// File: contracts/CurveFactory.sol



// SPDX-License-Identifier: MIT

pragma solidity 0.8.6;

import "@openzeppelin/contracts/proxy/Clones.sol";
import "./utils/OwnableUpgradeable.sol";
import "./utils/Timelock.sol";
import "./Curve.sol";

contract CurveFactory is OwnableUpgradeable {
    address public immutable CURVE_IMPL;
    address public immutable TIMELOCK_IMPL;

    address payable public platform; // platform commision account
    uint256 public platformRate; // % of total minting cost as platform commission
    uint256 public totalRateLimit;

    event CurveCreated(
        address indexed owner,
        address indexed curveAddr,
        uint256 initMintPrice,
        uint256 m,
        uint256 n,
        uint256 d
    );
    event SetPlatformParms(
        address payable _platform,
        uint256 _platformRate,
        uint256 _totalRateLimit
    );

    constructor(
        address payable _platform,
        uint256 _platformRate,
        uint256 _totalRateLimit,
        address _timelock
    ) {
        __Ownable_init(_timelock);
        _setPlatformParms(_platform, _platformRate, _totalRateLimit);
        CURVE_IMPL = address(new Curve());
        TIMELOCK_IMPL = address(new Timelock());
    }

    // set up the platform commission account and platform commission rate, only operable by contract owner, _platformRate is in pph
    // set the limit of total commission rate, only operable by contract owner, _totalRateLimit is in pph
    function setPlatformParms(
        address payable _platform,
        uint256 _platformRate,
        uint256 _totalRateLimit
    ) public onlyOwner {
        _setPlatformParms(_platform, _platformRate, _totalRateLimit);
    }

    // set up the platform parameters internal
    function _setPlatformParms(
        address payable _platform,
        uint256 _platformRate,
        uint256 _totalRateLimit
    ) internal {
        require(_platform != address(0), "Curve: platform address is zero.");
        require(
            _totalRateLimit <= 100 && _totalRateLimit >= _platformRate,
            "Curve: wrong rate"
        );

        platform = _platform;
        platformRate = _platformRate;
        totalRateLimit = _totalRateLimit;

        emit SetPlatformParms(_platform, _platformRate, _totalRateLimit);
    }

    /**
     * @dev creation of bonding curve with formular: f(x)=m*(x^N)+v
     * _receivingAddress: receivingAddress's commission account
     * _creatorRate: receivingAddress's commission rate
     * _initMintPrice: f(1) = m + v, the first PASS minting price
     * _erc20: collateral token(erc20) for miniting PASS on bonding curve, send 0x000...000 to appoint it as ETH instead of erc20 token
     * _m: m, slope of curve
     * _n,_d: _n/_d = N, exponent of the curve
     * _baseUri: base URI for PASS metadata
     */
    function createCurve(
        string memory _name,
        string memory _symbol,
        address payable _receivingAddress,
        uint256 _creatorRate,
        uint256 _initMintPrice,
        address _erc20,
        uint256 _m,
        uint256 _n,
        uint256 _d,
        string memory _baseUri,
        address _timelock
    ) public {
        // require(info.length == 3 && parms.length == 4);
        require(
            _creatorRate <= totalRateLimit - platformRate,
            "Curve: receivingAddress's commission rate is too high."
        );

        string[] memory infos = new string[](3);
        infos[0] = _name;
        infos[1] = _symbol;
        infos[2] = _baseUri;

        address[] memory addrs = new address[](4);
        addrs[0] = platform;
        addrs[1] = _receivingAddress;
        addrs[2] = _erc20;
        addrs[3] = _timelock == address(0) ? cloneTimelock() : _timelock;

        uint256[] memory parms = new uint256[](6);
        parms[0] = platformRate;
        parms[1] = _creatorRate;
        parms[2] = _initMintPrice;
        parms[3] = _m;
        parms[4] = _n;
        parms[5] = _d;

        address clone = Clones.clone(CURVE_IMPL);
        Curve(clone).initialize(infos, addrs, parms);
        emit CurveCreated(msg.sender, clone, _initMintPrice, _m, _n, _d);
    }

    function cloneTimelock() private returns (address payable newTimelock) {
        newTimelock = payable(Clones.clone(TIMELOCK_IMPL));

        uint256 minDelay = 2 days;
        address[] memory proposers = new address[](1);
        address[] memory executors = new address[](1);
        proposers[0] = msg.sender;
        executors[0] = address(0);

        Timelock(newTimelock).initialize(minDelay, proposers, executors);
        (minDelay, proposers, executors);

        return newTimelock;
    }
}

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



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

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

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

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

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

// File: contracts/utils/OwnableUpgradeable.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

import "@openzeppelin/contracts-upgradeable/proxy/utils/Initializable.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 OwnableUpgradeable is Initializable {
    address private _owner;

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

    /**
     * @dev Initializes the contract setting the deployer as the initial owner.
     */
    function __Ownable_init(address newOwner) internal initializer {
        _transferOwnership(newOwner);
    }

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

    /**
     * @dev Throws if called by any account other than the owner.
     */
    modifier onlyOwner() {
        require(owner() == msg.sender, "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);
    }

    function _transferOwnership(address newOwner) private {
        address oldOwner = _owner;
        _owner = newOwner;
        emit OwnershipTransferred(oldOwner, newOwner);
    }

    uint256[49] private __gap;
}

// File: contracts/utils/Timelock.sol



// SPDX-License-Identifier: GPL-3.0

pragma solidity ^0.8.0;
import "@openzeppelin/contracts-upgradeable/governance/TimelockControllerUpgradeable.sol";

contract Timelock is TimelockControllerUpgradeable {
    function initialize(
        uint256 minDelay,
        address[] memory proposers,
        address[] memory executors
    ) public initializer {
        __TimelockController_init(minDelay, proposers, executors);
    }
}

// File: contracts/Curve.sol



// SPDX-License-Identifier: MIT

pragma solidity 0.8.6;

import "@openzeppelin/contracts-upgradeable/proxy/utils/Initializable.sol";
import "@openzeppelin/contracts-upgradeable/token/ERC20/IERC20Upgradeable.sol";
import "@openzeppelin/contracts-upgradeable/token/ERC20/utils/SafeERC20Upgradeable.sol";
import "@openzeppelin/contracts-upgradeable/token/ERC1155/extensions/ERC1155BurnableUpgradeable.sol";
import "@openzeppelin/contracts-upgradeable/utils/CountersUpgradeable.sol";
import "./utils/OwnableUpgradeable.sol";
import "./math-utils/interfaces/IAnalyticMath.sol";

/**
 * @dev thePASS Bonding Curve - minting NFT through erc20 or eth
 * PASS is orgnization's erc1155 token on curve
 * erc20 or eth is collateral token on curve
 * Users can mint PASS via deposting erc20 collateral token into curve
 * thePASS Bonding Curve Formula: f(X) = m*(x^N)+v
 * f(x) = PASS Price when total supply of PASS is x
 * m, slope of bonding curve
 * x = total supply of PASS
 * N = n/d, represented by intPower when N is integer
 * v = virtual balance, Displacement of bonding curve
 */
contract Curve is
    Initializable,
    OwnableUpgradeable,
    ERC1155BurnableUpgradeable
{
    using CountersUpgradeable for CountersUpgradeable.Counter;
    using SafeERC20Upgradeable for IERC20Upgradeable;

    IAnalyticMath public constant ANALYTICMATH =
        IAnalyticMath(0x6F1bB529BEd91cD7f75b14d68933AeC9d71eb723); // Mathmatical method for calculating power function

    string public name; // Contract name
    string public symbol; // Contract symbol
    string public baseUri;

    // token id counter. For erc721 contract, PASS serial number = token id
    CountersUpgradeable.Counter private tokenIdTracker;

    uint256 public totalSupply; // total supply of erc1155 tokens

    IERC20Upgradeable public erc20; // collateral token on bonding curve
    uint256 public m; // slope of bonding curve
    uint256 public n; // numerator of exponent in curve power function
    uint256 public d; // denominator of exponent in curve power function
    uint256 public intPower; // when n/d is integer
    uint256 public virtualBalance; // vitual balance for setting a reasonable initial price

    mapping(uint256 => uint256) public decPowerCache; // cache of power function calculation result when exponent is decimal，n => cost
    uint256 public reserve; // reserve of collateral tokens stored in bonding curve AMM pool

    address payable public platform; // thePass platform's commission account
    uint256 public platformRate; // thePass platform's commission rate in pph

    address payable public receivingAddress; // receivingAddress's commission account
    uint256 public creatorRate; // receivingAddress's commission rate in pph

    event Minted(
        uint256 indexed tokenId,
        uint256 indexed cost,
        uint256 indexed reserveAfterMint,
        uint256 balance,
        uint256 platformProfit,
        uint256 creatorProfit
    );
    event Burned(
        address indexed account,
        uint256 indexed tokenId,
        uint256 balance,
        uint256 returnAmount,
        uint256 reserveAfterBurn
    );
    event BatchBurned(
        address indexed account,
        uint256[] tokenIds,
        uint256[] balances,
        uint256 returnAmount,
        uint256 reserveAfterBurn
    );
    event Withdraw(address indexed to, uint256 amount);

    /**
     * @dev constrcutor of bonding curve with formular: f(x)=m*(x^N)+v
     * _erc20: collateral token(erc20) for miniting PASS on bonding curve, send 0x000...000 to appoint it as eth instead of erc20 token
     * _initMintPrice: f(1) = m + v, the first PASS minting price
     * _m: m, slope of curve
     * _virtualBalance: v = f(1) - _m, virtual balance, displacement of curve
     * _n,_d: _n/_d = N, exponent of the curve
     * reserve: reserve of collateral tokens stored in bonding curve AMM pool, start with 0
     */
    function initialize(
        string[] memory infos, //[0]: _name,[1]: _symbol,[2]: _baseUri
        address[] memory addrs, //[0] _platform, [1]: _receivingAddress, [2]: _erc20 [3]: _timelock
        uint256[] memory parms //[0]_platformRate, [1]: _creatorRate, [2]: _initMintPrice, [3]: _m, [4]: _n, [5]: _d
    ) public virtual initializer {
        __Ownable_init(addrs[3]);
        __ERC1155_init(infos[2]);
        __ERC1155Burnable_init();

        tokenIdTracker = CountersUpgradeable.Counter({_value: 1});

        _setBasicInfo(infos[0], infos[1], infos[2], addrs[2]);
        _setFeeParameters(
            payable(addrs[0]),
            parms[0],
            payable(addrs[1]),
            parms[1]
        );
        _setCurveParms(parms[2], parms[3], parms[4], parms[5]);
    }

    // @receivingAddress commission account and rate initilization
    function _setFeeParameters(
        address payable _platform,
        uint256 _platformRate,
        address payable _receivingAddress,
        uint256 _createRate
    ) internal {
        require(_platform != address(0), "Curve: platform address is zero");
        require(
            _receivingAddress != address(0),
            "Curve: receivingAddress address is zero"
        );

        platform = _platform;
        platformRate = _platformRate;
        receivingAddress = _receivingAddress;
        creatorRate = _createRate;
    }

    // only contract admin can change beneficiary account
    function changeBeneficiary(address payable _newAddress) public onlyOwner {
        require(_newAddress != address(0), "Curve: new address is zero");

        receivingAddress = _newAddress;
    }

    /**
     * @dev each PASS minting transaction by depositing collateral erc20 tokens will create a new erc1155 token id sequentially
     * _balance: number of PASSes user want to mint
     * _amount: the maximum deposited amount set by the user
     * _maxPriceFistNFT: the maximum price for the first mintable PASS to prevent front-running with least gas consumption
     * return: token id
     */
    function mint(
        uint256 _balance,
        uint256 _amount,
        uint256 _maxPriceFirstPASS
    ) public returns (uint256) {
        require(address(erc20) != address(0), "Curve: erc20 address is null.");
        uint256 firstPrice = caculateCurrentCostToMint(1);
        require(
            _maxPriceFirstPASS >= firstPrice,
            "Curve: price exceeds slippage tolerance."
        );

        return _mint(_balance, _amount, false);
    }

    // for small amount of PASS minting, it will be unceessary to check the maximum price for the fist mintable PASS
    function mint(uint256 _balance, uint256 _amount) public returns (uint256) {
        require(address(erc20) != address(0), "Curve: erc20 address is null.");
        return _mint(_balance, _amount, false);
    }

    /**
     * @dev user burn PASS/PASSes to receive corresponding collateral tokens
     * _tokenId: the token id of PASS/PASSes to burn
     * _balance: the number of PASS/PASSes to burn
     */
    function burn(
        address _account,
        uint256 _tokenId,
        uint256 _balance
    ) public override {
        require(address(erc20) != address(0), "Curve: erc20 address is null.");

        // checks if allowed to burn
        super._burn(_account, _tokenId, _balance);

        uint256 burnReturn = getCurrentReturnToBurn(_balance);
        totalSupply -= _balance;
        reserve = reserve - burnReturn;

        erc20.safeTransfer(_account, burnReturn);

        emit Burned(_account, _tokenId, _balance, burnReturn, reserve);
    }

    // allow user to burn batches of PASSes with a set of token id
    function burnBatch(
        address _account,
        uint256[] memory _tokenIds,
        uint256[] memory _balances
    ) public override {
        require(address(erc20) != address(0), "Curve: erc20 address is null.");

        // checks if allowed to burn
        super._burnBatch(_account, _tokenIds, _balances);

        uint256 totalBalance;
        for (uint256 i = 0; i < _balances.length; i++) {
            totalBalance += _balances[i];
            totalSupply -= _balances[i];
        }

        uint256 burnReturn = getCurrentReturnToBurn(totalBalance);
        reserve = reserve - burnReturn;
        erc20.safeTransfer(_account, burnReturn);

        emit BatchBurned(_account, _tokenIds, _balances, burnReturn, reserve);
    }

    /**
     * @dev each PASS minting transaction by depositing ETHs will create a new erc1155 token id sequentially
     * _balance: number of PASSes user want to mint
     * _maxPriceFirstPASS: the maximum price for the first mintable PASS to prevent front-running with least gas consumption
     * return: token ID
     */
    function mintEth(uint256 _balance, uint256 _maxPriceFirstPASS)
        public
        payable
        returns (uint256)
    {
        require(
            address(erc20) == address(0),
            "Curve: erc20 address is NOT null."
        );
        uint256 firstPrice = caculateCurrentCostToMint(1);
        require(
            _maxPriceFirstPASS >= firstPrice,
            "Curve: price exceeds slippage tolerance."
        );

        return _mint(_balance, msg.value, true);
    }

    function mintEth(uint256 _balance) public payable returns (uint256) {
        require(
            address(erc20) == address(0),
            "Curve: erc20 address is NOT null."
        );

        return _mint(_balance, msg.value, true);
    }

    /**
     * @dev user burn PASS/PASSes to receive corresponding ETHs
     * _tokenId: the token id of PASS/PASSes to burn
     * _balance: the number of PASS/PASSes to burn
     */
    function burnEth(
        address _account,
        uint256 _tokenId,
        uint256 _balance
    ) public {
        require(
            address(erc20) == address(0),
            "Curve: erc20 address is NOT null."
        );
        super._burn(_account, _tokenId, _balance);

        uint256 burnReturn = getCurrentReturnToBurn(_balance);

        totalSupply -= _balance;

        reserve = reserve - burnReturn;
        payable(_account).transfer(burnReturn);

        emit Burned(_account, _tokenId, _balance, burnReturn, reserve);
    }

    // allow user to burn batches of PASSes with a set of token id
    function burnBatchETH(
        address _account,
        uint256[] memory _tokenIds,
        uint256[] memory _balances
    ) public {
        require(address(erc20) == address(0), "Curve: erc20 address is null.");
        super._burnBatch(_account, _tokenIds, _balances);

        uint256 totalBalance;
        for (uint256 i = 0; i < _balances.length; i++) {
            totalBalance += _balances[i];
            totalSupply -= _balances[i];
        }

        uint256 burnReturn = getCurrentReturnToBurn(totalBalance);

        reserve = reserve - burnReturn;
        payable(_account).transfer(burnReturn);

        emit BatchBurned(_account, _tokenIds, _balances, burnReturn, reserve);
    }

    function uri(uint256 _tokenId)
        public
        view
        override
        returns (string memory)
    {
        return string(abi.encodePacked(baseUri, toString(_tokenId)));
    }

    // get current supply of PASS
    function getCurrentSupply() public view returns (uint256) {
        return totalSupply;
    }

    // internal function to mint PASS
    function _mint(
        uint256 _balance,
        uint256 _amount,
        bool bETH
    ) private returns (uint256 tokenId) {
        uint256 mintCost = caculateCurrentCostToMint(_balance);
        require(_amount >= mintCost, "Curve: not enough token sent");

        address account = _msgSender();

        uint256 platformProfit = (mintCost * platformRate) / 100;
        uint256 creatorProfit = (mintCost * creatorRate) / 100;

        tokenId = tokenIdTracker.current(); // accumulate the token id
        tokenIdTracker.increment(); // automate token id increment

        totalSupply += _balance;
        _mint(account, tokenId, _balance, "");

        uint256 reserveCut = mintCost - platformProfit - creatorProfit;
        reserve = reserve + reserveCut;

        if (bETH) {
            // return overcharge eth
            if (_amount - (mintCost) > 0) {
                payable(account).transfer(_amount - (mintCost));
            }
            if (platformRate > 0) {
                platform.transfer(platformProfit);
            }
        } else {
            erc20.safeTransferFrom(account, address(this), mintCost);
            if (platformRate > 0) {
                erc20.safeTransfer(platform, platformProfit);
            }
        }

        emit Minted(
            tokenId,
            mintCost,
            reserve,
            _balance,
            platformProfit,
            creatorProfit
        );

        return tokenId; // returns tokenId in case its useful to check it
    }

    function _getEthBalance() internal view returns (uint256) {
        return address(this).balance;
    }

    function _getErc20Balance() internal view returns (uint256) {
        return IERC20Upgradeable(erc20).balanceOf(address(this));
    }

    /**
     * @dev internal function to calculate the cost of minting _balance PASSes in a transaction
     * _balance: number of PASS/PASSes to mint
     */
    function caculateCurrentCostToMint(uint256 _balance)
        internal
        returns (uint256)
    {
        uint256 curStartX = getCurrentSupply() + 1;
        uint256 totalCost;
        if (intPower > 0) {
            if (intPower <= 10) {
                uint256 intervalSum = caculateIntervalSum(
                    intPower,
                    curStartX,
                    curStartX + _balance - 1
                );
                totalCost = m * intervalSum + (virtualBalance * _balance);
            } else {
                for (uint256 i = curStartX; i < curStartX + _balance; i++) {
                    totalCost =
                        totalCost +
                        (m * (i**intPower) + (virtualBalance));
                }
            }
        } else {
            for (uint256 i = curStartX; i < curStartX + _balance; i++) {
                if (decPowerCache[i] == 0) {
                    (uint256 p, uint256 q) = ANALYTICMATH.pow(i, 1, n, d);
                    uint256 cost = virtualBalance + ((m * p) / q);
                    totalCost = totalCost + cost;
                    decPowerCache[i] = cost;
                } else {
                    totalCost = totalCost + decPowerCache[i];
                }
            }
        }
        return totalCost;
    }

    // external view function to query the current cost to mint a PASS/PASSes
    function getCurrentCostToMint(uint256 _balance)
        public
        view
        returns (uint256)
    {
        uint256 curStartX = getCurrentSupply() + 1;
        uint256 totalCost;
        if (intPower > 0) {
            if (intPower <= 10) {
                uint256 intervalSum = caculateIntervalSum(
                    intPower,
                    curStartX,
                    curStartX + _balance - 1
                );
                totalCost = m * (intervalSum) + (virtualBalance * _balance);
            } else {
                for (uint256 i = curStartX; i < curStartX + _balance; i++) {
                    totalCost =
                        totalCost +
                        (m * (i**intPower) + (virtualBalance));
                }
            }
        } else {
            for (uint256 i = curStartX; i < curStartX + _balance; i++) {
                (uint256 p, uint256 q) = ANALYTICMATH.pow(i, 1, n, d);
                uint256 cost = virtualBalance + ((m * p) / q);
                totalCost = totalCost + (cost);
            }
        }
        return totalCost;
    }

    /**
     * @dev calculate the return of burning _balance PASSes in a transaction
     * _balance: number of PASS/PASSes to be burned
     */
    function getCurrentReturnToBurn(uint256 _balance)
        public
        view
        returns (uint256)
    {
        uint256 curEndX = getCurrentSupply();
        _balance = _balance > curEndX ? curEndX : _balance;

        uint256 totalReturn;
        if (intPower > 0) {
            if (intPower <= 10) {
                uint256 intervalSum = caculateIntervalSum(
                    intPower,
                    curEndX - _balance + 1,
                    curEndX
                );
                totalReturn = m * intervalSum + (virtualBalance * (_balance));
            } else {
                for (uint256 i = curEndX; i > curEndX - _balance; i--) {
                    totalReturn =
                        totalReturn +
                        (m * (i**intPower) + (virtualBalance));
                }
            }
        } else {
            for (uint256 i = curEndX; i > curEndX - _balance; i--) {
                totalReturn = totalReturn + decPowerCache[i];
            }
        }
        totalReturn = (totalReturn * (100 - platformRate - creatorRate)) / 100;
        return totalReturn;
    }

    // Bernoulli's formula for calculating the sum of intervals between the two reserves
    function caculateIntervalSum(
        uint256 _power,
        uint256 _startX,
        uint256 _endX
    ) public pure returns (uint256) {
        return
            ANALYTICMATH.caculateIntPowerSum(_power, _endX) -
            ANALYTICMATH.caculateIntPowerSum(_power, _startX - 1);
    }

    // anyone can withdraw reserve of erc20 tokens/ETH to receivingAddress's beneficiary account
    function withdraw() public {
        if (address(erc20) == address(0)) {
            receivingAddress.transfer(_getEthBalance() - reserve); // withdraw eth to beneficiary account
            emit Withdraw(receivingAddress, _getEthBalance() - reserve);
        } else {
            erc20.safeTransfer(receivingAddress, _getErc20Balance() - reserve); // withdraw erc20 tokens to beneficiary account
            emit Withdraw(receivingAddress, _getErc20Balance() - reserve);
        }
    }

    function _setBasicInfo(
        string memory _name,
        string memory _symbol,
        string memory _baseUri,
        address _erc20
    ) internal {
        name = _name;
        symbol = _symbol;
        baseUri = _baseUri;
        erc20 = IERC20Upgradeable(_erc20);
    }

    function _setCurveParms(
        uint256 _initMintPrice,
        uint256 _m,
        uint256 _n,
        uint256 _d
    ) internal {
        m = _m;
        n = _n;
        if ((_n / _d) * _d == _n) {
            intPower = _n / _d;
        } else {
            d = _d;
        }

        virtualBalance = _initMintPrice - _m;
        reserve = 0;
    }

    /**
     * @dev Converts a `uint256` to its ASCII `string` decimal representation.
     */
    function toString(uint256 value) internal pure returns (string memory) {
        // Inspired by OraclizeAPI's implementation - MIT licence
        // https://github.com/oraclize/ethereum-api/blob/b42146b063c7d6ee1358846c198246239e9360e8/oraclizeAPI_0.4.25.sol

        if (value == 0) {
            return "0";
        }
        uint256 temp = value;
        uint256 digits;
        while (temp != 0) {
            digits++;
            temp /= 10;
        }
        bytes memory buffer = new bytes(digits);
        while (value != 0) {
            digits -= 1;
            buffer[digits] = bytes1(uint8(48 + uint256(value % 10)));
            value /= 10;
        }
        return string(buffer);
    }
}

// File: @openzeppelin/contracts-upgradeable/proxy/utils/Initializable.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.0 (proxy/utils/Initializable.sol)

pragma solidity ^0.8.0;

/**
 * @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 a proxied contract can't have 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.
 *
 * 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 initialize the implementation contract, you can either invoke the
 * initializer manually, or you can include a constructor to automatically mark it as initialized when it is deployed:
 *
 * [.hljs-theme-light.nopadding]
 * ```
 * /// @custom:oz-upgrades-unsafe-allow constructor
 * constructor() initializer {}
 * ```
 * ====
 */
abstract contract Initializable {
    /**
     * @dev Indicates that the contract has been initialized.
     */
    bool private _initialized;

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

    /**
     * @dev Modifier to protect an initializer function from being invoked twice.
     */
    modifier initializer() {
        require(_initializing || !_initialized, "Initializable: contract is already initialized");

        bool isTopLevelCall = !_initializing;
        if (isTopLevelCall) {
            _initializing = true;
            _initialized = true;
        }

        _;

        if (isTopLevelCall) {
            _initializing = false;
        }
    }
}

// File: @openzeppelin/contracts-upgradeable/governance/TimelockControllerUpgradeable.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.0 (governance/TimelockController.sol)

pragma solidity ^0.8.0;

import "../access/AccessControlUpgradeable.sol";
import "../proxy/utils/Initializable.sol";

/**
 * @dev Contract module which acts as a timelocked controller. When set as the
 * owner of an `Ownable` smart contract, it enforces a timelock on all
 * `onlyOwner` maintenance operations. This gives time for users of the
 * controlled contract to exit before a potentially dangerous maintenance
 * operation is applied.
 *
 * By default, this contract is self administered, meaning administration tasks
 * have to go through the timelock process. The proposer (resp executor) role
 * is in charge of proposing (resp executing) operations. A common use case is
 * to position this {TimelockController} as the owner of a smart contract, with
 * a multisig or a DAO as the sole proposer.
 *
 * _Available since v3.3._
 */
contract TimelockControllerUpgradeable is Initializable, AccessControlUpgradeable {
    bytes32 public constant TIMELOCK_ADMIN_ROLE = keccak256("TIMELOCK_ADMIN_ROLE");
    bytes32 public constant PROPOSER_ROLE = keccak256("PROPOSER_ROLE");
    bytes32 public constant EXECUTOR_ROLE = keccak256("EXECUTOR_ROLE");
    uint256 internal constant _DONE_TIMESTAMP = uint256(1);

    mapping(bytes32 => uint256) private _timestamps;
    uint256 private _minDelay;

    /**
     * @dev Emitted when a call is scheduled as part of operation `id`.
     */
    event CallScheduled(
        bytes32 indexed id,
        uint256 indexed index,
        address target,
        uint256 value,
        bytes data,
        bytes32 predecessor,
        uint256 delay
    );

    /**
     * @dev Emitted when a call is performed as part of operation `id`.
     */
    event CallExecuted(bytes32 indexed id, uint256 indexed index, address target, uint256 value, bytes data);

    /**
     * @dev Emitted when operation `id` is cancelled.
     */
    event Cancelled(bytes32 indexed id);

    /**
     * @dev Emitted when the minimum delay for future operations is modified.
     */
    event MinDelayChange(uint256 oldDuration, uint256 newDuration);

    /**
     * @dev Initializes the contract with a given `minDelay`.
     */
    function __TimelockController_init(
        uint256 minDelay,
        address[] memory proposers,
        address[] memory executors
    ) internal initializer {
        __Context_init_unchained();
        __ERC165_init_unchained();
        __AccessControl_init_unchained();
        __TimelockController_init_unchained(minDelay, proposers, executors);
    }

    function __TimelockController_init_unchained(
        uint256 minDelay,
        address[] memory proposers,
        address[] memory executors
    ) internal initializer {
        _setRoleAdmin(TIMELOCK_ADMIN_ROLE, TIMELOCK_ADMIN_ROLE);
        _setRoleAdmin(PROPOSER_ROLE, TIMELOCK_ADMIN_ROLE);
        _setRoleAdmin(EXECUTOR_ROLE, TIMELOCK_ADMIN_ROLE);

        // deployer + self administration
        _setupRole(TIMELOCK_ADMIN_ROLE, _msgSender());
        _setupRole(TIMELOCK_ADMIN_ROLE, address(this));

        // register proposers
        for (uint256 i = 0; i < proposers.length; ++i) {
            _setupRole(PROPOSER_ROLE, proposers[i]);
        }

        // register executors
        for (uint256 i = 0; i < executors.length; ++i) {
            _setupRole(EXECUTOR_ROLE, executors[i]);
        }

        _minDelay = minDelay;
        emit MinDelayChange(0, minDelay);
    }

    /**
     * @dev Modifier to make a function callable only by a certain role. In
     * addition to checking the sender's role, `address(0)` 's role is also
     * considered. Granting a role to `address(0)` is equivalent to enabling
     * this role for everyone.
     */
    modifier onlyRoleOrOpenRole(bytes32 role) {
        if (!hasRole(role, address(0))) {
            _checkRole(role, _msgSender());
        }
        _;
    }

    /**
     * @dev Contract might receive/hold ETH as part of the maintenance process.
     */
    receive() external payable {}

    /**
     * @dev Returns whether an id correspond to a registered operation. This
     * includes both Pending, Ready and Done operations.
     */
    function isOperation(bytes32 id) public view virtual returns (bool pending) {
        return getTimestamp(id) > 0;
    }

    /**
     * @dev Returns whether an operation is pending or not.
     */
    function isOperationPending(bytes32 id) public view virtual returns (bool pending) {
        return getTimestamp(id) > _DONE_TIMESTAMP;
    }

    /**
     * @dev Returns whether an operation is ready or not.
     */
    function isOperationReady(bytes32 id) public view virtual returns (bool ready) {
        uint256 timestamp = getTimestamp(id);
        return timestamp > _DONE_TIMESTAMP && timestamp <= block.timestamp;
    }

    /**
     * @dev Returns whether an operation is done or not.
     */
    function isOperationDone(bytes32 id) public view virtual returns (bool done) {
        return getTimestamp(id) == _DONE_TIMESTAMP;
    }

    /**
     * @dev Returns the timestamp at with an operation becomes ready (0 for
     * unset operations, 1 for done operations).
     */
    function getTimestamp(bytes32 id) public view virtual returns (uint256 timestamp) {
        return _timestamps[id];
    }

    /**
     * @dev Returns the minimum delay for an operation to become valid.
     *
     * This value can be changed by executing an operation that calls `updateDelay`.
     */
    function getMinDelay() public view virtual returns (uint256 duration) {
        return _minDelay;
    }

    /**
     * @dev Returns the identifier of an operation containing a single
     * transaction.
     */
    function hashOperation(
        address target,
        uint256 value,
        bytes calldata data,
        bytes32 predecessor,
        bytes32 salt
    ) public pure virtual returns (bytes32 hash) {
        return keccak256(abi.encode(target, value, data, predecessor, salt));
    }

    /**
     * @dev Returns the identifier of an operation containing a batch of
     * transactions.
     */
    function hashOperationBatch(
        address[] calldata targets,
        uint256[] calldata values,
        bytes[] calldata datas,
        bytes32 predecessor,
        bytes32 salt
    ) public pure virtual returns (bytes32 hash) {
        return keccak256(abi.encode(targets, values, datas, predecessor, salt));
    }

    /**
     * @dev Schedule an operation containing a single transaction.
     *
     * Emits a {CallScheduled} event.
     *
     * Requirements:
     *
     * - the caller must have the 'proposer' role.
     */
    function schedule(
        address target,
        uint256 value,
        bytes calldata data,
        bytes32 predecessor,
        bytes32 salt,
        uint256 delay
    ) public virtual onlyRole(PROPOSER_ROLE) {
        bytes32 id = hashOperation(target, value, data, predecessor, salt);
        _schedule(id, delay);
        emit CallScheduled(id, 0, target, value, data, predecessor, delay);
    }

    /**
     * @dev Schedule an operation containing a batch of transactions.
     *
     * Emits one {CallScheduled} event per transaction in the batch.
     *
     * Requirements:
     *
     * - the caller must have the 'proposer' role.
     */
    function scheduleBatch(
        address[] calldata targets,
        uint256[] calldata values,
        bytes[] calldata datas,
        bytes32 predecessor,
        bytes32 salt,
        uint256 delay
    ) public virtual onlyRole(PROPOSER_ROLE) {
        require(targets.length == values.length, "TimelockController: length mismatch");
        require(targets.length == datas.length, "TimelockController: length mismatch");

        bytes32 id = hashOperationBatch(targets, values, datas, predecessor, salt);
        _schedule(id, delay);
        for (uint256 i = 0; i < targets.length; ++i) {
            emit CallScheduled(id, i, targets[i], values[i], datas[i], predecessor, delay);
        }
    }

    /**
     * @dev Schedule an operation that is to becomes valid after a given delay.
     */
    function _schedule(bytes32 id, uint256 delay) private {
        require(!isOperation(id), "TimelockController: operation already scheduled");
        require(delay >= getMinDelay(), "TimelockController: insufficient delay");
        _timestamps[id] = block.timestamp + delay;
    }

    /**
     * @dev Cancel an operation.
     *
     * Requirements:
     *
     * - the caller must have the 'proposer' role.
     */
    function cancel(bytes32 id) public virtual onlyRole(PROPOSER_ROLE) {
        require(isOperationPending(id), "TimelockController: operation cannot be cancelled");
        delete _timestamps[id];

        emit Cancelled(id);
    }

    /**
     * @dev Execute an (ready) operation containing a single transaction.
     *
     * Emits a {CallExecuted} event.
     *
     * Requirements:
     *
     * - the caller must have the 'executor' role.
     */
    function execute(
        address target,
        uint256 value,
        bytes calldata data,
        bytes32 predecessor,
        bytes32 salt
    ) public payable virtual onlyRoleOrOpenRole(EXECUTOR_ROLE) {
        bytes32 id = hashOperation(target, value, data, predecessor, salt);
        _beforeCall(id, predecessor);
        _call(id, 0, target, value, data);
        _afterCall(id);
    }

    /**
     * @dev Execute an (ready) operation containing a batch of transactions.
     *
     * Emits one {CallExecuted} event per transaction in the batch.
     *
     * Requirements:
     *
     * - the caller must have the 'executor' role.
     */
    function executeBatch(
        address[] calldata targets,
        uint256[] calldata values,
        bytes[] calldata datas,
        bytes32 predecessor,
        bytes32 salt
    ) public payable virtual onlyRoleOrOpenRole(EXECUTOR_ROLE) {
        require(targets.length == values.length, "TimelockController: length mismatch");
        require(targets.length == datas.length, "TimelockController: length mismatch");

        bytes32 id = hashOperationBatch(targets, values, datas, predecessor, salt);
        _beforeCall(id, predecessor);
        for (uint256 i = 0; i < targets.length; ++i) {
            _call(id, i, targets[i], values[i], datas[i]);
        }
        _afterCall(id);
    }

    /**
     * @dev Checks before execution of an operation's calls.
     */
    function _beforeCall(bytes32 id, bytes32 predecessor) private view {
        require(isOperationReady(id), "TimelockController: operation is not ready");
        require(predecessor == bytes32(0) || isOperationDone(predecessor), "TimelockController: missing dependency");
    }

    /**
     * @dev Checks after execution of an operation's calls.
     */
    function _afterCall(bytes32 id) private {
        require(isOperationReady(id), "TimelockController: operation is not ready");
        _timestamps[id] = _DONE_TIMESTAMP;
    }

    /**
     * @dev Execute an operation's call.
     *
     * Emits a {CallExecuted} event.
     */
    function _call(
        bytes32 id,
        uint256 index,
        address target,
        uint256 value,
        bytes calldata data
    ) private {
        (bool success, ) = target.call{value: value}(data);
        require(success, "TimelockController: underlying transaction reverted");

        emit CallExecuted(id, index, target, value, data);
    }

    /**
     * @dev Changes the minimum timelock duration for future operations.
     *
     * Emits a {MinDelayChange} event.
     *
     * Requirements:
     *
     * - the caller must be the timelock itself. This can only be achieved by scheduling and later executing
     * an operation where the timelock is the target and the data is the ABI-encoded call to this function.
     */
    function updateDelay(uint256 newDelay) external virtual {
        require(msg.sender == address(this), "TimelockController: caller must be timelock");
        emit MinDelayChange(_minDelay, newDelay);
        _minDelay = newDelay;
    }
    uint256[48] private __gap;
}

// File: @openzeppelin/contracts-upgradeable/access/AccessControlUpgradeable.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.0 (access/AccessControl.sol)

pragma solidity ^0.8.0;

import "./IAccessControlUpgradeable.sol";
import "../utils/ContextUpgradeable.sol";
import "../utils/StringsUpgradeable.sol";
import "../utils/introspection/ERC165Upgradeable.sol";
import "../proxy/utils/Initializable.sol";

/**
 * @dev Contract module that allows children to implement role-based access
 * control mechanisms. This is a lightweight version that doesn't allow enumerating role
 * members except through off-chain means by accessing the contract event logs. Some
 * applications may benefit from on-chain enumerability, for those cases see
 * {AccessControlEnumerable}.
 *
 * Roles are referred to by their `bytes32` identifier. These should be exposed
 * in the external API and be unique. The best way to achieve this is by
 * using `public constant` hash digests:
 *
 * ```
 * bytes32 public constant MY_ROLE = keccak256("MY_ROLE");
 * ```
 *
 * Roles can be used to represent a set of permissions. To restrict access to a
 * function call, use {hasRole}:
 *
 * ```
 * function foo() public {
 *     require(hasRole(MY_ROLE, msg.sender));
 *     ...
 * }
 * ```
 *
 * Roles can be granted and revoked dynamically via the {grantRole} and
 * {revokeRole} functions. Each role has an associated admin role, and only
 * accounts that have a role's admin role can call {grantRole} and {revokeRole}.
 *
 * By default, the admin role for all roles is `DEFAULT_ADMIN_ROLE`, which means
 * that only accounts with this role will be able to grant or revoke other
 * roles. More complex role relationships can be created by using
 * {_setRoleAdmin}.
 *
 * WARNING: The `DEFAULT_ADMIN_ROLE` is also its own admin: it has permission to
 * grant and revoke this role. Extra precautions should be taken to secure
 * accounts that have been granted it.
 */
abstract contract AccessControlUpgradeable is Initializable, ContextUpgradeable, IAccessControlUpgradeable, ERC165Upgradeable {
    function __AccessControl_init() internal initializer {
        __Context_init_unchained();
        __ERC165_init_unchained();
        __AccessControl_init_unchained();
    }

    function __AccessControl_init_unchained() internal initializer {
    }
    struct RoleData {
        mapping(address => bool) members;
        bytes32 adminRole;
    }

    mapping(bytes32 => RoleData) private _roles;

    bytes32 public constant DEFAULT_ADMIN_ROLE = 0x00;

    /**
     * @dev Modifier that checks that an account has a specific role. Reverts
     * with a standardized message including the required role.
     *
     * The format of the revert reason is given by the following regular expression:
     *
     *  /^AccessControl: account (0x[0-9a-f]{40}) is missing role (0x[0-9a-f]{64})$/
     *
     * _Available since v4.1._
     */
    modifier onlyRole(bytes32 role) {
        _checkRole(role, _msgSender());
        _;
    }

    /**
     * @dev See {IERC165-supportsInterface}.
     */
    function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
        return interfaceId == type(IAccessControlUpgradeable).interfaceId || super.supportsInterface(interfaceId);
    }

    /**
     * @dev Returns `true` if `account` has been granted `role`.
     */
    function hasRole(bytes32 role, address account) public view override returns (bool) {
        return _roles[role].members[account];
    }

    /**
     * @dev Revert with a standard message if `account` is missing `role`.
     *
     * The format of the revert reason is given by the following regular expression:
     *
     *  /^AccessControl: account (0x[0-9a-f]{40}) is missing role (0x[0-9a-f]{64})$/
     */
    function _checkRole(bytes32 role, address account) internal view {
        if (!hasRole(role, account)) {
            revert(
                string(
                    abi.encodePacked(
                        "AccessControl: account ",
                        StringsUpgradeable.toHexString(uint160(account), 20),
                        " is missing role ",
                        StringsUpgradeable.toHexString(uint256(role), 32)
                    )
                )
            );
        }
    }

    /**
     * @dev Returns the admin role that controls `role`. See {grantRole} and
     * {revokeRole}.
     *
     * To change a role's admin, use {_setRoleAdmin}.
     */
    function getRoleAdmin(bytes32 role) public view override returns (bytes32) {
        return _roles[role].adminRole;
    }

    /**
     * @dev Grants `role` to `account`.
     *
     * If `account` had not been already granted `role`, emits a {RoleGranted}
     * event.
     *
     * Requirements:
     *
     * - the caller must have ``role``'s admin role.
     */
    function grantRole(bytes32 role, address account) public virtual override onlyRole(getRoleAdmin(role)) {
        _grantRole(role, account);
    }

    /**
     * @dev Revokes `role` from `account`.
     *
     * If `account` had been granted `role`, emits a {RoleRevoked} event.
     *
     * Requirements:
     *
     * - the caller must have ``role``'s admin role.
     */
    function revokeRole(bytes32 role, address account) public virtual override onlyRole(getRoleAdmin(role)) {
        _revokeRole(role, account);
    }

    /**
     * @dev Revokes `role` from the calling account.
     *
     * Roles are often managed via {grantRole} and {revokeRole}: this function's
     * purpose is to provide a mechanism for accounts to lose their privileges
     * if they are compromised (such as when a trusted device is misplaced).
     *
     * If the calling account had been revoked `role`, emits a {RoleRevoked}
     * event.
     *
     * Requirements:
     *
     * - the caller must be `account`.
     */
    function renounceRole(bytes32 role, address account) public virtual override {
        require(account == _msgSender(), "AccessControl: can only renounce roles for self");

        _revokeRole(role, account);
    }

    /**
     * @dev Grants `role` to `account`.
     *
     * If `account` had not been already granted `role`, emits a {RoleGranted}
     * event. Note that unlike {grantRole}, this function doesn't perform any
     * checks on the calling account.
     *
     * [WARNING]
     * ====
     * This function should only be called from the constructor when setting
     * up the initial roles for the system.
     *
     * Using this function in any other way is effectively circumventing the admin
     * system imposed by {AccessControl}.
     * ====
     *
     * NOTE: This function is deprecated in favor of {_grantRole}.
     */
    function _setupRole(bytes32 role, address account) internal virtual {
        _grantRole(role, account);
    }

    /**
     * @dev Sets `adminRole` as ``role``'s admin role.
     *
     * Emits a {RoleAdminChanged} event.
     */
    function _setRoleAdmin(bytes32 role, bytes32 adminRole) internal virtual {
        bytes32 previousAdminRole = getRoleAdmin(role);
        _roles[role].adminRole = adminRole;
        emit RoleAdminChanged(role, previousAdminRole, adminRole);
    }

    /**
     * @dev Grants `role` to `account`.
     *
     * Internal function without access restriction.
     */
    function _grantRole(bytes32 role, address account) internal virtual {
        if (!hasRole(role, account)) {
            _roles[role].members[account] = true;
            emit RoleGranted(role, account, _msgSender());
        }
    }

    /**
     * @dev Revokes `role` from `account`.
     *
     * Internal function without access restriction.
     */
    function _revokeRole(bytes32 role, address account) internal virtual {
        if (hasRole(role, account)) {
            _roles[role].members[account] = false;
            emit RoleRevoked(role, account, _msgSender());
        }
    }
    uint256[49] private __gap;
}

// File: @openzeppelin/contracts-upgradeable/access/IAccessControlUpgradeable.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.0 (access/IAccessControl.sol)

pragma solidity ^0.8.0;

/**
 * @dev External interface of AccessControl declared to support ERC165 detection.
 */
interface IAccessControlUpgradeable {
    /**
     * @dev Emitted when `newAdminRole` is set as ``role``'s admin role, replacing `previousAdminRole`
     *
     * `DEFAULT_ADMIN_ROLE` is the starting admin for all roles, despite
     * {RoleAdminChanged} not being emitted signaling this.
     *
     * _Available since v3.1._
     */
    event RoleAdminChanged(bytes32 indexed role, bytes32 indexed previousAdminRole, bytes32 indexed newAdminRole);

    /**
     * @dev Emitted when `account` is granted `role`.
     *
     * `sender` is the account that originated the contract call, an admin role
     * bearer except when using {AccessControl-_setupRole}.
     */
    event RoleGranted(bytes32 indexed role, address indexed account, address indexed sender);

    /**
     * @dev Emitted when `account` is revoked `role`.
     *
     * `sender` is the account that originated the contract call:
     *   - if using `revokeRole`, it is the admin role bearer
     *   - if using `renounceRole`, it is the role bearer (i.e. `account`)
     */
    event RoleRevoked(bytes32 indexed role, address indexed account, address indexed sender);

    /**
     * @dev Returns `true` if `account` has been granted `role`.
     */
    function hasRole(bytes32 role, address account) external view returns (bool);

    /**
     * @dev Returns the admin role that controls `role`. See {grantRole} and
     * {revokeRole}.
     *
     * To change a role's admin, use {AccessControl-_setRoleAdmin}.
     */
    function getRoleAdmin(bytes32 role) external view returns (bytes32);

    /**
     * @dev Grants `role` to `account`.
     *
     * If `account` had not been already granted `role`, emits a {RoleGranted}
     * event.
     *
     * Requirements:
     *
     * - the caller must have ``role``'s admin role.
     */
    function grantRole(bytes32 role, address account) external;

    /**
     * @dev Revokes `role` from `account`.
     *
     * If `account` had been granted `role`, emits a {RoleRevoked} event.
     *
     * Requirements:
     *
     * - the caller must have ``role``'s admin role.
     */
    function revokeRole(bytes32 role, address account) external;

    /**
     * @dev Revokes `role` from the calling account.
     *
     * Roles are often managed via {grantRole} and {revokeRole}: this function's
     * purpose is to provide a mechanism for accounts to lose their privileges
     * if they are compromised (such as when a trusted device is misplaced).
     *
     * If the calling account had been granted `role`, emits a {RoleRevoked}
     * event.
     *
     * Requirements:
     *
     * - the caller must be `account`.
     */
    function renounceRole(bytes32 role, address account) external;
}

// File: @openzeppelin/contracts-upgradeable/utils/ContextUpgradeable.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.0 (utils/Context.sol)

pragma solidity ^0.8.0;
import "../proxy/utils/Initializable.sol";

/**
 * @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 ContextUpgradeable is Initializable {
    function __Context_init() internal initializer {
        __Context_init_unchained();
    }

    function __Context_init_unchained() internal initializer {
    }
    function _msgSender() internal view virtual returns (address) {
        return msg.sender;
    }

    function _msgData() internal view virtual returns (bytes calldata) {
        return msg.data;
    }
    uint256[50] private __gap;
}

// File: @openzeppelin/contracts-upgradeable/utils/StringsUpgradeable.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.0 (utils/Strings.sol)

pragma solidity ^0.8.0;

/**
 * @dev String operations.
 */
library StringsUpgradeable {
    bytes16 private constant _HEX_SYMBOLS = "0123456789abcdef";

    /**
     * @dev Converts a `uint256` to its ASCII `string` decimal representation.
     */
    function toString(uint256 value) internal pure returns (string memory) {
        // Inspired by OraclizeAPI's implementation - MIT licence
        // https://github.com/oraclize/ethereum-api/blob/b42146b063c7d6ee1358846c198246239e9360e8/oraclizeAPI_0.4.25.sol

        if (value == 0) {
            return "0";
        }
        uint256 temp = value;
        uint256 digits;
        while (temp != 0) {
            digits++;
            temp /= 10;
        }
        bytes memory buffer = new bytes(digits);
        while (value != 0) {
            digits -= 1;
            buffer[digits] = bytes1(uint8(48 + uint256(value % 10)));
            value /= 10;
        }
        return string(buffer);
    }

    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation.
     */
    function toHexString(uint256 value) internal pure returns (string memory) {
        if (value == 0) {
            return "0x00";
        }
        uint256 temp = value;
        uint256 length = 0;
        while (temp != 0) {
            length++;
            temp >>= 8;
        }
        return toHexString(value, length);
    }

    /**
     * @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] = _HEX_SYMBOLS[value & 0xf];
            value >>= 4;
        }
        require(value == 0, "Strings: hex length insufficient");
        return string(buffer);
    }
}

// File: @openzeppelin/contracts-upgradeable/utils/introspection/ERC165Upgradeable.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.0 (utils/introspection/ERC165.sol)

pragma solidity ^0.8.0;

import "./IERC165Upgradeable.sol";
import "../../proxy/utils/Initializable.sol";

/**
 * @dev Implementation of the {IERC165} interface.
 *
 * Contracts that want to implement ERC165 should inherit from this contract and override {supportsInterface} to check
 * for the additional interface id that will be supported. For example:
 *
 * ```solidity
 * function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
 *     return interfaceId == type(MyInterface).interfaceId || super.supportsInterface(interfaceId);
 * }
 * ```
 *
 * Alternatively, {ERC165Storage} provides an easier to use but more expensive implementation.
 */
abstract contract ERC165Upgradeable is Initializable, IERC165Upgradeable {
    function __ERC165_init() internal initializer {
        __ERC165_init_unchained();
    }

    function __ERC165_init_unchained() internal initializer {
    }
    /**
     * @dev See {IERC165-supportsInterface}.
     */
    function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
        return interfaceId == type(IERC165Upgradeable).interfaceId;
    }
    uint256[50] private __gap;
}

// File: @openzeppelin/contracts-upgradeable/utils/introspection/IERC165Upgradeable.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.0 (utils/introspection/IERC165.sol)

pragma solidity ^0.8.0;

/**
 * @dev Interface of the ERC165 standard, as defined in the
 * https://eips.ethereum.org/EIPS/eip-165[EIP].
 *
 * Implementers can declare support of contract interfaces, which can then be
 * queried by others ({ERC165Checker}).
 *
 * For an implementation, see {ERC165}.
 */
interface IERC165Upgradeable {
    /**
     * @dev Returns true if this contract implements the interface defined by
     * `interfaceId`. See the corresponding
     * https://eips.ethereum.org/EIPS/eip-165#how-interfaces-are-identified[EIP section]
     * to learn more about how these ids are created.
     *
     * This function call must use less than 30 000 gas.
     */
    function supportsInterface(bytes4 interfaceId) external view returns (bool);
}

// File: @openzeppelin/contracts-upgradeable/token/ERC20/IERC20Upgradeable.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.0 (token/ERC20/IERC20.sol)

pragma solidity ^0.8.0;

/**
 * @dev Interface of the ERC20 standard as defined in the EIP.
 */
interface IERC20Upgradeable {
    /**
     * @dev Returns the amount of tokens in existence.
     */
    function totalSupply() external view returns (uint256);

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

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

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

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

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

    /**
     * @dev Emitted when `value` tokens are moved from one account (`from`) to
     * another (`to`).
     *
     * Note that `value` may be zero.
     */
    event Transfer(address indexed from, address indexed to, uint256 value);

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

// File: @openzeppelin/contracts-upgradeable/token/ERC20/utils/SafeERC20Upgradeable.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.0 (token/ERC20/utils/SafeERC20.sol)

pragma solidity ^0.8.0;

import "../IERC20Upgradeable.sol";
import "../../../utils/AddressUpgradeable.sol";

/**
 * @title SafeERC20
 * @dev Wrappers around ERC20 operations that throw on failure (when the token
 * contract returns false). Tokens that return no value (and instead revert or
 * throw on failure) are also supported, non-reverting calls are assumed to be
 * successful.
 * To use this library you can add a `using SafeERC20 for IERC20;` statement to your contract,
 * which allows you to call the safe operations as `token.safeTransfer(...)`, etc.
 */
library SafeERC20Upgradeable {
    using AddressUpgradeable for address;

    function safeTransfer(
        IERC20Upgradeable token,
        address to,
        uint256 value
    ) internal {
        _callOptionalReturn(token, abi.encodeWithSelector(token.transfer.selector, to, value));
    }

    function safeTransferFrom(
        IERC20Upgradeable token,
        address from,
        address to,
        uint256 value
    ) internal {
        _callOptionalReturn(token, abi.encodeWithSelector(token.transferFrom.selector, from, to, value));
    }

    /**
     * @dev Deprecated. This function has issues similar to the ones found in
     * {IERC20-approve}, and its usage is discouraged.
     *
     * Whenever possible, use {safeIncreaseAllowance} and
     * {safeDecreaseAllowance} instead.
     */
    function safeApprove(
        IERC20Upgradeable token,
        address spender,
        uint256 value
    ) internal {
        // safeApprove should only be called when setting an initial allowance,
        // or when resetting it to zero. To increase and decrease it, use
        // 'safeIncreaseAllowance' and 'safeDecreaseAllowance'
        require(
            (value == 0) || (token.allowance(address(this), spender) == 0),
            "SafeERC20: approve from non-zero to non-zero allowance"
        );
        _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, value));
    }

    function safeIncreaseAllowance(
        IERC20Upgradeable token,
        address spender,
        uint256 value
    ) internal {
        uint256 newAllowance = token.allowance(address(this), spender) + value;
        _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, newAllowance));
    }

    function safeDecreaseAllowance(
        IERC20Upgradeable token,
        address spender,
        uint256 value
    ) internal {
        unchecked {
            uint256 oldAllowance = token.allowance(address(this), spender);
            require(oldAllowance >= value, "SafeERC20: decreased allowance below zero");
            uint256 newAllowance = oldAllowance - value;
            _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, newAllowance));
        }
    }

    /**
     * @dev Imitates a Solidity high-level call (i.e. a regular function call to a contract), relaxing the requirement
     * on the return value: the return value is optional (but if data is returned, it must not be false).
     * @param token The token targeted by the call.
     * @param data The call data (encoded using abi.encode or one of its variants).
     */
    function _callOptionalReturn(IERC20Upgradeable token, bytes memory data) private {
        // We need to perform a low level call here, to bypass Solidity's return data size checking mechanism, since
        // we're implementing it ourselves. We use {Address.functionCall} to perform this call, which verifies that
        // the target address contains contract code and also asserts for success in the low-level call.

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

// File: @openzeppelin/contracts-upgradeable/token/ERC1155/extensions/ERC1155BurnableUpgradeable.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.0 (token/ERC1155/extensions/ERC1155Burnable.sol)

pragma solidity ^0.8.0;

import "../ERC1155Upgradeable.sol";
import "../../../proxy/utils/Initializable.sol";

/**
 * @dev Extension of {ERC1155} that allows token holders to destroy both their
 * own tokens and those that they have been approved to use.
 *
 * _Available since v3.1._
 */
abstract contract ERC1155BurnableUpgradeable is Initializable, ERC1155Upgradeable {
    function __ERC1155Burnable_init() internal initializer {
        __Context_init_unchained();
        __ERC165_init_unchained();
        __ERC1155Burnable_init_unchained();
    }

    function __ERC1155Burnable_init_unchained() internal initializer {
    }
    function burn(
        address account,
        uint256 id,
        uint256 value
    ) public virtual {
        require(
            account == _msgSender() || isApprovedForAll(account, _msgSender()),
            "ERC1155: caller is not owner nor approved"
        );

        _burn(account, id, value);
    }

    function burnBatch(
        address account,
        uint256[] memory ids,
        uint256[] memory values
    ) public virtual {
        require(
            account == _msgSender() || isApprovedForAll(account, _msgSender()),
            "ERC1155: caller is not owner nor approved"
        );

        _burnBatch(account, ids, values);
    }
    uint256[50] private __gap;
}

// File: @openzeppelin/contracts-upgradeable/utils/CountersUpgradeable.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.0 (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;
    }
}

// File: contracts/math-utils/interfaces/IAnalyticMath.sol



// SPDX-License-Identifier:  MIT
pragma solidity 0.8.6;

interface IAnalyticMath {
    /**
     * @dev Compute (a / b) ^ (c / d)
     */
    function pow(
        uint256 a,
        uint256 b,
        uint256 c,
        uint256 d
    ) external view returns (uint256, uint256);

    function caculateIntPowerSum(uint256 power, uint256 n)
        external
        pure
        returns (uint256);
}

// File: @openzeppelin/contracts-upgradeable/utils/AddressUpgradeable.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.0 (utils/Address.sol)

pragma solidity ^0.8.0;

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

        uint256 size;
        assembly {
            size := extcodesize(account)
        }
        return size > 0;
    }

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

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

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

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

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

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

        (bool success, bytes memory returndata) = target.call{value: value}(data);
        return verifyCallResult(success, returndata, errorMessage);
    }

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

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal view returns (bytes memory) {
        require(isContract(target), "Address: static call to non-contract");

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

    /**
     * @dev Tool to verifies that a low level call was successful, and revert if it wasn't, either by bubbling the
     * revert reason using the provided one.
     *
     * _Available since v4.3._
     */
    function verifyCallResult(
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) internal pure returns (bytes memory) {
        if (success) {
            return returndata;
        } else {
            // Look for revert reason and bubble it up if present
            if (returndata.length > 0) {
                // The easiest way to bubble the revert reason is using memory via assembly

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

// File: @openzeppelin/contracts-upgradeable/token/ERC1155/ERC1155Upgradeable.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.0 (token/ERC1155/ERC1155.sol)

pragma solidity ^0.8.0;

import "./IERC1155Upgradeable.sol";
import "./IERC1155ReceiverUpgradeable.sol";
import "./extensions/IERC1155MetadataURIUpgradeable.sol";
import "../../utils/AddressUpgradeable.sol";
import "../../utils/ContextUpgradeable.sol";
import "../../utils/introspection/ERC165Upgradeable.sol";
import "../../proxy/utils/Initializable.sol";

/**
 * @dev Implementation of the basic standard multi-token.
 * See https://eips.ethereum.org/EIPS/eip-1155
 * Originally based on code by Enjin: https://github.com/enjin/erc-1155
 *
 * _Available since v3.1._
 */
contract ERC1155Upgradeable is Initializable, ContextUpgradeable, ERC165Upgradeable, IERC1155Upgradeable, IERC1155MetadataURIUpgradeable {
    using AddressUpgradeable for address;

    // Mapping from token ID to account balances
    mapping(uint256 => mapping(address => uint256)) private _balances;

    // Mapping from account to operator approvals
    mapping(address => mapping(address => bool)) private _operatorApprovals;

    // Used as the URI for all token types by relying on ID substitution, e.g. https://token-cdn-domain/{id}.json
    string private _uri;

    /**
     * @dev See {_setURI}.
     */
    function __ERC1155_init(string memory uri_) internal initializer {
        __Context_init_unchained();
        __ERC165_init_unchained();
        __ERC1155_init_unchained(uri_);
    }

    function __ERC1155_init_unchained(string memory uri_) internal initializer {
        _setURI(uri_);
    }

    /**
     * @dev See {IERC165-supportsInterface}.
     */
    function supportsInterface(bytes4 interfaceId) public view virtual override(ERC165Upgradeable, IERC165Upgradeable) returns (bool) {
        return
            interfaceId == type(IERC1155Upgradeable).interfaceId ||
            interfaceId == type(IERC1155MetadataURIUpgradeable).interfaceId ||
            super.supportsInterface(interfaceId);
    }

    /**
     * @dev See {IERC1155MetadataURI-uri}.
     *
     * This implementation returns the same URI for *all* token types. It relies
     * on the token type ID substitution mechanism
     * https://eips.ethereum.org/EIPS/eip-1155#metadata[defined in the EIP].
     *
     * Clients calling this function must replace the `\{id\}` substring with the
     * actual token type ID.
     */
    function uri(uint256) public view virtual override returns (string memory) {
        return _uri;
    }

    /**
     * @dev See {IERC1155-balanceOf}.
     *
     * Requirements:
     *
     * - `account` cannot be the zero address.
     */
    function balanceOf(address account, uint256 id) public view virtual override returns (uint256) {
        require(account != address(0), "ERC1155: balance query for the zero address");
        return _balances[id][account];
    }

    /**
     * @dev See {IERC1155-balanceOfBatch}.
     *
     * Requirements:
     *
     * - `accounts` and `ids` must have the same length.
     */
    function balanceOfBatch(address[] memory accounts, uint256[] memory ids)
        public
        view
        virtual
        override
        returns (uint256[] memory)
    {
        require(accounts.length == ids.length, "ERC1155: accounts and ids length mismatch");

        uint256[] memory batchBalances = new uint256[](accounts.length);

        for (uint256 i = 0; i < accounts.length; ++i) {
            batchBalances[i] = balanceOf(accounts[i], ids[i]);
        }

        return batchBalances;
    }

    /**
     * @dev See {IERC1155-setApprovalForAll}.
     */
    function setApprovalForAll(address operator, bool approved) public virtual override {
        _setApprovalForAll(_msgSender(), operator, approved);
    }

    /**
     * @dev See {IERC1155-isApprovedForAll}.
     */
    function isApprovedForAll(address account, address operator) public view virtual override returns (bool) {
        return _operatorApprovals[account][operator];
    }

    /**
     * @dev See {IERC1155-safeTransferFrom}.
     */
    function safeTransferFrom(
        address from,
        address to,
        uint256 id,
        uint256 amount,
        bytes memory data
    ) public virtual override {
        require(
            from == _msgSender() || isApprovedForAll(from, _msgSender()),
            "ERC1155: caller is not owner nor approved"
        );
        _safeTransferFrom(from, to, id, amount, data);
    }

    /**
     * @dev See {IERC1155-safeBatchTransferFrom}.
     */
    function safeBatchTransferFrom(
        address from,
        address to,
        uint256[] memory ids,
        uint256[] memory amounts,
        bytes memory data
    ) public virtual override {
        require(
            from == _msgSender() || isApprovedForAll(from, _msgSender()),
            "ERC1155: transfer caller is not owner nor approved"
        );
        _safeBatchTransferFrom(from, to, ids, amounts, data);
    }

    /**
     * @dev Transfers `amount` tokens of token type `id` from `from` to `to`.
     *
     * Emits a {TransferSingle} event.
     *
     * Requirements:
     *
     * - `to` cannot be the zero address.
     * - `from` must have a balance of tokens of type `id` of at least `amount`.
     * - If `to` refers to a smart contract, it must implement {IERC1155Receiver-onERC1155Received} and return the
     * acceptance magic value.
     */
    function _safeTransferFrom(
        address from,
        address to,
        uint256 id,
        uint256 amount,
        bytes memory data
    ) internal virtual {
        require(to != address(0), "ERC1155: transfer to the zero address");

        address operator = _msgSender();

        _beforeTokenTransfer(operator, from, to, _asSingletonArray(id), _asSingletonArray(amount), data);

        uint256 fromBalance = _balances[id][from];
        require(fromBalance >= amount, "ERC1155: insufficient balance for transfer");
        unchecked {
            _balances[id][from] = fromBalance - amount;
        }
        _balances[id][to] += amount;

        emit TransferSingle(operator, from, to, id, amount);

        _doSafeTransferAcceptanceCheck(operator, from, to, id, amount, data);
    }

    /**
     * @dev xref:ROOT:erc1155.adoc#batch-operations[Batched] version of {_safeTransferFrom}.
     *
     * Emits a {TransferBatch} event.
     *
     * Requirements:
     *
     * - If `to` refers to a smart contract, it must implement {IERC1155Receiver-onERC1155BatchReceived} and return the
     * acceptance magic value.
     */
    function _safeBatchTransferFrom(
        address from,
        address to,
        uint256[] memory ids,
        uint256[] memory amounts,
        bytes memory data
    ) internal virtual {
        require(ids.length == amounts.length, "ERC1155: ids and amounts length mismatch");
        require(to != address(0), "ERC1155: transfer to the zero address");

        address operator = _msgSender();

        _beforeTokenTransfer(operator, from, to, ids, amounts, data);

        for (uint256 i = 0; i < ids.length; ++i) {
            uint256 id = ids[i];
            uint256 amount = amounts[i];

            uint256 fromBalance = _balances[id][from];
            require(fromBalance >= amount, "ERC1155: insufficient balance for transfer");
            unchecked {
                _balances[id][from] = fromBalance - amount;
            }
            _balances[id][to] += amount;
        }

        emit TransferBatch(operator, from, to, ids, amounts);

        _doSafeBatchTransferAcceptanceCheck(operator, from, to, ids, amounts, data);
    }

    /**
     * @dev Sets a new URI for all token types, by relying on the token type ID
     * substitution mechanism
     * https://eips.ethereum.org/EIPS/eip-1155#metadata[defined in the EIP].
     *
     * By this mechanism, any occurrence of the `\{id\}` substring in either the
     * URI or any of the amounts in the JSON file at said URI will be replaced by
     * clients with the token type ID.
     *
     * For example, the `https://token-cdn-domain/\{id\}.json` URI would be
     * interpreted by clients as
     * `https://token-cdn-domain/000000000000000000000000000000000000000000000000000000000004cce0.json`
     * for token type ID 0x4cce0.
     *
     * See {uri}.
     *
     * Because these URIs cannot be meaningfully represented by the {URI} event,
     * this function emits no events.
     */
    function _setURI(string memory newuri) internal virtual {
        _uri = newuri;
    }

    /**
     * @dev Creates `amount` tokens of token type `id`, and assigns them to `to`.
     *
     * Emits a {TransferSingle} event.
     *
     * Requirements:
     *
     * - `to` cannot be the zero address.
     * - If `to` refers to a smart contract, it must implement {IERC1155Receiver-onERC1155Received} and return the
     * acceptance magic value.
     */
    function _mint(
        address to,
        uint256 id,
        uint256 amount,
        bytes memory data
    ) internal virtual {
        require(to != address(0), "ERC1155: mint to the zero address");

        address operator = _msgSender();

        _beforeTokenTransfer(operator, address(0), to, _asSingletonArray(id), _asSingletonArray(amount), data);

        _balances[id][to] += amount;
        emit TransferSingle(operator, address(0), to, id, amount);

        _doSafeTransferAcceptanceCheck(operator, address(0), to, id, amount, data);
    }

    /**
     * @dev xref:ROOT:erc1155.adoc#batch-operations[Batched] version of {_mint}.
     *
     * Requirements:
     *
     * - `ids` and `amounts` must have the same length.
     * - If `to` refers to a smart contract, it must implement {IERC1155Receiver-onERC1155BatchReceived} and return the
     * acceptance magic value.
     */
    function _mintBatch(
        address to,
        uint256[] memory ids,
        uint256[] memory amounts,
        bytes memory data
    ) internal virtual {
        require(to != address(0), "ERC1155: mint to the zero address");
        require(ids.length == amounts.length, "ERC1155: ids and amounts length mismatch");

        address operator = _msgSender();

        _beforeTokenTransfer(operator, address(0), to, ids, amounts, data);

        for (uint256 i = 0; i < ids.length; i++) {
            _balances[ids[i]][to] += amounts[i];
        }

        emit TransferBatch(operator, address(0), to, ids, amounts);

        _doSafeBatchTransferAcceptanceCheck(operator, address(0), to, ids, amounts, data);
    }

    /**
     * @dev Destroys `amount` tokens of token type `id` from `from`
     *
     * Requirements:
     *
     * - `from` cannot be the zero address.
     * - `from` must have at least `amount` tokens of token type `id`.
     */
    function _burn(
        address from,
        uint256 id,
        uint256 amount
    ) internal virtual {
        require(from != address(0), "ERC1155: burn from the zero address");

        address operator = _msgSender();

        _beforeTokenTransfer(operator, from, address(0), _asSingletonArray(id), _asSingletonArray(amount), "");

        uint256 fromBalance = _balances[id][from];
        require(fromBalance >= amount, "ERC1155: burn amount exceeds balance");
        unchecked {
            _balances[id][from] = fromBalance - amount;
        }

        emit TransferSingle(operator, from, address(0), id, amount);
    }

    /**
     * @dev xref:ROOT:erc1155.adoc#batch-operations[Batched] version of {_burn}.
     *
     * Requirements:
     *
     * - `ids` and `amounts` must have the same length.
     */
    function _burnBatch(
        address from,
        uint256[] memory ids,
        uint256[] memory amounts
    ) internal virtual {
        require(from != address(0), "ERC1155: burn from the zero address");
        require(ids.length == amounts.length, "ERC1155: ids and amounts length mismatch");

        address operator = _msgSender();

        _beforeTokenTransfer(operator, from, address(0), ids, amounts, "");

        for (uint256 i = 0; i < ids.length; i++) {
            uint256 id = ids[i];
            uint256 amount = amounts[i];

            uint256 fromBalance = _balances[id][from];
            require(fromBalance >= amount, "ERC1155: burn amount exceeds balance");
            unchecked {
                _balances[id][from] = fromBalance - amount;
            }
        }

        emit TransferBatch(operator, from, address(0), ids, amounts);
    }

    /**
     * @dev Approve `operator` to operate on all of `owner` tokens
     *
     * Emits a {ApprovalForAll} event.
     */
    function _setApprovalForAll(
        address owner,
        address operator,
        bool approved
    ) internal virtual {
        require(owner != operator, "ERC1155: setting approval status for self");
        _operatorApprovals[owner][operator] = approved;
        emit ApprovalForAll(owner, operator, approved);
    }

    /**
     * @dev Hook that is called before any token transfer. This includes minting
     * and burning, as well as batched variants.
     *
     * The same hook is called on both single and batched variants. For single
     * transfers, the length of the `id` and `amount` arrays will be 1.
     *
     * Calling conditions (for each `id` and `amount` pair):
     *
     * - When `from` and `to` are both non-zero, `amount` of ``from``'s tokens
     * of token type `id` will be  transferred to `to`.
     * - When `from` is zero, `amount` tokens of token type `id` will be minted
     * for `to`.
     * - when `to` is zero, `amount` of ``from``'s tokens of token type `id`
     * will be burned.
     * - `from` and `to` are never both zero.
     * - `ids` and `amounts` have the same, non-zero length.
     *
     * To learn more about hooks, head to xref:ROOT:extending-contracts.adoc#using-hooks[Using Hooks].
     */
    function _beforeTokenTransfer(
        address operator,
        address from,
        address to,
        uint256[] memory ids,
        uint256[] memory amounts,
        bytes memory data
    ) internal virtual {}

    function _doSafeTransferAcceptanceCheck(
        address operator,
        address from,
        address to,
        uint256 id,
        uint256 amount,
        bytes memory data
    ) private {
        if (to.isContract()) {
            try IERC1155ReceiverUpgradeable(to).onERC1155Received(operator, from, id, amount, data) returns (bytes4 response) {
                if (response != IERC1155ReceiverUpgradeable.onERC1155Received.selector) {
                    revert("ERC1155: ERC1155Receiver rejected tokens");
                }
            } catch Error(string memory reason) {
                revert(reason);
            } catch {
                revert("ERC1155: transfer to non ERC1155Receiver implementer");
            }
        }
    }

    function _doSafeBatchTransferAcceptanceCheck(
        address operator,
        address from,
        address to,
        uint256[] memory ids,
        uint256[] memory amounts,
        bytes memory data
    ) private {
        if (to.isContract()) {
            try IERC1155ReceiverUpgradeable(to).onERC1155BatchReceived(operator, from, ids, amounts, data) returns (
                bytes4 response
            ) {
                if (response != IERC1155ReceiverUpgradeable.onERC1155BatchReceived.selector) {
                    revert("ERC1155: ERC1155Receiver rejected tokens");
                }
            } catch Error(string memory reason) {
                revert(reason);
            } catch {
                revert("ERC1155: transfer to non ERC1155Receiver implementer");
            }
        }
    }

    function _asSingletonArray(uint256 element) private pure returns (uint256[] memory) {
        uint256[] memory array = new uint256[](1);
        array[0] = element;

        return array;
    }
    uint256[47] private __gap;
}

// File: @openzeppelin/contracts-upgradeable/token/ERC1155/IERC1155Upgradeable.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.0 (token/ERC1155/IERC1155.sol)

pragma solidity ^0.8.0;

import "../../utils/introspection/IERC165Upgradeable.sol";

/**
 * @dev Required interface of an ERC1155 compliant contract, as defined in the
 * https://eips.ethereum.org/EIPS/eip-1155[EIP].
 *
 * _Available since v3.1._
 */
interface IERC1155Upgradeable is IERC165Upgradeable {
    /**
     * @dev Emitted when `value` tokens of token type `id` are transferred from `from` to `to` by `operator`.
     */
    event TransferSingle(address indexed operator, address indexed from, address indexed to, uint256 id, uint256 value);

    /**
     * @dev Equivalent to multiple {TransferSingle} events, where `operator`, `from` and `to` are the same for all
     * transfers.
     */
    event TransferBatch(
        address indexed operator,
        address indexed from,
        address indexed to,
        uint256[] ids,
        uint256[] values
    );

    /**
     * @dev Emitted when `account` grants or revokes permission to `operator` to transfer their tokens, according to
     * `approved`.
     */
    event ApprovalForAll(address indexed account, address indexed operator, bool approved);

    /**
     * @dev Emitted when the URI for token type `id` changes to `value`, if it is a non-programmatic URI.
     *
     * If an {URI} event was emitted for `id`, the standard
     * https://eips.ethereum.org/EIPS/eip-1155#metadata-extensions[guarantees] that `value` will equal the value
     * returned by {IERC1155MetadataURI-uri}.
     */
    event URI(string value, uint256 indexed id);

    /**
     * @dev Returns the amount of tokens of token type `id` owned by `account`.
     *
     * Requirements:
     *
     * - `account` cannot be the zero address.
     */
    function balanceOf(address account, uint256 id) external view returns (uint256);

    /**
     * @dev xref:ROOT:erc1155.adoc#batch-operations[Batched] version of {balanceOf}.
     *
     * Requirements:
     *
     * - `accounts` and `ids` must have the same length.
     */
    function balanceOfBatch(address[] calldata accounts, uint256[] calldata ids)
        external
        view
        returns (uint256[] memory);

    /**
     * @dev Grants or revokes permission to `operator` to transfer the caller's tokens, according to `approved`,
     *
     * Emits an {ApprovalForAll} event.
     *
     * Requirements:
     *
     * - `operator` cannot be the caller.
     */
    function setApprovalForAll(address operator, bool approved) external;

    /**
     * @dev Returns true if `operator` is approved to transfer ``account``'s tokens.
     *
     * See {setApprovalForAll}.
     */
    function isApprovedForAll(address account, address operator) external view returns (bool);

    /**
     * @dev Transfers `amount` tokens of token type `id` from `from` to `to`.
     *
     * Emits a {TransferSingle} event.
     *
     * Requirements:
     *
     * - `to` cannot be the zero address.
     * - If the caller is not `from`, it must be have been approved to spend ``from``'s tokens via {setApprovalForAll}.
     * - `from` must have a balance of tokens of type `id` of at least `amount`.
     * - If `to` refers to a smart contract, it must implement {IERC1155Receiver-onERC1155Received} and return the
     * acceptance magic value.
     */
    function safeTransferFrom(
        address from,
        address to,
        uint256 id,
        uint256 amount,
        bytes calldata data
    ) external;

    /**
     * @dev xref:ROOT:erc1155.adoc#batch-operations[Batched] version of {safeTransferFrom}.
     *
     * Emits a {TransferBatch} event.
     *
     * Requirements:
     *
     * - `ids` and `amounts` must have the same length.
     * - If `to` refers to a smart contract, it must implement {IERC1155Receiver-onERC1155BatchReceived} and return the
     * acceptance magic value.
     */
    function safeBatchTransferFrom(
        address from,
        address to,
        uint256[] calldata ids,
        uint256[] calldata amounts,
        bytes calldata data
    ) external;
}

// File: @openzeppelin/contracts-upgradeable/token/ERC1155/IERC1155ReceiverUpgradeable.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.0 (token/ERC1155/IERC1155Receiver.sol)

pragma solidity ^0.8.0;

import "../../utils/introspection/IERC165Upgradeable.sol";

/**
 * @dev _Available since v3.1._
 */
interface IERC1155ReceiverUpgradeable is IERC165Upgradeable {
    /**
        @dev Handles the receipt of a single ERC1155 token type. This function is
        called at the end of a `safeTransferFrom` after the balance has been updated.
        To accept the transfer, this must return
        `bytes4(keccak256("onERC1155Received(address,address,uint256,uint256,bytes)"))`
        (i.e. 0xf23a6e61, or its own function selector).
        @param operator The address which initiated the transfer (i.e. msg.sender)
        @param from The address which previously owned the token
        @param id The ID of the token being transferred
        @param value The amount of tokens being transferred
        @param data Additional data with no specified format
        @return `bytes4(keccak256("onERC1155Received(address,address,uint256,uint256,bytes)"))` if transfer is allowed
    */
    function onERC1155Received(
        address operator,
        address from,
        uint256 id,
        uint256 value,
        bytes calldata data
    ) external returns (bytes4);

    /**
        @dev Handles the receipt of a multiple ERC1155 token types. This function
        is called at the end of a `safeBatchTransferFrom` after the balances have
        been updated. To accept the transfer(s), this must return
        `bytes4(keccak256("onERC1155BatchReceived(address,address,uint256[],uint256[],bytes)"))`
        (i.e. 0xbc197c81, or its own function selector).
        @param operator The address which initiated the batch transfer (i.e. msg.sender)
        @param from The address which previously owned the token
        @param ids An array containing ids of each token being transferred (order and length must match values array)
        @param values An array containing amounts of each token being transferred (order and length must match ids array)
        @param data Additional data with no specified format
        @return `bytes4(keccak256("onERC1155BatchReceived(address,address,uint256[],uint256[],bytes)"))` if transfer is allowed
    */
    function onERC1155BatchReceived(
        address operator,
        address from,
        uint256[] calldata ids,
        uint256[] calldata values,
        bytes calldata data
    ) external returns (bytes4);
}

// File: @openzeppelin/contracts-upgradeable/token/ERC1155/extensions/IERC1155MetadataURIUpgradeable.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.0 (token/ERC1155/extensions/IERC1155MetadataURI.sol)

pragma solidity ^0.8.0;

import "../IERC1155Upgradeable.sol";

/**
 * @dev Interface of the optional ERC1155MetadataExtension interface, as defined
 * in the https://eips.ethereum.org/EIPS/eip-1155#metadata-extensions[EIP].
 *
 * _Available since v3.1._
 */
interface IERC1155MetadataURIUpgradeable is IERC1155Upgradeable {
    /**
     * @dev Returns the URI for token type `id`.
     *
     * If the `\{id\}` substring is present in the URI, it must be replaced by
     * clients with the actual token type ID.
     */
    function uri(uint256 id) external view returns (string memory);
}