// SPDX-License-Identifier: MIT


pragma solidity =0.7.6;


library Strings {
  // via https://github.com/oraclize/ethereum-api/blob/master/oraclizeAPI_0.5.sol
  function strConcat(string memory _a, string memory _b, string memory _c, string memory _d, string memory _e) internal pure returns (string memory) {
    bytes memory _ba = bytes(_a);
    bytes memory _bb = bytes(_b);
    bytes memory _bc = bytes(_c);
    bytes memory _bd = bytes(_d);
    bytes memory _be = bytes(_e);
    string memory abcde = new string(_ba.length + _bb.length + _bc.length + _bd.length + _be.length);
    bytes memory babcde = bytes(abcde);
    uint k = 0;
    for (uint i = 0; i < _ba.length; i++) babcde[k++] = _ba[i];
    for (uint i = 0; i < _bb.length; i++) babcde[k++] = _bb[i];
    for (uint i = 0; i < _bc.length; i++) babcde[k++] = _bc[i];
    for (uint i = 0; i < _bd.length; i++) babcde[k++] = _bd[i];
    for (uint i = 0; i < _be.length; i++) babcde[k++] = _be[i];
    return string(babcde);
  }

  function strConcat(string memory _a, string memory _b, string memory _c, string memory _d) internal pure returns (string memory) {
    return strConcat(_a, _b, _c, _d, "");
  }

  function strConcat(string memory _a, string memory _b, string memory _c) internal pure returns (string memory) {
    return strConcat(_a, _b, _c, "", "");
  }

  function strConcat(string memory _a, string memory _b) internal pure returns (string memory) {
    return strConcat(_a, _b, "", "", "");
  }

  function uint2str(uint _i) internal pure returns (string memory _uintAsString) {
    if (_i == 0) {
      return "0";
    }
    uint j = _i;
    uint len;
    while (j != 0) {
      len++;
      j /= 10;
    }
    bytes memory bstr = new bytes(len);
    uint k = len - 1;
    while (_i != 0) {
      bstr[k--] = byte(uint8(48 + _i % 10));
      _i /= 10;
    }
    return string(bstr);
  }

  function fromAddress(address addr) internal pure returns(string memory) {
    bytes20 addrBytes = bytes20(addr);
    bytes16 hexAlphabet = "0123456789abcdef";
    bytes memory result = new bytes(42);
    result[0] = '0';
    result[1] = 'x';
    for (uint i = 0; i < 20; i++) {
      result[i * 2 + 2] = hexAlphabet[uint8(addrBytes[i] >> 4)];
      result[i * 2 + 3] = hexAlphabet[uint8(addrBytes[i] & 0x0f)];
    }
    return string(result);
  }
}

/**
 * @dev Wrappers over Solidity's arithmetic operations with added overflow
 * checks.
 *
 * Arithmetic operations in Solidity wrap on overflow. This can easily result
 * in bugs, because programmers usually assume that an overflow raises an
 * error, which is the standard behavior in high level programming languages.
 * `SafeMath` restores this intuition by reverting the transaction when an
 * operation overflows.
 *
 * Using this library instead of the unchecked operations eliminates an entire
 * class of bugs, so it's recommended to use it always.
 */
library SafeMath {
    /**
     * @dev Returns the addition of two unsigned integers, with an overflow flag.
     *
     * _Available since v3.4._
     */
    function tryAdd(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        uint256 c = a + b;
        if (c < a) return (false, 0);
        return (true, c);
    }

    /**
     * @dev Returns the substraction of two unsigned integers, with an overflow flag.
     *
     * _Available since v3.4._
     */
    function trySub(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        if (b > a) return (false, 0);
        return (true, a - b);
    }

    /**
     * @dev Returns the multiplication of two unsigned integers, with an overflow flag.
     *
     * _Available since v3.4._
     */
    function tryMul(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        // Gas optimization: this is cheaper than requiring 'a' not being zero, but the
        // benefit is lost if 'b' is also tested.
        // See: https://github.com/OpenZeppelin/openzeppelin-contracts/pull/522
        if (a == 0) return (true, 0);
        uint256 c = a * b;
        if (c / a != b) return (false, 0);
        return (true, c);
    }

    /**
     * @dev Returns the division of two unsigned integers, with a division by zero flag.
     *
     * _Available since v3.4._
     */
    function tryDiv(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        if (b == 0) return (false, 0);
        return (true, a / b);
    }

    /**
     * @dev Returns the remainder of dividing two unsigned integers, with a division by zero flag.
     *
     * _Available since v3.4._
     */
    function tryMod(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        if (b == 0) return (false, 0);
        return (true, a % b);
    }

    /**
     * @dev Returns the addition of two unsigned integers, reverting on
     * overflow.
     *
     * Counterpart to Solidity's `+` operator.
     *
     * Requirements:
     *
     * - Addition cannot overflow.
     */
    function add(uint256 a, uint256 b) internal pure returns (uint256) {
        uint256 c = a + b;
        require(c >= a, "SafeMath: addition overflow");
        return c;
    }

    /**
     * @dev Returns the subtraction of two unsigned integers, reverting on
     * overflow (when the result is negative).
     *
     * Counterpart to Solidity's `-` operator.
     *
     * Requirements:
     *
     * - Subtraction cannot overflow.
     */
    function sub(uint256 a, uint256 b) internal pure returns (uint256) {
        require(b <= a, "SafeMath: subtraction overflow");
        return a - b;
    }

    /**
     * @dev Returns the multiplication of two unsigned integers, reverting on
     * overflow.
     *
     * Counterpart to Solidity's `*` operator.
     *
     * Requirements:
     *
     * - Multiplication cannot overflow.
     */
    function mul(uint256 a, uint256 b) internal pure returns (uint256) {
        if (a == 0) return 0;
        uint256 c = a * b;
        require(c / a == b, "SafeMath: multiplication overflow");
        return c;
    }

    /**
     * @dev Returns the integer division of two unsigned integers, reverting on
     * division by zero. The result is rounded towards zero.
     *
     * Counterpart to Solidity's `/` operator. Note: this function uses a
     * `revert` opcode (which leaves remaining gas untouched) while Solidity
     * uses an invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function div(uint256 a, uint256 b) internal pure returns (uint256) {
        require(b > 0, "SafeMath: division by zero");
        return a / b;
    }

    /**
     * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
     * reverting when dividing by zero.
     *
     * Counterpart to Solidity's `%` operator. This function uses a `revert`
     * opcode (which leaves remaining gas untouched) while Solidity uses an
     * invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function mod(uint256 a, uint256 b) internal pure returns (uint256) {
        require(b > 0, "SafeMath: modulo by zero");
        return a % b;
    }

    /**
     * @dev Returns the subtraction of two unsigned integers, reverting with custom message on
     * overflow (when the result is negative).
     *
     * CAUTION: This function is deprecated because it requires allocating memory for the error
     * message unnecessarily. For custom revert reasons use {trySub}.
     *
     * Counterpart to Solidity's `-` operator.
     *
     * Requirements:
     *
     * - Subtraction cannot overflow.
     */
    function sub(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
        require(b <= a, errorMessage);
        return a - b;
    }

    /**
     * @dev Returns the integer division of two unsigned integers, reverting with custom message on
     * division by zero. The result is rounded towards zero.
     *
     * CAUTION: This function is deprecated because it requires allocating memory for the error
     * message unnecessarily. For custom revert reasons use {tryDiv}.
     *
     * Counterpart to Solidity's `/` operator. Note: this function uses a
     * `revert` opcode (which leaves remaining gas untouched) while Solidity
     * uses an invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function div(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
        require(b > 0, errorMessage);
        return a / b;
    }

    /**
     * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
     * reverting with custom message when dividing by zero.
     *
     * CAUTION: This function is deprecated because it requires allocating memory for the error
     * message unnecessarily. For custom revert reasons use {tryMod}.
     *
     * Counterpart to Solidity's `%` operator. This function uses a `revert`
     * opcode (which leaves remaining gas untouched) while Solidity uses an
     * invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function mod(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
        require(b > 0, errorMessage);
        return a % b;
    }
}

library Address {
    /**
     * @dev Returns true if `account` is a contract.
     *
     * [IMPORTANT]
     * ====
     * It is unsafe to assume that an address for which this function returns
     * false is an externally-owned account (EOA) and not a contract.
     *
     * Among others, `isContract` will return false for the following
     * types of addresses:
     *
     *  - an externally-owned account
     *  - a contract in construction
     *  - an address where a contract will be created
     *  - an address where a contract lived, but was destroyed
     * ====
     */
    function isContract(address account) internal view returns (bool) {
        // This method relies on extcodesize, which returns 0 for contracts in
        // construction, since the code is only stored at the end of the
        // constructor execution.

        uint256 size;
        // solhint-disable-next-line no-inline-assembly
        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");

        // solhint-disable-next-line avoid-low-level-calls, avoid-call-value
        (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");

        // solhint-disable-next-line avoid-low-level-calls
        (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");

        // solhint-disable-next-line avoid-low-level-calls
        (bool success, bytes memory returndata) = target.staticcall(data);
        return _verifyCallResult(success, returndata, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a delegate call.
     *
     * _Available since v3.4._
     */
    function functionDelegateCall(address target, bytes memory data) internal returns (bytes memory) {
        return functionDelegateCall(target, data, "Address: low-level delegate call failed");
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a delegate call.
     *
     * _Available since v3.4._
     */
    function functionDelegateCall(address target, bytes memory data, string memory errorMessage) internal returns (bytes memory) {
        require(isContract(target), "Address: delegate call to non-contract");

        // solhint-disable-next-line avoid-low-level-calls
        (bool success, bytes memory returndata) = target.delegatecall(data);
        return _verifyCallResult(success, returndata, errorMessage);
    }

    function _verifyCallResult(bool success, bytes memory returndata, string memory errorMessage) private 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

                // solhint-disable-next-line no-inline-assembly
                assembly {
                    let returndata_size := mload(returndata)
                    revert(add(32, returndata), returndata_size)
                }
            } else {
                revert(errorMessage);
            }
        }
    }
}

/**
 * @dev Library used to query support of an interface declared via {IERC165}.
 *
 * Note that these functions return the actual result of the query: they do not
 * `revert` if an interface is not supported. It is up to the caller to decide
 * what to do in these cases.
 */
library ERC165Checker {
    // As per the EIP-165 spec, no interface should ever match 0xffffffff
    bytes4 private constant _INTERFACE_ID_INVALID = 0xffffffff;

    /*
     * bytes4(keccak256('supportsInterface(bytes4)')) == 0x01ffc9a7
     */
    bytes4 private constant _INTERFACE_ID_ERC165 = 0x01ffc9a7;

    /**
     * @dev Returns true if `account` supports the {IERC165} interface,
     */
    function supportsERC165(address account) internal view returns (bool) {
        // Any contract that implements ERC165 must explicitly indicate support of
        // InterfaceId_ERC165 and explicitly indicate non-support of InterfaceId_Invalid
        return _supportsERC165Interface(account, _INTERFACE_ID_ERC165) &&
            !_supportsERC165Interface(account, _INTERFACE_ID_INVALID);
    }

    /**
     * @dev Returns true if `account` supports the interface defined by
     * `interfaceId`. Support for {IERC165} itself is queried automatically.
     *
     * See {IERC165-supportsInterface}.
     */
    function supportsInterface(address account, bytes4 interfaceId) internal view returns (bool) {
        // query support of both ERC165 as per the spec and support of _interfaceId
        return supportsERC165(account) &&
            _supportsERC165Interface(account, interfaceId);
    }

    /**
     * @dev Returns a boolean array where each value corresponds to the
     * interfaces passed in and whether they're supported or not. This allows
     * you to batch check interfaces for a contract where your expectation
     * is that some interfaces may not be supported.
     *
     * See {IERC165-supportsInterface}.
     *
     * _Available since v3.4._
     */
    function getSupportedInterfaces(address account, bytes4[] memory interfaceIds) internal view returns (bool[] memory) {
        // an array of booleans corresponding to interfaceIds and whether they're supported or not
        bool[] memory interfaceIdsSupported = new bool[](interfaceIds.length);

        // query support of ERC165 itself
        if (supportsERC165(account)) {
            // query support of each interface in interfaceIds
            for (uint256 i = 0; i < interfaceIds.length; i++) {
                interfaceIdsSupported[i] = _supportsERC165Interface(account, interfaceIds[i]);
            }
        }

        return interfaceIdsSupported;
    }

    /**
     * @dev Returns true if `account` supports all the interfaces defined in
     * `interfaceIds`. Support for {IERC165} itself is queried automatically.
     *
     * Batch-querying can lead to gas savings by skipping repeated checks for
     * {IERC165} support.
     *
     * See {IERC165-supportsInterface}.
     */
    function supportsAllInterfaces(address account, bytes4[] memory interfaceIds) internal view returns (bool) {
        // query support of ERC165 itself
        if (!supportsERC165(account)) {
            return false;
        }

        // query support of each interface in _interfaceIds
        for (uint256 i = 0; i < interfaceIds.length; i++) {
            if (!_supportsERC165Interface(account, interfaceIds[i])) {
                return false;
            }
        }

        // all interfaces supported
        return true;
    }

    /**
     * @notice Query if a contract implements an interface, does not check ERC165 support
     * @param account The address of the contract to query for support of an interface
     * @param interfaceId The interface identifier, as specified in ERC-165
     * @return true if the contract at account indicates support of the interface with
     * identifier interfaceId, false otherwise
     * @dev Assumes that account contains a contract that supports ERC165, otherwise
     * the behavior of this method is undefined. This precondition can be checked
     * with {supportsERC165}.
     * Interface identification is specified in ERC-165.
     */
    function _supportsERC165Interface(address account, bytes4 interfaceId) private view returns (bool) {
        // success determines whether the staticcall succeeded and result determines
        // whether the contract at account indicates support of _interfaceId
        (bool success, bool result) = _callERC165SupportsInterface(account, interfaceId);

        return (success && result);
    }

    /**
     * @notice Calls the function with selector 0x01ffc9a7 (ERC165) and suppresses throw
     * @param account The address of the contract to query for support of an interface
     * @param interfaceId The interface identifier, as specified in ERC-165
     * @return success true if the STATICCALL succeeded, false otherwise
     * @return result true if the STATICCALL succeeded and the contract at account
     * indicates support of the interface with identifier interfaceId, false otherwise
     */
    function _callERC165SupportsInterface(address account, bytes4 interfaceId)
        private
        view
        returns (bool, bool)
    {
        bytes memory encodedParams = abi.encodeWithSelector(_INTERFACE_ID_ERC165, interfaceId);
        (bool success, bytes memory result) = account.staticcall{ gas: 30000 }(encodedParams);
        if (result.length < 32) return (false, false);
        return (success, abi.decode(result, (bool)));
    }
}


/*
 * @dev Provides information about the current execution context, including the
 * sender of the transaction and its data. While these are generally available
 * via msg.sender and msg.data, they should not be accessed in such a direct
 * manner, since when dealing with GSN meta-transactions the account sending and
 * paying for execution may not be the actual sender (as far as an application
 * is concerned).
 *
 * This contract is only required for intermediate, library-like contracts.
 */
abstract contract Context {
    function _msgSender() internal view virtual returns (address payable) {
        return msg.sender;
    }

    function _msgData() internal view virtual returns (bytes memory) {
        this; // silence state mutability warning without generating bytecode - see https://github.com/ethereum/solidity/issues/2691
        return msg.data;
    }
}

/**
 * @dev Contract module which provides a basic access control mechanism, where
 * there is an account (an owner) that can be granted exclusive access to
 * specific functions.
 *
 * By default, the owner account will be the one that deploys the contract. This
 * can later be changed with {transferOwnership}.
 *
 * This module is used through inheritance. It will make available the modifier
 * `onlyOwner`, which can be applied to your functions to restrict their use to
 * the owner.
 */
abstract contract Ownable is Context {
    address private _owner;

    event OwnershipTransferred(address indexed previousOwner, address indexed newOwner);

    /**
     * @dev Initializes the contract setting the deployer as the initial owner.
     */
    constructor () internal {
        address msgSender = _msgSender();
        _owner = msgSender;
        emit OwnershipTransferred(address(0), msgSender);
    }

    /**
     * @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() == _msgSender(), "Ownable: caller is not the owner");
        _;
    }

    /**
     * @dev Leaves the contract without owner. It will not be possible to call
     * `onlyOwner` functions anymore. Can only be called by the current owner.
     *
     * NOTE: Renouncing ownership will leave the contract without an owner,
     * thereby removing any functionality that is only available to the owner.
     */
    function renounceOwnership() public virtual onlyOwner {
        emit OwnershipTransferred(_owner, address(0));
        _owner = 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");
        emit OwnershipTransferred(_owner, newOwner);
        _owner = newOwner;
    }
}

/**
 * @dev Contract module that helps prevent reentrant calls to a function.
 *
 * Inheriting from `ReentrancyGuard` will make the {nonReentrant} modifier
 * available, which can be applied to functions to make sure there are no nested
 * (reentrant) calls to them.
 *
 * Note that because there is a single `nonReentrant` guard, functions marked as
 * `nonReentrant` may not call one another. This can be worked around by making
 * those functions `private`, and then adding `external` `nonReentrant` entry
 * points to them.
 *
 * TIP: If you would like to learn more about reentrancy and alternative ways
 * to protect against it, check out our blog post
 * https://blog.openzeppelin.com/reentrancy-after-istanbul/[Reentrancy After Istanbul].
 */
abstract contract ReentrancyGuard {
    // Booleans are more expensive than uint256 or any type that takes up a full
    // word because each write operation emits an extra SLOAD to first read the
    // slot's contents, replace the bits taken up by the boolean, and then write
    // back. This is the compiler's defense against contract upgrades and
    // pointer aliasing, and it cannot be disabled.

    // The values being non-zero value makes deployment a bit more expensive,
    // but in exchange the refund on every call to nonReentrant will be lower in
    // amount. Since refunds are capped to a percentage of the total
    // transaction's gas, it is best to keep them low in cases like this one, to
    // increase the likelihood of the full refund coming into effect.
    uint256 private constant _NOT_ENTERED = 1;
    uint256 private constant _ENTERED = 2;

    uint256 private _status;

    constructor () internal {
        _status = _NOT_ENTERED;
    }

    /**
     * @dev Prevents a contract from calling itself, directly or indirectly.
     * Calling a `nonReentrant` function from another `nonReentrant`
     * function is not supported. It is possible to prevent this from happening
     * by making the `nonReentrant` function external, and make it call a
     * `private` function that does the actual work.
     */
    modifier nonReentrant() {
        // On the first call to nonReentrant, _notEntered will be true
        require(_status != _ENTERED, "ReentrancyGuard: reentrant call");

        // Any calls to nonReentrant after this point will fail
        _status = _ENTERED;

        _;

        // By storing the original value once again, a refund is triggered (see
        // https://eips.ethereum.org/EIPS/eip-2200)
        _status = _NOT_ENTERED;
    }
}

/**
 * @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 IERC165 {
    /**
     * @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);
}

/**
 * @dev Implementation of the {IERC165} interface.
 *
 * Contracts may inherit from this and call {_registerInterface} to declare
 * their support of an interface.
 */
abstract contract ERC165 is IERC165 {
    /*
     * bytes4(keccak256('supportsInterface(bytes4)')) == 0x01ffc9a7
     */
    bytes4 private constant _INTERFACE_ID_ERC165 = 0x01ffc9a7;

    /**
     * @dev Mapping of interface ids to whether or not it's supported.
     */
    mapping(bytes4 => bool) private _supportedInterfaces;

    constructor () internal {
        // Derived contracts need only register support for their own interfaces,
        // we register support for ERC165 itself here
        _registerInterface(_INTERFACE_ID_ERC165);
    }

    /**
     * @dev See {IERC165-supportsInterface}.
     *
     * Time complexity O(1), guaranteed to always use less than 30 000 gas.
     */
    function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
        return _supportedInterfaces[interfaceId];
    }

    /**
     * @dev Registers the contract as an implementer of the interface defined by
     * `interfaceId`. Support of the actual ERC165 interface is automatic and
     * registering its interface id is not required.
     *
     * See {IERC165-supportsInterface}.
     *
     * Requirements:
     *
     * - `interfaceId` cannot be the ERC165 invalid interface (`0xffffffff`).
     */
    function _registerInterface(bytes4 interfaceId) internal virtual {
        require(interfaceId != 0xffffffff, "ERC165: invalid interface id");
        _supportedInterfaces[interfaceId] = true;
    }
}


/**
 * @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 IERC1155 is IERC165 {
    /**
     * @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;
}

/**
 * @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 IERC1155MetadataURI is IERC1155 {
    /**
     * @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);
}

/**
 * _Available since v3.1._
 */
interface IERC1155Receiver is IERC165 {

    /**
        @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);
}


/**
 *
 * @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 ERC1155 is Context, ERC165, IERC1155, IERC1155MetadataURI {
    using SafeMath for uint256;
    using Address 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;

    /*
     *     bytes4(keccak256('balanceOf(address,uint256)')) == 0x00fdd58e
     *     bytes4(keccak256('balanceOfBatch(address[],uint256[])')) == 0x4e1273f4
     *     bytes4(keccak256('setApprovalForAll(address,bool)')) == 0xa22cb465
     *     bytes4(keccak256('isApprovedForAll(address,address)')) == 0xe985e9c5
     *     bytes4(keccak256('safeTransferFrom(address,address,uint256,uint256,bytes)')) == 0xf242432a
     *     bytes4(keccak256('safeBatchTransferFrom(address,address,uint256[],uint256[],bytes)')) == 0x2eb2c2d6
     *
     *     => 0x00fdd58e ^ 0x4e1273f4 ^ 0xa22cb465 ^
     *        0xe985e9c5 ^ 0xf242432a ^ 0x2eb2c2d6 == 0xd9b67a26
     */
    bytes4 private constant _INTERFACE_ID_ERC1155 = 0xd9b67a26;

    /*
     *     bytes4(keccak256('uri(uint256)')) == 0x0e89341c
     */
    bytes4 private constant _INTERFACE_ID_ERC1155_METADATA_URI = 0x0e89341c;

    /**
     * @dev See {_setURI}.
     */
    constructor (string memory uri_) public {
        _setURI(uri_);

        // register the supported interfaces to conform to ERC1155 via ERC165
        _registerInterface(_INTERFACE_ID_ERC1155);

        // register the supported interfaces to conform to ERC1155MetadataURI via ERC165
        _registerInterface(_INTERFACE_ID_ERC1155_METADATA_URI);
    }

    /**
     * @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) external 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 {
        require(_msgSender() != operator, "ERC1155: setting approval status for self");

        _operatorApprovals[_msgSender()][operator] = approved;
        emit ApprovalForAll(_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(to != address(0), "ERC1155: transfer to the zero address");
        require(
            from == _msgSender() || isApprovedForAll(from, _msgSender()),
            "ERC1155: caller is not owner nor approved"
        );

        address operator = _msgSender();

        _beforeTokenTransfer(operator, from, to, _asSingletonArray(id), _asSingletonArray(amount), data);

        _balances[id][from] = _balances[id][from].sub(amount, "ERC1155: insufficient balance for transfer");
        _balances[id][to] = _balances[id][to].add(amount);

        emit TransferSingle(operator, from, to, id, amount);

        _doSafeTransferAcceptanceCheck(operator, 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(ids.length == amounts.length, "ERC1155: ids and amounts length mismatch");
        require(to != address(0), "ERC1155: transfer to the zero address");
        require(
            from == _msgSender() || isApprovedForAll(from, _msgSender()),
            "ERC1155: transfer caller is not owner nor approved"
        );

        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];

            _balances[id][from] = _balances[id][from].sub(
                amount,
                "ERC1155: insufficient balance for transfer"
            );
            _balances[id][to] = _balances[id][to].add(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 `account`.
     *
     * Emits a {TransferSingle} event.
     *
     * Requirements:
     *
     * - `account` cannot be the zero address.
     * - If `account` refers to a smart contract, it must implement {IERC1155Receiver-onERC1155Received} and return the
     * acceptance magic value.
     */
    function _mint(address account, uint256 id, uint256 amount, bytes memory data) internal virtual {
        require(account != address(0), "ERC1155: mint to the zero address");

        address operator = _msgSender();

        _beforeTokenTransfer(operator, address(0), account, _asSingletonArray(id), _asSingletonArray(amount), data);

        _balances[id][account] = _balances[id][account].add(amount);
        emit TransferSingle(operator, address(0), account, id, amount);

        _doSafeTransferAcceptanceCheck(operator, address(0), account, 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 (uint i = 0; i < ids.length; i++) {
            _balances[ids[i]][to] = amounts[i].add(_balances[ids[i]][to]);
        }

        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 `account`
     *
     * Requirements:
     *
     * - `account` cannot be the zero address.
     * - `account` must have at least `amount` tokens of token type `id`.
     */
    function _burn(address account, uint256 id, uint256 amount) internal virtual {
        require(account != address(0), "ERC1155: burn from the zero address");

        address operator = _msgSender();

        _beforeTokenTransfer(operator, account, address(0), _asSingletonArray(id), _asSingletonArray(amount), "");

        _balances[id][account] = _balances[id][account].sub(
            amount,
            "ERC1155: burn amount exceeds balance"
        );

        emit TransferSingle(operator, account, 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 account, uint256[] memory ids, uint256[] memory amounts) internal virtual {
        require(account != address(0), "ERC1155: burn from the zero address");
        require(ids.length == amounts.length, "ERC1155: ids and amounts length mismatch");

        address operator = _msgSender();

        _beforeTokenTransfer(operator, account, address(0), ids, amounts, "");

        for (uint i = 0; i < ids.length; i++) {
            _balances[ids[i]][account] = _balances[ids[i]][account].sub(
                amounts[i],
                "ERC1155: burn amount exceeds balance"
            );
        }

        emit TransferBatch(operator, account, address(0), ids, amounts);
    }

    /**
     * @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 IERC1155Receiver(to).onERC1155Received(operator, from, id, amount, data) returns (bytes4 response) {
                if (response != IERC1155Receiver(to).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 IERC1155Receiver(to).onERC1155BatchReceived(operator, from, ids, amounts, data) returns (bytes4 response) {
                if (response != IERC1155Receiver(to).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;
    }
}

contract DreamBeats is Ownable, ERC1155, ReentrancyGuard {
    using SafeMath for uint256;
    using Strings for string;
    using Address for address payable;
    
    
    // key: LPID, value: boolean lpDropped | true iff drop is live for token with LPID
    mapping (uint256 => bool) private _lpDropped;
    
    
    // key: LPID, value: totalSupply of that LP.
    mapping(uint256 => uint256) public totalSupply;

    // key: LPID, value: string that is that LPs name.
    mapping(uint256 => string) public lpName;
    
    // key: address, value: isBlacklisted
    mapping(address => bool) public lpNameBlacklist;
    
    

    // Supply restriction on lp prints, 0 indexed, so 150 per lp
    uint256 constant public MAX_DREAM_SUPPLY = 149;


    // bonding curve values
    uint256 public A = 300;
    uint256 public B = 8;
    uint256 public C = 8;
    uint256 public SIG_DIGITS = 4;

    // bit things
    uint256 BITSHIFT_AMOUNT = 8;

    // baseURI for token metadata url, override ERC1155
    string _baseURI = "https://dreambeats.io/metadata/";

    // Contract name
    string public name = "DreamBeats";
    // Contract symbol
    string public symbol = "DB";

    // contract state
    bool isPaused = true;


    constructor() ERC1155("") {}

    modifier whenNotPaused() {
        require(!isPaused, "Contract is paused, we're adjusting something, please try again in a bit!");
        _;
    }
    
    modifier whenPaused() {
        require(isPaused, "Contract is not paused.");
        _;
    }
    
    /**
     * MINTING
     */

    /**
     * @dev function to mint og lp or lp with lpID 'lpID'
     *
     * Requirements: 
     * - lpID drop must be live
     * - total supply of lpID must be less than MAX_DREAM_SUPPLY
     * - msg.value must be AT LEAST the current print price
     */
    function mint(uint256 lpID) public payable  nonReentrant whenNotPaused returns (uint256) {
        // Confirm drop is live for lpID
        
        require(_lpDropped[lpID] == true, "Drop not live");
        
        // verify totalSupply of lp is under MAX_DREAM_SUPPLY
        require(totalSupply[lpID] < MAX_DREAM_SUPPLY, "Max supply reached");

        // Get price to mint current print, verify that the value of tx has enough
        uint256 newSupply = totalSupply[lpID] + 1;

        // 0 indexed print prices
        uint256 printPrice = getPrintPrice(newSupply - 1);
        require(msg.value >= printPrice, "Insufficient funds");

        // Set Supply to newSupply
        totalSupply[lpID] = newSupply;

        if (totalSupply[lpID] == 1) {
            // The case where they are minting the og LP
            
            //Mint lpID
            _mint(msg.sender, lpID, 1, "");

            // refund extra eth sent
            _refundSender(printPrice);
            return lpID;
        }

        // compute tokenID
        uint256 tokenID = getPrintTokenIdFromLpId(lpID);

        // Mint token
        _mint(msg.sender, tokenID, 1, "");

        // Refund buyer for any extra eth sent
        _refundSender(printPrice);
        return tokenID;
    }

    /**
     * FUNCTIONS FOR ORIGINAL LP OWNERS
     */
     
    /**
     * @dev function to name lp with 'lpID' 'lpNameToSet'
     *
     * Requirements: 
     * - msg.sender must own the original LP
     * - lpNameToSet must be under 32 bytes 
     * 
     * Note: string of size 32 bytes not always equivalent to length of 32
     */
    function nameLp(uint256 lpId, string memory lpNameToSet) public whenNotPaused {
        require(!lpNameBlacklist[msg.sender], "You are blacklisted from naming.");
        require(balanceOf(msg.sender, lpId) == 1, "You don't own the og LP!");
        require(bytes(lpNameToSet).length <= 32, "Max name size is 32 bytes.");

        lpName[lpId] = lpNameToSet;
    }

    

    /**
     * PUBLIC GETTERS
     */
     
    /**
     * @dev get price for print 'printNum'
     *
     * Note: printNum == totalSupply at time of minting since we're 0 indexed
     * 
     */
    function getPrintPrice(uint256 printNum) public view returns (uint256 price) {
        uint256 decimals = 10 ** SIG_DIGITS;

        // A + Bx + Cx^2
        price = A.add(B.mul(printNum)).add(C.mul(printNum ** 2));

        // convert to wei
        price = price.mul(1 ether).div(decimals);
    }
    
    /**
     * @dev get totalSupply of lp with 'lpID'
     *
     */
    function lpPrintsSupply(uint256 lpID) public view returns (uint256) {
        return totalSupply[lpID];
    }

    /**
     * @dev get print tokenID for original lp with id lpID
     * 
     * Note: overlap possible bc of the small shift we use but we're not going to drop that many.
     *
     */
    function getPrintTokenIdFromLpId(uint256 lpID) public view returns (uint256) {
        return (lpID + 1) << BITSHIFT_AMOUNT;
    }
    
    /**
     * @dev get original lp lpID for print tokenID
     * 
     * Note: overlap possible bc of the small shift we use but we're not going to drop that many.
     *
     */
    function getLpIdfromPrintTokenId(uint256 printID) public view returns (uint256) {
        return (printID >> BITSHIFT_AMOUNT) - 1;
    }
        
    /**
     * @dev is token with tokenID an original Lp?
     * 
     * Note: the two ranges can overlap but we're not going to drop that many.
     *
     */
    function isOriginalLp(uint256 tokenID) public pure returns (bool) {
        // 256 is 1 << 8, smallest possible id a token can be at until overflow which we will never hit
        // imagine doing over 256 of these clips we would die
        return (tokenID < 256);
    }

    /**
     * @dev get URI for token '_id
     * 
     */
    function uri(uint256 _id) external override view returns (string memory) {
        
        if (!isOriginalLp(_id)) {
            require(totalSupply[getLpIdfromPrintTokenId(_id)] > 0, "URI query for nonexistent token");
        } else {
            require(totalSupply[_id] > 0, "URI query for nonexistent token");
        }
        
        return Strings.strConcat(
            _baseURI,
            Strings.uint2str(_id)
        );
    }



    /**
     * INTERNAL UTILITY FUNCTIONS
     */
     
    
    /**
     * @dev refund msg.value in excess of 'printPrice'
     * 
     */
    function _refundSender(uint256 printPrice) internal {
        if (msg.value.sub(printPrice) > 0) {
            msg.sender.sendValue(msg.value.sub(printPrice));
        }
    }


    /**
     * OWNER UTILITY FUNCTIONS
     */
    
    
    /**
     * @dev adjust bonding curve, set new A, B, C, and SIG_DIGITS
     * 
     */
    function adjustBondingCurve(uint256 a, uint256 b, uint256 c, uint256 sigdigits) external onlyOwner whenPaused {
        (A, B, C, SIG_DIGITS) = (a, b, c, sigdigits);
    }
    
    /**
     * @dev set _baseURI to newBaseURI
     * 
     */
    function updateBaseURI(string memory newBaseURI) external onlyOwner whenPaused {
        _baseURI = newBaseURI;
    }

    /**
     * @dev drop lp with lpIDs in lplist
     * 
     * require: none of the lpIDs can already have been dropped     
     * 
     */
    function dropLP(uint[] memory lpList) external onlyOwner whenPaused {
        for (uint i=0; i<lpList.length; i++) {
            require(!_lpDropped[lpList[i]], "Drop is already live.");
            _lpDropped[lpList[i]] = true;
        }
    }
    
    /**
     * @dev drop lp with lpIDs in lplist and mint the original LP
     * 
     * require: none of the lpIDs can already have been dropped     
     * 
     */
    function dropLPAndMint(uint[] memory lpList) external onlyOwner whenPaused {
        for (uint i=0; i<lpList.length; i++) {
            require(!_lpDropped[lpList[i]], "Drop is already live.");
            
            _lpDropped[lpList[i]] = true;
            
            // set totalSupply to 1
            totalSupply[lpList[i]] = 1;

            //Mint lpID
            _mint(msg.sender, lpList[i], 1, "");
        }
    }
    
    /**
     * @dev set BITSHIFT_AMOUNT to b  
     * 
     */
    function setBitShift(uint256 b) external onlyOwner whenPaused {
        BITSHIFT_AMOUNT = b;
    
    }
    
    /**
     * @dev withdraw all funds
     * 
     */
    function withdraw() external onlyOwner nonReentrant {
        msg.sender.sendValue(address(this).balance);
    }
    
    /**
     * @dev set isPaused to pause
     * 
     * note: pausing is required before making any changes to the contract including drops
     * 
     */
    function setPause(bool pause) external onlyOwner {
        isPaused = pause;
    
    }
    
    /**
     * @dev set name of lpID back to default and blacklist address _addressToBlacklist that named it from renaming.
     * 
     * note: we hope we never have to use this.
     * 
     */
    function resetNameAndBlackList(uint256 lpID, address _addressToBlacklist) external onlyOwner whenPaused {
        lpName[lpID] = "";
        lpNameBlacklist[_addressToBlacklist] = true;
    }
    
    /**
     * @dev remove address _addressToRemove from blacklist 
     * 
     * 
     */
    function removeAddressFromBlacklist(address _addressToRemove) external onlyOwner whenPaused {
        lpNameBlacklist[_addressToRemove] = false;
    }
    
    
}