Address Details

contract

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity 0.8.18;

import { ERC20PermitUpgradeable } from "./patched/ERC20PermitUpgradeable.sol";
import { ERC20Upgradeable } from "./patched/ERC20Upgradeable.sol";

import { IStableTokenV2 } from "../interfaces/IStableTokenV2.sol";
import { CalledByVm } from "../common/CalledByVm.sol";

/**
 * @title ERC20 token with minting and burning permissioned to a broker and validators.
 */
contract StableTokenV2 is ERC20PermitUpgradeable, IStableTokenV2, CalledByVm {
  address public validators;
  address public broker;
  address public exchange;

  event TransferComment(string comment);
  event BrokerUpdated(address broker);
  event ValidatorsUpdated(address validators);
  event ExchangeUpdated(address exchange);

  /**
   * @dev Restricts a function so it can only be executed by an address that's allowed to mint.
   * Currently that's the broker, validators, or exchange.
   */
  modifier onlyMinter() {
    address sender = _msgSender();
    require(sender == broker || sender == validators || sender == exchange, "StableTokenV2: not allowed to mint");
    _;
  }

  /**
   * @dev Restricts a function so it can only be executed by an address that's allowed to burn.
   * Currently that's the broker or exchange.
   */
  modifier onlyBurner() {
    address sender = _msgSender();
    require(sender == broker || sender == exchange, "StableTokenV2: not allowed to burn");
    _;
  }

  /**
   * @notice The constructor for the StableTokenV2 contract.
   * @dev Should be called with disable=true in deployments when
   * it's accessed through a Proxy.
   * Call this with disable=false during testing, when used
   * without a proxy.
   * @param disable Set to true to run `_disableInitializers()` inherited from
   * openzeppelin-contracts-upgradeable/Initializable.sol
   */
  constructor(bool disable) {
    if (disable) {
      _disableInitializers();
    }
  }

  /**
   * @notice Initializes a StableTokenV2.
   * It keeps the same signature as the original initialize() function
   * in legacy/StableToken.sol
   * @param _name The name of the stable token (English)
   * @param _symbol A short symbol identifying the token (e.g. "cUSD")
   * deprecated-param decimals Tokens are divisible to this many decimal places.
   * deprecated-param registryAddress Address of the Registry contract.
   * deprecated-param inflationRate Weekly inflation rate.
   * deprecated-param inflationFactorUpdatePeriod How often the inflation factor is updated, in seconds.
   * @param initialBalanceAddresses Array of addresses with an initial balance.
   * @param initialBalanceValues Array of balance values corresponding to initialBalanceAddresses.
   * deprecated-param exchangeIdentifier String identifier of exchange in registry (for specific fiat pairs)
   */
  function initialize(
    string calldata _name,
    string calldata _symbol,
    uint8, // deprecated: decimals
    address, // deprecated: registryAddress,
    uint256, // deprecated: inflationRate,
    uint256, // deprecated:  inflationFactorUpdatePeriod,
    address[] calldata initialBalanceAddresses,
    uint256[] calldata initialBalanceValues,
    string calldata // deprecated: exchangeIdentifier
  ) external initializer {
    __ERC20_init_unchained(_name, _symbol);
    __ERC20Permit_init(_symbol);
    _transferOwnership(_msgSender());

    require(initialBalanceAddresses.length == initialBalanceValues.length, "Array length mismatch");
    for (uint256 i = 0; i < initialBalanceAddresses.length; i += 1) {
      _mint(initialBalanceAddresses[i], initialBalanceValues[i]);
    }
  }

  /**
   * @notice Initializes a StableTokenV2 contract
   * when upgrading from legacy/StableToken.sol.
   * It sets the addresses that were previously read from the Registry.
   * It runs the ERC20PermitUpgradeable initializer.
   * @dev This function is only callable once.
   * @param _broker The address of the Broker contract.
   * @param _validators The address of the Validators contract.
   * @param _exchange The address of the Exchange contract.
   */
  function initializeV2(
    address _broker,
    address _validators,
    address _exchange
  ) external reinitializer(2) onlyOwner {
    _setBroker(_broker);
    _setValidators(_validators);
    _setExchange(_exchange);
    __ERC20Permit_init(symbol());
  }

  /**
   * @notice Sets the address of the Broker contract.
   * @dev This function is only callable by the owner.
   * @param _broker The address of the Broker contract.
   */
  function setBroker(address _broker) external onlyOwner {
    _setBroker(_broker);
  }

  /**
   * @notice Sets the address of the Validators contract.
   * @dev This function is only callable by the owner.
   * @param _validators The address of the Validators contract.
   */
  function setValidators(address _validators) external onlyOwner {
    _setValidators(_validators);
  }

  /**
   * @notice Sets the address of the Exchange contract.
   * @dev This function is only callable by the owner.
   * @param _exchange The address of the Exchange contract.
   */
  function setExchange(address _exchange) external onlyOwner {
    _setExchange(_exchange);
  }

  /**
   * @notice Transfer token for a specified address
   * @param to The address to transfer to.
   * @param value The amount to be transferred.
   * @param comment The transfer comment.
   * @return True if the transaction succeeds.
   */
  function transferWithComment(
    address to,
    uint256 value,
    string calldata comment
  ) external returns (bool) {
    emit TransferComment(comment);
    return transfer(to, value);
  }

  /**
   * @notice Mints new StableToken and gives it to 'to'.
   * @param to The account for which to mint tokens.
   * @param value The amount of StableToken to mint.
   */
  function mint(address to, uint256 value) external onlyMinter returns (bool) {
    _mint(to, value);
    return true;
  }

  /**
   * @notice Burns StableToken from the balance of msg.sender.
   * @param value The amount of StableToken to burn.
   */
  function burn(uint256 value) external onlyBurner returns (bool) {
    _burn(msg.sender, value);
    return true;
  }

  /**
   * @notice Set the address of the Broker contract and emit an event
   * @param _broker The address of the Broker contract.
   */
  function _setBroker(address _broker) internal {
    broker = _broker;
    emit BrokerUpdated(_broker);
  }

  /**
   * @notice Set the address of the Validators contract and emit an event
   * @param _validators The address of the Validators contract.
   */
  function _setValidators(address _validators) internal {
    validators = _validators;
    emit ValidatorsUpdated(_validators);
  }

  /**
   * @notice Set the address of the Exchange contract and emit an event
   * @param _exchange The address of the Exchange contract.
   */
  function _setExchange(address _exchange) internal {
    exchange = _exchange;
    emit ExchangeUpdated(_exchange);
  }

  /// @inheritdoc ERC20Upgradeable
  function transferFrom(
    address from,
    address to,
    uint256 amount
  ) public override(ERC20Upgradeable, IStableTokenV2) returns (bool) {
    return ERC20Upgradeable.transferFrom(from, to, amount);
  }

  /// @inheritdoc ERC20Upgradeable
  function transfer(address to, uint256 amount) public override(ERC20Upgradeable, IStableTokenV2) returns (bool) {
    return ERC20Upgradeable.transfer(to, amount);
  }

  /// @inheritdoc ERC20Upgradeable
  function balanceOf(address account) public view override(ERC20Upgradeable, IStableTokenV2) returns (uint256) {
    return ERC20Upgradeable.balanceOf(account);
  }

  /// @inheritdoc ERC20Upgradeable
  function approve(address spender, uint256 amount) public override(ERC20Upgradeable, IStableTokenV2) returns (bool) {
    return ERC20Upgradeable.approve(spender, amount);
  }

  /// @inheritdoc ERC20Upgradeable
  function allowance(address owner, address spender)
    public
    view
    override(ERC20Upgradeable, IStableTokenV2)
    returns (uint256)
  {
    return ERC20Upgradeable.allowance(owner, spender);
  }

  /// @inheritdoc ERC20Upgradeable
  function totalSupply() public view override(ERC20Upgradeable, IStableTokenV2) returns (uint256) {
    return ERC20Upgradeable.totalSupply();
  }

  /// @inheritdoc ERC20PermitUpgradeable
  function permit(
    address owner,
    address spender,
    uint256 value,
    uint256 deadline,
    uint8 v,
    bytes32 r,
    bytes32 s
  ) public override(ERC20PermitUpgradeable, IStableTokenV2) {
    ERC20PermitUpgradeable.permit(owner, spender, value, deadline, v, r, s);
  }

  /**
   * @notice Reserve balance for making payments for gas in this StableToken currency.
   * @param from The account to reserve balance from
   * @param value The amount of balance to reserve
   * @dev Note that this function is called by the protocol when paying for tx fees in this
   * currency. After the tx is executed, gas is refunded to the sender and credited to the
   * various tx fee recipients via a call to `creditGasFees`.
   */
  function debitGasFees(address from, uint256 value) external onlyVm {
    _burn(from, value);
  }

  /**
   * @notice Alternative function to credit balance after making payments
   * for gas in this StableToken currency.
   * @param from The account to debit balance from
   * @param feeRecipient Coinbase address
   * @param gatewayFeeRecipient Gateway address
   * @param communityFund Community fund address
   * @param refund amount to be refunded by the VM
   * @param tipTxFee Coinbase fee
   * @param baseTxFee Community fund fee
   * @param gatewayFee Gateway fee
   * @dev Note that this function is called by the protocol when paying for tx fees in this
   * currency. Before the tx is executed, gas is debited from the sender via a call to
   * `debitGasFees`.
   */
  function creditGasFees(
    address from,
    address feeRecipient,
    address gatewayFeeRecipient,
    address communityFund,
    uint256 refund,
    uint256 tipTxFee,
    uint256 gatewayFee,
    uint256 baseTxFee
  ) external onlyVm {
    uint256 amountToBurn;
    _mint(from, refund + tipTxFee + gatewayFee + baseTxFee);

    if (feeRecipient != address(0)) {
      _transfer(from, feeRecipient, tipTxFee);
    } else if (tipTxFee > 0) {
      amountToBurn += tipTxFee;
    }

    if (gatewayFeeRecipient != address(0)) {
      _transfer(from, gatewayFeeRecipient, gatewayFee);
    } else if (gatewayFee > 0) {
      amountToBurn += gatewayFee;
    }

    if (communityFund != address(0)) {
      _transfer(from, communityFund, baseTxFee);
    } else if (baseTxFee > 0) {
      amountToBurn += baseTxFee;
    }

    if (amountToBurn > 0) {
      _burn(from, amountToBurn);
    }
  }
}
        

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity >=0.5.13 <0.8.19;

contract CalledByVm {
  modifier onlyVm() {
    require(msg.sender == address(0), "Only VM can call");
    _;
  }
}
          

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity >=0.5.17 <0.8.19;

interface IStableTokenV2 {
  function totalSupply() external view returns (uint256);

  function balanceOf(address account) external view returns (uint256);

  function transfer(address recipient, uint256 amount) external returns (bool);

  function allowance(address owner, address spender) external view returns (uint256);

  function approve(address spender, uint256 amount) external returns (bool);

  function transferFrom(
    address sender,
    address recipient,
    uint256 amount
  ) external returns (bool);

  function mint(address, uint256) external returns (bool);

  function burn(uint256) external returns (bool);

  function permit(
    address owner,
    address spender,
    uint256 value,
    uint256 deadline,
    uint8 v,
    bytes32 r,
    bytes32 s
  ) external;

  /**
   * @notice Transfer token for a specified address
   * @param to The address to transfer to.
   * @param value The amount to be transferred.
   * @param comment The transfer comment.
   * @return True if the transaction succeeds.
   */
  function transferWithComment(
    address to,
    uint256 value,
    string calldata comment
  ) external returns (bool);

  /**
   * @notice Initializes a StableTokenV2.
   * It keeps the same signature as the original initialize() function
   * in legacy/StableToken.sol
   * @param _name The name of the stable token (English)
   * @param _symbol A short symbol identifying the token (e.g. "cUSD")
   * deprecated-param decimals Tokens are divisible to this many decimal places.
   * deprecated-param registryAddress Address of the Registry contract.
   * deprecated-param inflationRate Weekly inflation rate.
   * deprecated-param inflationFactorUpdatePeriod How often the inflation factor is updated, in seconds.
   * @param initialBalanceAddresses Array of addresses with an initial balance.
   * @param initialBalanceValues Array of balance values corresponding to initialBalanceAddresses.
   * deprecated-param exchangeIdentifier String identifier of exchange in registry (for specific fiat pairs)
   */
  function initialize(
    string calldata _name,
    string calldata _symbol,
    uint8, // deprecated: decimals
    address, // deprecated: registryAddress,
    uint256, // deprecated: inflationRate,
    uint256, // deprecated:  inflationFactorUpdatePeriod,
    address[] calldata initialBalanceAddresses,
    uint256[] calldata initialBalanceValues,
    string calldata // deprecated: exchangeIdentifier
  ) external;

  /**
   * @notice Initializes a StableTokenV2 contract
   * when upgrading from legacy/StableToken.sol.
   * It sets the addresses that were previously read from the Registry.
   * It runs the ERC20PermitUpgradeable initializer.
   * @dev This function is only callable once.
   * @param _broker The address of the Broker contract.
   * @param _validators The address of the Validators contract.
   * @param _exchange The address of the Exchange contract.
   */
  function initializeV2(
    address _broker,
    address _validators,
    address _exchange
  ) external;

  /**
   * @notice Gets the address of the Broker contract.
   */
  function broker() external returns (address);

  /**
   * @notice Gets the address of the Validators contract.
   */
  function validators() external returns (address);

  /**
   * @notice Gets the address of the Exchange contract.
   */
  function exchange() external returns (address);

  function debitGasFees(address from, uint256 value) external;

  function creditGasFees(
    address from,
    address feeRecipient,
    address gatewayFeeRecipient,
    address communityFund,
    uint256 refund,
    uint256 tipTxFee,
    uint256 gatewayFee,
    uint256 baseTxFee
  ) external;
}
          

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (token/ERC20/extensions/draft-ERC20Permit.sol)
/*
 * 🔥 MentoLabs: This is a copied file from v4.8.0 of OZ-Upgradable,
 * and only changes the import of ERC20Upgradeable to be the local one
 * which is modified in order to keep storage variables consistent
 * with the pervious implementation of StableToken.
 * See ./README.md for more details.
 */

pragma solidity ^0.8.0;

import "./ERC20Upgradeable.sol";

import "openzeppelin-contracts-upgradeable/contracts/token/ERC20/extensions/draft-IERC20PermitUpgradeable.sol";
import "openzeppelin-contracts-upgradeable/contracts/utils/cryptography/ECDSAUpgradeable.sol";
import "openzeppelin-contracts-upgradeable/contracts/utils/cryptography/EIP712Upgradeable.sol";
import "openzeppelin-contracts-upgradeable/contracts/utils/CountersUpgradeable.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._
 *
 * @custom:storage-size 51
 */
abstract contract ERC20PermitUpgradeable is ERC20Upgradeable, IERC20PermitUpgradeable, EIP712Upgradeable {
  using CountersUpgradeable for CountersUpgradeable.Counter;

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

  // solhint-disable-next-line var-name-mixedcase
  bytes32 private constant _PERMIT_TYPEHASH =
    keccak256("Permit(address owner,address spender,uint256 value,uint256 nonce,uint256 deadline)");
  /**
   * @dev In previous versions `_PERMIT_TYPEHASH` was declared as `immutable`.
   * However, to ensure consistency with the upgradeable transpiler, we will continue
   * to reserve a slot.
   * @custom:oz-renamed-from _PERMIT_TYPEHASH
   */
  // solhint-disable-next-line var-name-mixedcase
  bytes32 private _PERMIT_TYPEHASH_DEPRECATED_SLOT;

  /**
   * @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.
   */
  function __ERC20Permit_init(string memory name) internal onlyInitializing {
    __EIP712_init_unchained(name, "1");
  }

  function __ERC20Permit_init_unchained(string memory) internal onlyInitializing {}

  /**
   * @dev See {IERC20Permit-permit}.
   */
  function permit(
    address owner,
    address spender,
    uint256 value,
    uint256 deadline,
    uint8 v,
    bytes32 r,
    bytes32 s
  ) public virtual override {
    require(block.timestamp <= deadline, "ERC20Permit: expired deadline");

    bytes32 structHash = keccak256(abi.encode(_PERMIT_TYPEHASH, owner, spender, value, _useNonce(owner), deadline));

    bytes32 hash = _hashTypedDataV4(structHash);

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

    _approve(owner, spender, value);
  }

  /**
   * @dev See {IERC20Permit-nonces}.
   */
  function nonces(address owner) public view virtual 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();
  }

  /**
   * @dev "Consume a nonce": return the current value and increment.
   *
   * _Available since v4.1._
   */
  function _useNonce(address owner) internal virtual returns (uint256 current) {
    CountersUpgradeable.Counter storage nonce = _nonces[owner];
    current = nonce.current();
    nonce.increment();
  }

  /**
   * @dev This empty reserved space is put in place to allow future versions to add new
   * variables without shifting down storage in the inheritance chain.
   * See https://docs.openzeppelin.com/contracts/4.x/upgradeable#storage_gaps
   */
  uint256[49] private __gap;
}
          

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (token/ERC20/ERC20.sol)
/*
 * 🔥 MentoLabs: This is a copied file from v4.8.0 of OZ-Upgradable, which only changes
 * the ordering of storage variables to keep it consistent with the existing
 * StableToken, so this can act as a new implementation for the proxy.
 * See ./README.md for more details.
 */

pragma solidity ^0.8.0;

import "openzeppelin-contracts-upgradeable/contracts/token/ERC20/IERC20Upgradeable.sol";
import "openzeppelin-contracts-upgradeable/contracts/token/ERC20/extensions/IERC20MetadataUpgradeable.sol";
import "openzeppelin-contracts-upgradeable/contracts/proxy/utils/Initializable.sol";
import "openzeppelin-contracts-next/contracts/access/Ownable.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.openzeppelin.com/t/how-to-implement-erc20-supply-mechanisms/226[How
 * to implement supply mechanisms].
 *
 * We have followed general OpenZeppelin Contracts guidelines: functions revert
 * instead returning `false` on failure. This behavior is nonetheless
 * conventional and does not conflict with the expectations of ERC20
 * applications.
 *
 * Additionally, an {Approval} event is emitted on calls to {transferFrom}.
 * This allows applications to reconstruct the allowance for all accounts just
 * by listening to said events. Other implementations of the EIP may not emit
 * these events, as it isn't required by the specification.
 *
 * Finally, the non-standard {decreaseAllowance} and {increaseAllowance}
 * functions have been added to mitigate the well-known issues around setting
 * allowances. See {IERC20-approve}.
 */
contract ERC20Upgradeable is Ownable, Initializable, IERC20Upgradeable, IERC20MetadataUpgradeable {
  address private __deprecated_registry_storage_slot__;
  string private _name;
  string private _symbol;
  uint8 private __deprecated_decimals_storage_slot__;

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

  uint256[4] private __deprecated_inflationState_storage_slot__;
  bytes32 private __deprecated_exchangeRegistryId_storage_slot__;

  /**
   * @dev Sets the values for {name} and {symbol}.
   *
   * The default value of {decimals} is 18. To select a different value for
   * {decimals} you should overload it.
   *
   * All two of these values are immutable: they can only be set once during
   * construction.
   */
  function __ERC20_init(string memory name_, string memory symbol_) internal onlyInitializing {
    __ERC20_init_unchained(name_, symbol_);
  }

  function __ERC20_init_unchained(string memory name_, string memory symbol_) internal onlyInitializing {
    _name = name_;
    _symbol = symbol_;
  }

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

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

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

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

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

  /**
   * @dev See {IERC20-transfer}.
   *
   * Requirements:
   *
   * - `to` cannot be the zero address.
   * - the caller must have a balance of at least `amount`.
   */
  function transfer(address to, uint256 amount) public virtual override returns (bool) {
    address owner = _msgSender();
    _transfer(owner, to, 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}.
   *
   * NOTE: If `amount` is the maximum `uint256`, the allowance is not updated on
   * `transferFrom`. This is semantically equivalent to an infinite approval.
   *
   * Requirements:
   *
   * - `spender` cannot be the zero address.
   */
  function approve(address spender, uint256 amount) public virtual override returns (bool) {
    address owner = _msgSender();
    _approve(owner, 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}.
   *
   * NOTE: Does not update the allowance if the current allowance
   * is the maximum `uint256`.
   *
   * Requirements:
   *
   * - `from` and `to` cannot be the zero address.
   * - `from` must have a balance of at least `amount`.
   * - the caller must have allowance for ``from``'s tokens of at least
   * `amount`.
   */
  function transferFrom(
    address from,
    address to,
    uint256 amount
  ) public virtual override returns (bool) {
    address spender = _msgSender();
    _spendAllowance(from, spender, amount);
    _transfer(from, to, amount);
    return true;
  }

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

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

    return true;
  }

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

    _beforeTokenTransfer(from, to, amount);

    uint256 fromBalance = _balances[from];
    require(fromBalance >= amount, "ERC20: transfer amount exceeds balance");
    unchecked {
      _balances[from] = fromBalance - amount;
      // Overflow not possible: the sum of all balances is capped by totalSupply, and the sum is preserved by
      // decrementing then incrementing.
      _balances[to] += amount;
    }

    emit Transfer(from, to, amount);

    _afterTokenTransfer(from, to, amount);
  }

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

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

    _totalSupply += amount;
    unchecked {
      // Overflow not possible: balance + amount is at most totalSupply + amount, which is checked above.
      _balances[account] += amount;
    }
    emit Transfer(address(0), account, amount);

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

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

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

    uint256 accountBalance = _balances[account];
    require(accountBalance >= amount, "ERC20: burn amount exceeds balance");
    unchecked {
      _balances[account] = accountBalance - amount;
      // Overflow not possible: amount <= accountBalance <= totalSupply.
      _totalSupply -= amount;
    }

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

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

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

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

  /**
   * @dev Updates `owner` s allowance for `spender` based on spent `amount`.
   *
   * Does not update the allowance amount in case of infinite allowance.
   * Revert if not enough allowance is available.
   *
   * Might emit an {Approval} event.
   */
  function _spendAllowance(
    address owner,
    address spender,
    uint256 amount
  ) internal virtual {
    uint256 currentAllowance = allowance(owner, spender);
    if (currentAllowance != type(uint256).max) {
      require(currentAllowance >= amount, "ERC20: insufficient allowance");
      unchecked {
        _approve(owner, spender, currentAllowance - amount);
      }
    }
  }

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

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

  /**
   * @dev This empty reserved space is put in place to allow future versions to add new
   * variables without shifting down storage in the inheritance chain.
   * See https://docs.openzeppelin.com/contracts/4.x/upgradeable#storage_gaps
   */
  uint256[40] private __gap;
}
          

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

pragma solidity ^0.8.0;

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

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

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

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

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

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

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

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

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

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

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

pragma solidity ^0.8.0;

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

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

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.1) (proxy/utils/Initializable.sol)

pragma solidity ^0.8.2;

import "../../utils/AddressUpgradeable.sol";

/**
 * @dev This is a base contract to aid in writing upgradeable contracts, or any kind of contract that will be deployed
 * behind a proxy. Since proxied contracts do not make use of a constructor, it's common to move constructor logic to an
 * external initializer function, usually called `initialize`. It then becomes necessary to protect this initializer
 * function so it can only be called once. The {initializer} modifier provided by this contract will have this effect.
 *
 * The initialization functions use a version number. Once a version number is used, it is consumed and cannot be
 * reused. This mechanism prevents re-execution of each "step" but allows the creation of new initialization steps in
 * case an upgrade adds a module that needs to be initialized.
 *
 * For example:
 *
 * [.hljs-theme-light.nopadding]
 * ```
 * contract MyToken is ERC20Upgradeable {
 *     function initialize() initializer public {
 *         __ERC20_init("MyToken", "MTK");
 *     }
 * }
 * contract MyTokenV2 is MyToken, ERC20PermitUpgradeable {
 *     function initializeV2() reinitializer(2) public {
 *         __ERC20Permit_init("MyToken");
 *     }
 * }
 * ```
 *
 * TIP: To avoid leaving the proxy in an uninitialized state, the initializer function should be called as early as
 * possible by providing the encoded function call as the `_data` argument to {ERC1967Proxy-constructor}.
 *
 * CAUTION: When used with inheritance, manual care must be taken to not invoke a parent initializer twice, or to ensure
 * that all initializers are idempotent. This is not verified automatically as constructors are by Solidity.
 *
 * [CAUTION]
 * ====
 * Avoid leaving a contract uninitialized.
 *
 * An uninitialized contract can be taken over by an attacker. This applies to both a proxy and its implementation
 * contract, which may impact the proxy. To prevent the implementation contract from being used, you should invoke
 * the {_disableInitializers} function in the constructor to automatically lock it when it is deployed:
 *
 * [.hljs-theme-light.nopadding]
 * ```
 * /// @custom:oz-upgrades-unsafe-allow constructor
 * constructor() {
 *     _disableInitializers();
 * }
 * ```
 * ====
 */
abstract contract Initializable {
    /**
     * @dev Indicates that the contract has been initialized.
     * @custom:oz-retyped-from bool
     */
    uint8 private _initialized;

    /**
     * @dev Indicates that the contract is in the process of being initialized.
     */
    bool private _initializing;

    /**
     * @dev Triggered when the contract has been initialized or reinitialized.
     */
    event Initialized(uint8 version);

    /**
     * @dev A modifier that defines a protected initializer function that can be invoked at most once. In its scope,
     * `onlyInitializing` functions can be used to initialize parent contracts.
     *
     * Similar to `reinitializer(1)`, except that functions marked with `initializer` can be nested in the context of a
     * constructor.
     *
     * Emits an {Initialized} event.
     */
    modifier initializer() {
        bool isTopLevelCall = !_initializing;
        require(
            (isTopLevelCall && _initialized < 1) || (!AddressUpgradeable.isContract(address(this)) && _initialized == 1),
            "Initializable: contract is already initialized"
        );
        _initialized = 1;
        if (isTopLevelCall) {
            _initializing = true;
        }
        _;
        if (isTopLevelCall) {
            _initializing = false;
            emit Initialized(1);
        }
    }

    /**
     * @dev A modifier that defines a protected reinitializer function that can be invoked at most once, and only if the
     * contract hasn't been initialized to a greater version before. In its scope, `onlyInitializing` functions can be
     * used to initialize parent contracts.
     *
     * A reinitializer may be used after the original initialization step. This is essential to configure modules that
     * are added through upgrades and that require initialization.
     *
     * When `version` is 1, this modifier is similar to `initializer`, except that functions marked with `reinitializer`
     * cannot be nested. If one is invoked in the context of another, execution will revert.
     *
     * Note that versions can jump in increments greater than 1; this implies that if multiple reinitializers coexist in
     * a contract, executing them in the right order is up to the developer or operator.
     *
     * WARNING: setting the version to 255 will prevent any future reinitialization.
     *
     * Emits an {Initialized} event.
     */
    modifier reinitializer(uint8 version) {
        require(!_initializing && _initialized < version, "Initializable: contract is already initialized");
        _initialized = version;
        _initializing = true;
        _;
        _initializing = false;
        emit Initialized(version);
    }

    /**
     * @dev Modifier to protect an initialization function so that it can only be invoked by functions with the
     * {initializer} and {reinitializer} modifiers, directly or indirectly.
     */
    modifier onlyInitializing() {
        require(_initializing, "Initializable: contract is not initializing");
        _;
    }

    /**
     * @dev Locks the contract, preventing any future reinitialization. This cannot be part of an initializer call.
     * Calling this in the constructor of a contract will prevent that contract from being initialized or reinitialized
     * to any version. It is recommended to use this to lock implementation contracts that are designed to be called
     * through proxies.
     *
     * Emits an {Initialized} event the first time it is successfully executed.
     */
    function _disableInitializers() internal virtual {
        require(!_initializing, "Initializable: contract is initializing");
        if (_initialized < type(uint8).max) {
            _initialized = type(uint8).max;
            emit Initialized(type(uint8).max);
        }
    }

    /**
     * @dev Returns the highest version that has been initialized. See {reinitializer}.
     */
    function _getInitializedVersion() internal view returns (uint8) {
        return _initialized;
    }

    /**
     * @dev Returns `true` if the contract is currently initializing. See {onlyInitializing}.
     */
    function _isInitializing() internal view returns (bool) {
        return _initializing;
    }
}
          

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

pragma solidity ^0.8.0;

/**
 * @dev Interface of the ERC20 standard as defined in the EIP.
 */
interface IERC20Upgradeable {
    /**
     * @dev Emitted when `value` tokens are moved from one account (`from`) to
     * another (`to`).
     *
     * Note that `value` may be zero.
     */
    event Transfer(address indexed from, address indexed to, uint256 value);

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

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

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

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

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

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

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

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

pragma solidity ^0.8.0;

import "../IERC20Upgradeable.sol";

/**
 * @dev Interface for the optional metadata functions from the ERC20 standard.
 *
 * _Available since v4.1._
 */
interface IERC20MetadataUpgradeable is IERC20Upgradeable {
    /**
     * @dev Returns the name of the token.
     */
    function name() external view returns (string memory);

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

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

// 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 IERC20PermitUpgradeable {
    /**
     * @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
// OpenZeppelin Contracts (last updated v4.8.0) (utils/Address.sol)

pragma solidity ^0.8.1;

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

        return account.code.length > 0;
    }

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

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

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

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

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

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

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

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

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

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

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

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

pragma solidity ^0.8.0;

/**
 * @title Counters
 * @author Matt Condon (@shrugs)
 * @dev Provides counters that can only be incremented, decremented or reset. 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;`
 */
library CountersUpgradeable {
    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 {
        unchecked {
            counter._value += 1;
        }
    }

    function decrement(Counter storage counter) internal {
        uint256 value = counter._value;
        require(value > 0, "Counter: decrement overflow");
        unchecked {
            counter._value = value - 1;
        }
    }

    function reset(Counter storage counter) internal {
        counter._value = 0;
    }
}
          

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

pragma solidity ^0.8.0;

import "./math/MathUpgradeable.sol";

/**
 * @dev String operations.
 */
library StringsUpgradeable {
    bytes16 private constant _SYMBOLS = "0123456789abcdef";
    uint8 private constant _ADDRESS_LENGTH = 20;

    /**
     * @dev Converts a `uint256` to its ASCII `string` decimal representation.
     */
    function toString(uint256 value) internal pure returns (string memory) {
        unchecked {
            uint256 length = MathUpgradeable.log10(value) + 1;
            string memory buffer = new string(length);
            uint256 ptr;
            /// @solidity memory-safe-assembly
            assembly {
                ptr := add(buffer, add(32, length))
            }
            while (true) {
                ptr--;
                /// @solidity memory-safe-assembly
                assembly {
                    mstore8(ptr, byte(mod(value, 10), _SYMBOLS))
                }
                value /= 10;
                if (value == 0) break;
            }
            return buffer;
        }
    }

    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation.
     */
    function toHexString(uint256 value) internal pure returns (string memory) {
        unchecked {
            return toHexString(value, MathUpgradeable.log256(value) + 1);
        }
    }

    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation with fixed length.
     */
    function toHexString(uint256 value, uint256 length) internal pure returns (string memory) {
        bytes memory buffer = new bytes(2 * length + 2);
        buffer[0] = "0";
        buffer[1] = "x";
        for (uint256 i = 2 * length + 1; i > 1; --i) {
            buffer[i] = _SYMBOLS[value & 0xf];
            value >>= 4;
        }
        require(value == 0, "Strings: hex length insufficient");
        return string(buffer);
    }

    /**
     * @dev Converts an `address` with fixed length of 20 bytes to its not checksummed ASCII `string` hexadecimal representation.
     */
    function toHexString(address addr) internal pure returns (string memory) {
        return toHexString(uint256(uint160(addr)), _ADDRESS_LENGTH);
    }
}
          

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

pragma solidity ^0.8.0;

import "../StringsUpgradeable.sol";

/**
 * @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 ECDSAUpgradeable {
    enum RecoverError {
        NoError,
        InvalidSignature,
        InvalidSignatureLength,
        InvalidSignatureS,
        InvalidSignatureV // Deprecated in v4.8
    }

    function _throwError(RecoverError error) private pure {
        if (error == RecoverError.NoError) {
            return; // no error: do nothing
        } else if (error == RecoverError.InvalidSignature) {
            revert("ECDSA: invalid signature");
        } else if (error == RecoverError.InvalidSignatureLength) {
            revert("ECDSA: invalid signature length");
        } else if (error == RecoverError.InvalidSignatureS) {
            revert("ECDSA: invalid signature 's' value");
        }
    }

    /**
     * @dev Returns the address that signed a hashed message (`hash`) with
     * `signature` or error string. 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.
     *
     * Documentation for signature generation:
     * - with https://web3js.readthedocs.io/en/v1.3.4/web3-eth-accounts.html#sign[Web3.js]
     * - with https://docs.ethers.io/v5/api/signer/#Signer-signMessage[ethers]
     *
     * _Available since v4.3._
     */
    function tryRecover(bytes32 hash, bytes memory signature) internal pure returns (address, RecoverError) {
        if (signature.length == 65) {
            bytes32 r;
            bytes32 s;
            uint8 v;
            // ecrecover takes the signature parameters, and the only way to get them
            // currently is to use assembly.
            /// @solidity memory-safe-assembly
            assembly {
                r := mload(add(signature, 0x20))
                s := mload(add(signature, 0x40))
                v := byte(0, mload(add(signature, 0x60)))
            }
            return tryRecover(hash, v, r, s);
        } else {
            return (address(0), RecoverError.InvalidSignatureLength);
        }
    }

    /**
     * @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) {
        (address recovered, RecoverError error) = tryRecover(hash, signature);
        _throwError(error);
        return recovered;
    }

    /**
     * @dev Overload of {ECDSA-tryRecover} that receives the `r` and `vs` short-signature fields separately.
     *
     * See https://eips.ethereum.org/EIPS/eip-2098[EIP-2098 short signatures]
     *
     * _Available since v4.3._
     */
    function tryRecover(
        bytes32 hash,
        bytes32 r,
        bytes32 vs
    ) internal pure returns (address, RecoverError) {
        bytes32 s = vs & bytes32(0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff);
        uint8 v = uint8((uint256(vs) >> 255) + 27);
        return tryRecover(hash, v, r, s);
    }

    /**
     * @dev Overload of {ECDSA-recover} that receives the `r and `vs` short-signature fields separately.
     *
     * _Available since v4.2._
     */
    function recover(
        bytes32 hash,
        bytes32 r,
        bytes32 vs
    ) internal pure returns (address) {
        (address recovered, RecoverError error) = tryRecover(hash, r, vs);
        _throwError(error);
        return recovered;
    }

    /**
     * @dev Overload of {ECDSA-tryRecover} that receives the `v`,
     * `r` and `s` signature fields separately.
     *
     * _Available since v4.3._
     */
    function tryRecover(
        bytes32 hash,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) internal pure returns (address, RecoverError) {
        // 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 (301): 0 < s < secp256k1n ÷ 2 + 1, and for v in (302): 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.
        if (uint256(s) > 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A0) {
            return (address(0), RecoverError.InvalidSignatureS);
        }

        // If the signature is valid (and not malleable), return the signer address
        address signer = ecrecover(hash, v, r, s);
        if (signer == address(0)) {
            return (address(0), RecoverError.InvalidSignature);
        }

        return (signer, RecoverError.NoError);
    }

    /**
     * @dev Overload of {ECDSA-recover} that receives the `v`,
     * `r` and `s` signature fields separately.
     */
    function recover(
        bytes32 hash,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) internal pure returns (address) {
        (address recovered, RecoverError error) = tryRecover(hash, v, r, s);
        _throwError(error);
        return recovered;
    }

    /**
     * @dev Returns an Ethereum Signed Message, created from a `hash`. This
     * produces hash corresponding to the one signed with the
     * https://eth.wiki/json-rpc/API#eth_sign[`eth_sign`]
     * JSON-RPC method as part of EIP-191.
     *
     * 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));
    }

    /**
     * @dev Returns an Ethereum Signed Message, created from `s`. This
     * produces hash corresponding to the one signed with the
     * https://eth.wiki/json-rpc/API#eth_sign[`eth_sign`]
     * JSON-RPC method as part of EIP-191.
     *
     * See {recover}.
     */
    function toEthSignedMessageHash(bytes memory s) internal pure returns (bytes32) {
        return keccak256(abi.encodePacked("\x19Ethereum Signed Message:\n", StringsUpgradeable.toString(s.length), s));
    }

    /**
     * @dev Returns an Ethereum Signed Typed Data, created from a
     * `domainSeparator` and a `structHash`. This produces hash corresponding
     * to the one signed with the
     * https://eips.ethereum.org/EIPS/eip-712[`eth_signTypedData`]
     * JSON-RPC method as part of EIP-712.
     *
     * See {recover}.
     */
    function toTypedDataHash(bytes32 domainSeparator, bytes32 structHash) internal pure returns (bytes32) {
        return keccak256(abi.encodePacked("\x19\x01", domainSeparator, structHash));
    }
}
          

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (utils/cryptography/EIP712.sol)

pragma solidity ^0.8.0;

import "./ECDSAUpgradeable.sol";
import "../../proxy/utils/Initializable.sol";

/**
 * @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._
 *
 * @custom:storage-size 52
 */
abstract contract EIP712Upgradeable is Initializable {
    /* solhint-disable var-name-mixedcase */
    bytes32 private _HASHED_NAME;
    bytes32 private _HASHED_VERSION;
    bytes32 private constant _TYPE_HASH = keccak256("EIP712Domain(string name,string version,uint256 chainId,address verifyingContract)");

    /* 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].
     */
    function __EIP712_init(string memory name, string memory version) internal onlyInitializing {
        __EIP712_init_unchained(name, version);
    }

    function __EIP712_init_unchained(string memory name, string memory version) internal onlyInitializing {
        bytes32 hashedName = keccak256(bytes(name));
        bytes32 hashedVersion = keccak256(bytes(version));
        _HASHED_NAME = hashedName;
        _HASHED_VERSION = hashedVersion;
    }

    /**
     * @dev Returns the domain separator for the current chain.
     */
    function _domainSeparatorV4() internal view returns (bytes32) {
        return _buildDomainSeparator(_TYPE_HASH, _EIP712NameHash(), _EIP712VersionHash());
    }

    function _buildDomainSeparator(
        bytes32 typeHash,
        bytes32 nameHash,
        bytes32 versionHash
    ) private view returns (bytes32) {
        return keccak256(abi.encode(typeHash, nameHash, versionHash, block.chainid, 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 ECDSAUpgradeable.toTypedDataHash(_domainSeparatorV4(), structHash);
    }

    /**
     * @dev The hash of the name parameter for the EIP712 domain.
     *
     * NOTE: This function reads from storage by default, but can be redefined to return a constant value if gas costs
     * are a concern.
     */
    function _EIP712NameHash() internal virtual view returns (bytes32) {
        return _HASHED_NAME;
    }

    /**
     * @dev The hash of the version parameter for the EIP712 domain.
     *
     * NOTE: This function reads from storage by default, but can be redefined to return a constant value if gas costs
     * are a concern.
     */
    function _EIP712VersionHash() internal virtual view returns (bytes32) {
        return _HASHED_VERSION;
    }

    /**
     * @dev This empty reserved space is put in place to allow future versions to add new
     * variables without shifting down storage in the inheritance chain.
     * See https://docs.openzeppelin.com/contracts/4.x/upgradeable#storage_gaps
     */
    uint256[50] private __gap;
}
          

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

pragma solidity ^0.8.0;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

            // Use the Newton-Raphson iteration to improve the precision. Thanks to Hensel's lifting lemma, this also works
            // in modular arithmetic, doubling the correct bits in each step.
            inverse *= 2 - denominator * inverse; // inverse mod 2^8
            inverse *= 2 - denominator * inverse; // inverse mod 2^16
            inverse *= 2 - denominator * inverse; // inverse mod 2^32
            inverse *= 2 - denominator * inverse; // inverse mod 2^64
            inverse *= 2 - denominator * inverse; // inverse mod 2^128
            inverse *= 2 - denominator * inverse; // inverse mod 2^256

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

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

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

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

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

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

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

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

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

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

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

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