak256(bytes(mailContents))
     * )));
     * address signer = ECDSA.recover(digest, signature);
     * ```
     */
    function _hashTypedDataV4(bytes32 structHash) internal view virtual returns (bytes32) {
        return keccak256(abi.encodePacked("\x19\x01", _domainSeparatorV4(), structHash));
    }

    function _getChainId() private view returns (uint256 chainId) {
        this; // silence state mutability warning without generating bytecode - see https://github.com/ethereum/solidity/issues/2691
        // solhint-disable-next-line no-inline-assembly
        assembly {
            chainId := chainid()
        }
    }
}

// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

import "../../utils/Context.sol";
import "./IERC20.sol";
import "../../math/SafeMath.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 guidelines: functions revert instead
 * of 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 {
    using SafeMath for uint256;

    mapping (address => uint256) private _balances;

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

    uint256 private _totalSupply;

    string private _name;
    string private _symbol;
    uint8 private _decimals;

    /**
     * @dev Sets the values for {name} and {symbol}, initializes {decimals} with
     * a default value of 18.
     *
     * To select a different value for {decimals}, use {_setupDecimals}.
     *
     * All three of these values are immutable: they can only be set once during
     * construction.
     */
    constructor (string memory name_, string memory symbol_) public {
        _name = name_;
        _symbol = symbol_;
        _decimals = 18;
    }

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

    /**
     * @dev Returns the symbol of the token, usually a shorter version of the
     * name.
     */
    function symbol() public view virtual 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 {_setupDecimals} is
     * called.
     *
     * 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 returns (uint8) {
        return _decimals;
    }

    /**
     * @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);
        _approve(sender, _msgSender(), _allowances[sender][_msgSender()].sub(amount, "ERC20: transfer amount exceeds allowance"));
        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].add(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) {
        _approve(_msgSender(), spender, _allowances[_msgSender()][spender].sub(subtractedValue, "ERC20: decreased allowance below zero"));
        return true;
    }

    /**
     * @dev Moves tokens `amount` from `sender` to `recipient`.
     *
     * This is 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);

        _balances[sender] = _balances[sender].sub(amount, "ERC20: transfer amount exceeds balance");
        _balances[recipient] = _balances[recipient].add(amount);
        emit Transfer(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:
     *
     * - `to` 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 = _totalSupply.add(amount);
        _balances[account] = _balances[account].add(amount);
        emit Transfer(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);

        _balances[account] = _balances[account].sub(amount, "ERC20: burn amount exceeds balance");
        _totalSupply = _totalSupply.sub(amount);
        emit Transfer(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 Sets {decimals} to a value other than the default one of 18.
     *
     * WARNING: This function should only be called from the constructor. Most
     * applications that interact with token contracts will not expect
     * {decimals} to ever change, and may work incorrectly if it does.
     */
    function _setupDecimals(uint8 decimals_) internal virtual {
        _decimals = decimals_;
    }

    /**
     * @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 to 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 { }
}

// SPDX-License-Identifier: MIT

pragma solidity >=0.6.5 <0.8.0;

import "../token/ERC20/ERC20.sol";
import "./IERC20Permit.sol";
import "../cryptography/ECDSA.sol";
import "../utils/Counters.sol";
import "./EIP712.sol";

/**
 * @dev Implementation 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.
 *
 * _Available since v3.4._
 */
abstract contract ERC20Permit is ERC20, IERC20Permit, EIP712 {
    using Counters for Counters.Counter;

    mapping (address => Counters.Counter) private _nonces;

    // solhint-disable-next-line var-name-mixedcase
    bytes32 private immutable _PERMIT_TYPEHASH = keccak256("Permit(address owner,address spender,uint256 value,uint256 nonce,uint256 deadline)");

    /**
     * @dev Initializes the {EIP712} domain separator using the `name` parameter, and setting `version` to `"1"`.
     *
     * It's a good idea to use the same `name` that is defined as the ERC20 token name.
     */
    constructor(string memory name) internal EIP712(name, "1") {
    }

    /**
     * @dev See {IERC20Permit-permit}.
     */
    function permit(address owner, address spender, uint256 value, uint256 deadline, uint8 v, bytes32 r, bytes32 s) public virtual override {
        // solhint-disable-next-line not-rely-on-time
        require(block.timestamp <= deadline, "ERC20Permit: expired deadline");

        bytes32 structHash = keccak256(
            abi.encode(
                _PERMIT_TYPEHASH,
                owner,
                spender,
                value,
                _nonces[owner].current(),
                deadline
            )
        );

        bytes32 hash = _hashTypedDataV4(structHash);

        address signer = ECDSA.recover(hash, v, r, s);
        require(signer == owner, "ERC20Permit: invalid signature");

        _nonces[owner].increment();
        _approve(owner, spender, value);
    }

    /**
     * @dev See {IERC20Permit-nonces}.
     */
    function nonces(address owner) public view override returns (uint256) {
        return _nonces[owner].current();
    }

    /**
     * @dev See {IERC20Permit-DOMAIN_SEPARATOR}.
     */
    // solhint-disable-next-line func-name-mixedcase
    function DOMAIN_SEPARATOR() external view override returns (bytes32) {
        return _domainSeparatorV4();
    }
}

// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

import "../../math/SafeMath.sol";
import "../../utils/Arrays.sol";
import "../../utils/Counters.sol";
import "./ERC20.sol";

/**
 * @dev This contract extends an ERC20 token with a snapshot mechanism. When a snapshot is created, the balances and
 * total supply at the time are recorded for later access.
 *
 * This can be used to safely create mechanisms based on token balances such as trustless dividends or weighted voting.
 * In naive implementations it's possible to perform a "double spend" attack by reusing the same balance from different
 * accounts. By using snapshots to calculate dividends or voting power, those attacks no longer apply. It can also be
 * used to create an efficient ERC20 forking mechanism.
 *
 * Snapshots are created by the internal {_snapshot} function, which will emit the {Snapshot} event and return a
 * snapshot id. To get the total supply at the time of a snapshot, call the function {totalSupplyAt} with the snapshot
 * id. To get the balance of an account at the time of a snapshot, call the {balanceOfAt} function with the snapshot id
 * and the account address.
 *
 * ==== Gas Costs
 *
 * Snapshots are efficient. Snapshot creation is _O(1)_. Retrieval of balances or total supply from a snapshot is _O(log
 * n)_ in the number of snapshots that have been created, although _n_ for a specific account will generally be much
 * smaller since identical balances in subsequent snapshots are stored as a single entry.
 *
 * There is a constant overhead for normal ERC20 transfers due to the additional snapshot bookkeeping. This overhead is
 * only significant for the first transfer that immediately follows a snapshot for a particular account. Subsequent
 * transfers will have normal cost until the next snapshot, and so on.
 */
abstract contract ERC20Snapshot is ERC20 {
    // Inspired by Jordi Baylina's MiniMeToken to record historical balances:
    // https://github.com/Giveth/minimd/blob/ea04d950eea153a04c51fa510b068b9dded390cb/contracts/MiniMeToken.sol

    using SafeMath for uint256;
    using Arrays for uint256[];
    using Counters for Counters.Counter;

    // Snapshotted values have arrays of ids and the value corresponding to that id. These could be an array of a
    // Snapshot struct, but that would impede usage of functions that work on an array.
    struct Snapshots {
        uint256[] ids;
        uint256[] values;
    }

    mapping (address => Snapshots) private _accountBalanceSnapshots;
    Snapshots private _totalSupplySnapshots;

    // Snapshot ids increase monotonically, with the first value being 1. An id of 0 is invalid.
    Counters.Counter private _currentSnapshotId;

    /**
     * @dev Emitted by {_snapshot} when a snapshot identified by `id` is created.
     */
    event Snapshot(uint256 id);

    /**
     * @dev Creates a new snapshot and returns its snapshot id.
     *
     * Emits a {Snapshot} event that contains the same id.
     *
     * {_snapshot} is `internal` and you have to decide how to expose it externally. Its usage may be restricted to a
     * set of accounts, for example using {AccessControl}, or it may be open to the public.
     *
     * [WARNING]
     * ====
     * While an open way of calling {_snapshot} is required for certain trust minimization mechanisms such as forking,
     * you must consider that it can potentially be used by attackers in two ways.
     *
     * First, it can be used to increase the cost of retrieval of values from snapshots, although it will grow
     * logarithmically thus rendering this attack ineffective in the long term. Second, it can be used to target
     * specific accounts and increase the cost of ERC20 transfers for them, in the ways specified in the Gas Costs
     * section above.
     *
     * We haven't measured the actual numbers; if this is something you're interested in please reach out to us.
     * ====
     */
    function _snapshot() internal virtual returns (uint256) {
        _currentSnapshotId.increment();

        uint256 currentId = _currentSnapshotId.current();
        emit Snapshot(currentId);
        return currentId;
    }

    /**
     * @dev Retrieves the balance of `account` at the time `snapshotId` was created.
     */
    function balanceOfAt(address account, uint256 snapshotId) public view virtual returns (uint256) {
        (bool snapshotted, uint256 value) = _valueAt(snapshotId, _accountBalanceSnapshots[account]);

        return snapshotted ? value : balanceOf(account);
    }

    /**
     * @dev Retrieves the total supply at the time `snapshotId` was created.
     */
    function totalSupplyAt(uint256 snapshotId) public view virtual returns(uint256) {
        (bool snapshotted, uint256 value) = _valueAt(snapshotId, _totalSupplySnapshots);

        return snapshotted ? value : totalSupply();
    }


    // Update balance and/or total supply snapshots before the values are modified. This is implemented
    // in the _beforeTokenTransfer hook, which is executed for _mint, _burn, and _transfer operations.
    function _beforeTokenTransfer(address from, address to, uint256 amount) internal virtual override {
      super._beforeTokenTransfer(from, to, amount);

      if (from == address(0)) {
        // mint
        _updateAccountSnapshot(to);
        _updateTotalSupplySnapshot();
      } else if (to == address(0)) {
        // burn
        _updateAccountSnapshot(from);
        _updateTotalSupplySnapshot();
      } else {
        // transfer
        _updateAccountSnapshot(from);
        _updateAccountSnapshot(to);
      }
    }

    function _valueAt(uint256 snapshotId, Snapshots storage snapshots)
        private view returns (bool, uint256)
    {
        require(snapshotId > 0, "ERC20Snapshot: id is 0");
        // solhint-disable-next-line max-line-length
        require(snapshotId <= _currentSnapshotId.current(), "ERC20Snapshot: nonexistent id");

        // When a valid snapshot is queried, there are three possibilities:
        //  a) The queried value was not modified after the snapshot was taken. Therefore, a snapshot entry was never
        //  created for this id, and all stored snapshot ids are smaller than the requested one. The value that corresponds
        //  to this id is the current one.
        //  b) The queried value was modified after the snapshot was taken. Therefore, there will be an entry with the
        //  requested id, and its value is the one to return.
        //  c) More snapshots were created after the requested one, and the queried value was later modified. There will be
        //  no entry for the requested id: the value that corresponds to it is that of the smallest snapshot id that is
        //  larger than the requested one.
        //
        // In summary, we need to find an element in an array, returning the index of the smallest value that is larger if
        // it is not found, unless said value doesn't exist (e.g. when all values are smaller). Arrays.findUpperBound does
        // exactly this.

        uint256 index = snapshots.ids.findUpperBound(snapshotId);

        if (index == snapshots.ids.length) {
            return (false, 0);
        } else {
            return (true, snapshots.values[index]);
        }
    }

    function _updateAccountSnapshot(address account) private {
        _updateSnapshot(_accountBalanceSnapshots[account], balanceOf(account));
    }

    function _updateTotalSupplySnapshot() private {
        _updateSnapshot(_totalSupplySnapshots, totalSupply());
    }

    function _updateSnapshot(Snapshots storage snapshots, uint256 currentValue) private {
        uint256 currentId = _currentSnapshotId.current();
        if (_lastSnapshotId(snapshots.ids) < currentId) {
            snapshots.ids.push(currentId);
            snapshots.values.push(currentValue);
        }
    }

    function _lastSnapshotId(uint256[] storage ids) private view returns (uint256) {
        if (ids.length == 0) {
            return 0;
        } else {
            return ids[ids.length - 1];
        }
    }
}

// SPDX-License-Identifier: Unlicense

pragma solidity 0.7.6;

import "@openzeppelin/contracts/drafts/ERC20Permit.sol";
import "@openzeppelin/contracts/token/ERC20/ERC20Snapshot.sol";

contract Gamma is ERC20Permit, ERC20Snapshot {

    address public owner;
    modifier onlyOwner {
        require(msg.sender == owner, "only owner");
        _;
    }

    constructor(
        string memory name,
        string memory symbol,
        uint8 decimals
    ) ERC20Permit(name) ERC20(name, symbol){
      owner = msg.sender;
      _setupDecimals(decimals);
      _mint(owner, 100000000000000000000000000);
    }

    function snapshot() onlyOwner external {
      _snapshot();
    }

    function transferOwnership(address newOwner) external onlyOwner {
      owner = newOwner;
    }

    function _beforeTokenTransfer(address from, address to, uint256 amount) internal override(ERC20, ERC20Snapshot) {
      super._beforeTokenTransfer(from, to, amount);
    }

}

// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <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);
}

// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <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);
}

// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

/**
 * @dev Standard math utilities missing in the Solidity language.
 */
library Math {
    /**
     * @dev Returns the largest of two numbers.
     */
    function max(uint256 a, uint256 b) internal pure returns (uint256) {
        return a >= b ? a : b;
    }

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

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

// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

/**
 * @dev Wrappers over Solidity's arithmetic operations with added overflow
 * checks.
 *
 * Arithmetic operations in Solidity wrap on overflow. This can easily result
 * in bugs, because programmers usually assume that an overflow raises an
 * error, which is the standard behavior in high level programming languages.
 * `SafeMath` restores this intuition by reverting the transaction when 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.
 */
library SafeMath {
    /**
     * @dev Returns the addition of two unsigned integers, with an overflow flag.
     *
     * _Available since v3.4._
     */
    function tryAdd(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        uint256 c = a + b;
        if (c < a) return (false, 0);
        return (true, c);
    }

    /**
     * @dev Returns the substraction of two unsigned integers, with an overflow flag.
     *
     * _Available since v3.4._
     */
    function trySub(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        if (b > a) return (false, 0);
        return (true, a - b);
    }

    /**
     * @dev Returns the multiplication of two unsigned integers, with an overflow flag.
     *
     * _Available since v3.4._
     */
    function tryMul(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        // Gas optimization: this is cheaper than requiring 'a' not being zero, but the
        // benefit is lost if 'b' is also tested.
        // See: https://github.com/OpenZeppelin/openzeppelin-contracts/pull/522
        if (a == 0) return (true, 0);
        uint256 c = a * b;
        if (c / a != b) return (false, 0);
        return (true, c);
    }

    /**
     * @dev Returns the division of two unsigned integers, with a division by zero flag.
     *
     * _Available since v3.4._
     */
    function tryDiv(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        if (b == 0) return (false, 0);
        return (true, a / b);
    }

    /**
     * @dev Returns the remainder of dividing two unsigned integers, with a division by zero flag.
     *
     * _Available since v3.4._
     */
    function tryMod(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        if (b == 0) return (false, 0);
        return (true, a % b);
    }

    /**
     * @dev Returns the addition of two unsigned integers, reverting on
     * overflow.
     *
     * Counterpart to Solidity's `+` operator.
     *
     * Requirements:
     *
     * - Addition cannot overflow.
     */
    function add(uint256 a, uint256 b) internal pure returns (uint256) {
        uint256 c = a + b;
        require(c >= a, "SafeMath: addition overflow");
        return c;
    }

    /**
     * @dev Returns the subtraction of two unsigned integers, reverting on
     * overflow (when the result is negative).
     *
     * Counterpart to Solidity's `-` operator.
     *
     * Requirements:
     *
     * - Subtraction cannot overflow.
     */
    function sub(uint256 a, uint256 b) internal pure returns (uint256) {
        require(b <= a, "SafeMath: subtraction overflow");
        return a - b;
    }

    /**
     * @dev Returns the multiplication of two unsigned integers, reverting on
     * overflow.
     *
     * Counterpart to Solidity's `*` operator.
     *
     * Requirements:
     *
     * - Multiplication cannot overflow.
     */
    function mul(uint256 a, uint256 b) internal pure returns (uint256) {
        if (a == 0) return 0;
        uint256 c = a * b;
        require(c / a == b, "SafeMath: multiplication overflow");
        return c;
    }

    /**
     * @dev Returns the integer division of two unsigned integers, reverting on
     * division by zero. The result is rounded towards zero.
     *
     * Counterpart to Solidity's `/` operator. Note: this function uses a
     * `revert` opcode (which leaves remaining gas untouched) while Solidity
     * uses an invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function div(uint256 a, uint256 b) internal pure returns (uint256) {
        require(b > 0, "SafeMath: division by zero");
        return a / b;
    }

    /**
     * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
     * reverting when dividing by zero.
     *
     * Counterpart to Solidity's `%` operator. This function uses a `revert`
     * opcode (which leaves remaining gas untouched) while Solidity uses an
     * invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function mod(uint256 a, uint256 b) internal pure returns (uint256) {
        require(b > 0, "SafeMath: modulo by zero");
        return a % b;
    }

    /**
     * @dev Returns the subtraction of two unsigned integers, reverting with custom message on
     * overflow (when the result is negative).
     *
     * CAUTION: This function is deprecated because it requires allocating memory for the error
     * message unnecessarily. For custom revert reasons use {trySub}.
     *
     * Counterpart to Solidity's `-` operator.
     *
     * Requirements:
     *
     * - Subtraction cannot overflow.
     */
    function sub(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
        require(b <= a, errorMessage);
        return a - b;
    }

    /**
     * @dev Returns the integer division of two unsigned integers, reverting with custom message on
     * division by zero. The result is rounded towards zero.
     *
     * CAUTION: This function is deprecated because it requires allocating memory for the error
     * message unnecessarily. For custom revert reasons use {tryDiv}.
     *
     * Counterpart to Solidity's `/` operator. Note: this function uses a
     * `revert` opcode (which leaves remaining gas untouched) while Solidity
     * uses an invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function div(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
        require(b > 0, errorMessage);
        return a / b;
    }

    /**
     * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
     * reverting with custom message when dividing by zero.
     *
     * CAUTION: This function is deprecated because it requires allocating memory for the error
     * message unnecessarily. For custom revert reasons use {tryMod}.
     *
     * Counterpart to Solidity's `%` operator. This function uses a `revert`
     * opcode (which leaves remaining gas untouched) while Solidity uses an
     * invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function mod(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
        require(b > 0, errorMessage);
        return a % b;
    }
}

{
  "compilationTarget": {
    "contracts/Gamma.sol": "Gamma"
  },
  "evmVersion": "istanbul",
  "libraries": {},
  "metadata": {
    "bytecodeHash": "none"
  },
  "optimizer": {
    "enabled": true,
    "runs": 800
  },
  "remappings": []
}