pragma solidity 0.6.12;


// 
/**
 * @dev Interface of the ERC20 standard as defined in the EIP.
 */
interface IERC20 {
    /**
     * @dev Returns the amount of tokens in existence.
     */
    function totalSupply() external view returns (uint256);

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

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

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

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

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

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

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

// 
/**
 * @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, 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) {
        return sub(a, b, "SafeMath: subtraction overflow");
    }

    /**
     * @dev Returns the subtraction of two unsigned integers, reverting with custom message on
     * overflow (when the result is negative).
     *
     * 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);
        uint256 c = a - b;

        return c;
    }

    /**
     * @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) {
        // 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 0;
        }

        uint256 c = a * b;
        require(c / a == b, "SafeMath: multiplication overflow");

        return c;
    }

    /**
     * @dev Returns the integer division of two unsigned integers. Reverts 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) {
        return div(a, b, "SafeMath: division by zero");
    }

    /**
     * @dev Returns the integer division of two unsigned integers. Reverts with custom message 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, string memory errorMessage) internal pure returns (uint256) {
        require(b > 0, errorMessage);
        uint256 c = a / b;
        // assert(a == b * c + a % b); // There is no case in which this doesn't hold

        return c;
    }

    /**
     * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
     * Reverts 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) {
        return mod(a, b, "SafeMath: modulo by zero");
    }

    /**
     * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
     * Reverts with custom message 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, string memory errorMessage) internal pure returns (uint256) {
        require(b != 0, errorMessage);
        return a % b;
    }
}

// 
/**
 * @dev Collection of functions related to the address type
 */
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 v3.3._
     */
    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 v3.3._
     */
    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);
            }
        }
    }
}

// 
/**
 * @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 SafeERC20 {
    using SafeMath for uint256;
    using Address for address;

    function safeTransfer(IERC20 token, address to, uint256 value) internal {
        _callOptionalReturn(token, abi.encodeWithSelector(token.transfer.selector, to, value));
    }

    function safeTransferFrom(IERC20 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(IERC20 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'
        // solhint-disable-next-line max-line-length
        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(IERC20 token, address spender, uint256 value) internal {
        uint256 newAllowance = token.allowance(address(this), spender).add(value);
        _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, newAllowance));
    }

    function safeDecreaseAllowance(IERC20 token, address spender, uint256 value) internal {
        uint256 newAllowance = token.allowance(address(this), spender).sub(value, "SafeERC20: decreased allowance below zero");
        _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(IERC20 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
            // solhint-disable-next-line max-line-length
            require(abi.decode(returndata, (bool)), "SafeERC20: ERC20 operation did not succeed");
        }
    }
}

// 
/**
 * @dev Library for managing
 * https://en.wikipedia.org/wiki/Set_(abstract_data_type)[sets] of primitive
 * types.
 *
 * Sets have the following properties:
 *
 * - Elements are added, removed, and checked for existence in constant time
 * (O(1)).
 * - Elements are enumerated in O(n). No guarantees are made on the ordering.
 *
 * ```
 * contract Example {
 *     // Add the library methods
 *     using EnumerableSet for EnumerableSet.AddressSet;
 *
 *     // Declare a set state variable
 *     EnumerableSet.AddressSet private mySet;
 * }
 * ```
 *
 * As of v3.0.0, only sets of type `address` (`AddressSet`) and `uint256`
 * (`UintSet`) are supported.
 */
library EnumerableSet {
    // To implement this library for multiple types with as little code
    // repetition as possible, we write it in terms of a generic Set type with
    // bytes32 values.
    // The Set implementation uses private functions, and user-facing
    // implementations (such as AddressSet) are just wrappers around the
    // underlying Set.
    // This means that we can only create new EnumerableSets for types that fit
    // in bytes32.

    struct Set {
        // Storage of set values
        bytes32[] _values;

        // Position of the value in the `values` array, plus 1 because index 0
        // means a value is not in the set.
        mapping (bytes32 => uint256) _indexes;
    }

    /**
     * @dev Add a value to a set. O(1).
     *
     * Returns true if the value was added to the set, that is if it was not
     * already present.
     */
    function _add(Set storage set, bytes32 value) private returns (bool) {
        if (!_contains(set, value)) {
            set._values.push(value);
            // The value is stored at length-1, but we add 1 to all indexes
            // and use 0 as a sentinel value
            set._indexes[value] = set._values.length;
            return true;
        } else {
            return false;
        }
    }

    /**
     * @dev Removes a value from a set. O(1).
     *
     * Returns true if the value was removed from the set, that is if it was
     * present.
     */
    function _remove(Set storage set, bytes32 value) private returns (bool) {
        // We read and store the value's index to prevent multiple reads from the same storage slot
        uint256 valueIndex = set._indexes[value];

        if (valueIndex != 0) { // Equivalent to contains(set, value)
            // To delete an element from the _values array in O(1), we swap the element to delete with the last one in
            // the array, and then remove the last element (sometimes called as 'swap and pop').
            // This modifies the order of the array, as noted in {at}.

            uint256 toDeleteIndex = valueIndex - 1;
            uint256 lastIndex = set._values.length - 1;

            // When the value to delete is the last one, the swap operation is unnecessary. However, since this occurs
            // so rarely, we still do the swap anyway to avoid the gas cost of adding an 'if' statement.

            bytes32 lastvalue = set._values[lastIndex];

            // Move the last value to the index where the value to delete is
            set._values[toDeleteIndex] = lastvalue;
            // Update the index for the moved value
            set._indexes[lastvalue] = toDeleteIndex + 1; // All indexes are 1-based

            // Delete the slot where the moved value was stored
            set._values.pop();

            // Delete the index for the deleted slot
            delete set._indexes[value];

            return true;
        } else {
            return false;
        }
    }

    /**
     * @dev Returns true if the value is in the set. O(1).
     */
    function _contains(Set storage set, bytes32 value) private view returns (bool) {
        return set._indexes[value] != 0;
    }

    /**
     * @dev Returns the number of values on the set. O(1).
     */
    function _length(Set storage set) private view returns (uint256) {
        return set._values.length;
    }

   /**
    * @dev Returns the value stored at position `index` in the set. O(1).
    *
    * Note that there are no guarantees on the ordering of values inside the
    * array, and it may change when more values are added or removed.
    *
    * Requirements:
    *
    * - `index` must be strictly less than {length}.
    */
    function _at(Set storage set, uint256 index) private view returns (bytes32) {
        require(set._values.length > index, "EnumerableSet: index out of bounds");
        return set._values[index];
    }

    // AddressSet

    struct AddressSet {
        Set _inner;
    }

    /**
     * @dev Add a value to a set. O(1).
     *
     * Returns true if the value was added to the set, that is if it was not
     * already present.
     */
    function add(AddressSet storage set, address value) internal returns (bool) {
        return _add(set._inner, bytes32(uint256(value)));
    }

    /**
     * @dev Removes a value from a set. O(1).
     *
     * Returns true if the value was removed from the set, that is if it was
     * present.
     */
    function remove(AddressSet storage set, address value) internal returns (bool) {
        return _remove(set._inner, bytes32(uint256(value)));
    }

    /**
     * @dev Returns true if the value is in the set. O(1).
     */
    function contains(AddressSet storage set, address value) internal view returns (bool) {
        return _contains(set._inner, bytes32(uint256(value)));
    }

    /**
     * @dev Returns the number of values in the set. O(1).
     */
    function length(AddressSet storage set) internal view returns (uint256) {
        return _length(set._inner);
    }

   /**
    * @dev Returns the value stored at position `index` in the set. O(1).
    *
    * Note that there are no guarantees on the ordering of values inside the
    * array, and it may change when more values are added or removed.
    *
    * Requirements:
    *
    * - `index` must be strictly less than {length}.
    */
    function at(AddressSet storage set, uint256 index) internal view returns (address) {
        return address(uint256(_at(set._inner, index)));
    }


    // UintSet

    struct UintSet {
        Set _inner;
    }

    /**
     * @dev Add a value to a set. O(1).
     *
     * Returns true if the value was added to the set, that is if it was not
     * already present.
     */
    function add(UintSet storage set, uint256 value) internal returns (bool) {
        return _add(set._inner, bytes32(value));
    }

    /**
     * @dev Removes a value from a set. O(1).
     *
     * Returns true if the value was removed from the set, that is if it was
     * present.
     */
    function remove(UintSet storage set, uint256 value) internal returns (bool) {
        return _remove(set._inner, bytes32(value));
    }

    /**
     * @dev Returns true if the value is in the set. O(1).
     */
    function contains(UintSet storage set, uint256 value) internal view returns (bool) {
        return _contains(set._inner, bytes32(value));
    }

    /**
     * @dev Returns the number of values on the set. O(1).
     */
    function length(UintSet storage set) internal view returns (uint256) {
        return _length(set._inner);
    }

   /**
    * @dev Returns the value stored at position `index` in the set. O(1).
    *
    * Note that there are no guarantees on the ordering of values inside the
    * array, and it may change when more values are added or removed.
    *
    * Requirements:
    *
    * - `index` must be strictly less than {length}.
    */
    function at(UintSet storage set, uint256 index) internal view returns (uint256) {
        return uint256(_at(set._inner, index));
    }
}

// 
/*
 * @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.
 */
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 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 Implementation of the {IERC20} interface.
 *
 * This implementation is agnostic to the way tokens are created. This means
 * that a supply mechanism has to be added in a derived contract using {_mint}.
 * For a generic mechanism see {ERC20PresetMinterPauser}.
 *
 * TIP: For a detailed writeup see our guide
 * https://forum.zeppelin.solutions/t/how-to-implement-erc20-supply-mechanisms/226[How
 * to implement supply mechanisms].
 *
 * We have followed general OpenZeppelin guidelines: functions revert instead
 * of returning `false` on failure. This behavior is nonetheless conventional
 * and does not conflict with the expectations of ERC20 applications.
 *
 * Additionally, an {Approval} event is emitted on calls to {transferFrom}.
 * This allows applications to reconstruct the allowance for all accounts just
 * by listening to said events. Other implementations of the EIP may not emit
 * these events, as it isn't required by the specification.
 *
 * Finally, the non-standard {decreaseAllowance} and {increaseAllowance}
 * functions have been added to mitigate the well-known issues around setting
 * allowances. See {IERC20-approve}.
 */
contract ERC20 is Context, IERC20 {
    using SafeMath for uint256;

    mapping (address => uint256) private _balances;

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

    uint256 private _totalSupply;

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

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

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

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

    /**
     * @dev Returns the number of decimals used to get its user representation.
     * For example, if `decimals` equals `2`, a balance of `505` tokens should
     * be displayed to a user as `5,05` (`505 / 10 ** 2`).
     *
     * Tokens usually opt for a value of 18, imitating the relationship between
     * Ether and Wei. This is the value {ERC20} uses, unless {_setupDecimals} is
     * called.
     *
     * NOTE: This information is only used for _display_ purposes: it in
     * no way affects any of the arithmetic of the contract, including
     * {IERC20-balanceOf} and {IERC20-transfer}.
     */
    function decimals() public view returns (uint8) {
        return _decimals;
    }

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

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

    /**
     * @dev See {IERC20-transfer}.
     *
     * Requirements:
     *
     * - `recipient` cannot be the zero address.
     * - the caller must have a balance of at least `amount`.
     */
    function transfer(address recipient, uint256 amount) public virtual override returns (bool) {
        _transfer(_msgSender(), recipient, amount);
        return true;
    }

    /**
     * @dev See {IERC20-allowance}.
     */
    function allowance(address owner, address spender) public view virtual override returns (uint256) {
        return _allowances[owner][spender];
    }

    /**
     * @dev See {IERC20-approve}.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     */
    function approve(address spender, uint256 amount) public virtual override returns (bool) {
        _approve(_msgSender(), spender, amount);
        return true;
    }

    /**
     * @dev See {IERC20-transferFrom}.
     *
     * Emits an {Approval} event indicating the updated allowance. This is not
     * required by the EIP. See the note at the beginning of {ERC20}.
     *
     * Requirements:
     *
     * - `sender` and `recipient` cannot be the zero address.
     * - `sender` must have a balance of at least `amount`.
     * - the caller must have allowance for ``sender``'s tokens of at least
     * `amount`.
     */
    function transferFrom(address sender, address recipient, uint256 amount) public virtual override returns (bool) {
        _transfer(sender, recipient, amount);
        _approve(sender, _msgSender(), _allowances[sender][_msgSender()].sub(amount, "ERC20: transfer amount exceeds allowance"));
        return true;
    }

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

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

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

        _beforeTokenTransfer(sender, recipient, amount);

        _balances[sender] = _balances[sender].sub(amount, "ERC20: transfer amount exceeds balance");
        _balances[recipient] = _balances[recipient].add(amount);
        emit Transfer(sender, recipient, amount);
    }

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

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

        _totalSupply = _totalSupply.add(amount);
        _balances[account] = _balances[account].add(amount);
        emit Transfer(address(0), account, amount);
    }

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

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

        _balances[account] = _balances[account].sub(amount, "ERC20: burn amount exceeds balance");
        _totalSupply = _totalSupply.sub(amount);
        emit Transfer(account, address(0), amount);
    }

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

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

    /**
     * @dev Sets {decimals} to a value other than the default one of 18.
     *
     * WARNING: This function should only be called from the constructor. Most
     * applications that interact with token contracts will not expect
     * {decimals} to ever change, and may work incorrectly if it does.
     */
    function _setupDecimals(uint8 decimals_) internal {
        _decimals = decimals_;
    }

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

// 
// LumosToken
contract LumosToken is ERC20("Lumos", "LMS"), Ownable {
    /// @notice Creates `_amount` token to `_to`. Must only be called by the owner
    function mint(address _to, uint256 _amount) public onlyOwner {
        _mint(_to, _amount);
    }
}

interface IUniswapV2Pair {
    event Approval(address indexed owner, address indexed spender, uint value);
    event Transfer(address indexed from, address indexed to, uint value);

    function name() external pure returns (string memory);
    function symbol() external pure returns (string memory);
    function decimals() external pure returns (uint8);
    function totalSupply() external view returns (uint);
    function balanceOf(address owner) external view returns (uint);
    function allowance(address owner, address spender) external view returns (uint);

    function approve(address spender, uint value) external returns (bool);
    function transfer(address to, uint value) external returns (bool);
    function transferFrom(address from, address to, uint value) external returns (bool);

    function DOMAIN_SEPARATOR() external view returns (bytes32);
    function PERMIT_TYPEHASH() external pure returns (bytes32);
    function nonces(address owner) external view returns (uint);

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

    event Mint(address indexed sender, uint amount0, uint amount1);
    event Burn(address indexed sender, uint amount0, uint amount1, address indexed to);
    event Swap(
        address indexed sender,
        uint amount0In,
        uint amount1In,
        uint amount0Out,
        uint amount1Out,
        address indexed to
    );
    event Sync(uint112 reserve0, uint112 reserve1);

    function MINIMUM_LIQUIDITY() external pure returns (uint);
    function factory() external view returns (address);
    function token0() external view returns (address);
    function token1() external view returns (address);
    function getReserves() external view returns (uint112 reserve0, uint112 reserve1, uint32 blockTimestampLast);
    function price0CumulativeLast() external view returns (uint);
    function price1CumulativeLast() external view returns (uint);
    function kLast() external view returns (uint);

    function mint(address to) external returns (uint liquidity);
    function burn(address to) external returns (uint amount0, uint amount1);
    function swap(uint amount0Out, uint amount1Out, address to, bytes calldata data) external;
    function skim(address to) external;
    function sync() external;

    function initialize(address, address) external;
}

// 
// computes square roots using the babylonian method
// https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method
library Babylonian {
    function sqrt(uint y) internal pure returns (uint z) {
        if (y > 3) {
            z = y;
            uint x = y / 2 + 1;
            while (x < z) {
                z = x;
                x = (y / x + x) / 2;
            }
        } else if (y != 0) {
            z = 1;
        }
        // else z = 0
    }
}

// 
// a library for handling binary fixed point numbers (https://en.wikipedia.org/wiki/Q_(number_format))
library FixedPoint {
    // range: [0, 2**112 - 1]
    // resolution: 1 / 2**112
    struct uq112x112 {
        uint224 _x;
    }

    // range: [0, 2**144 - 1]
    // resolution: 1 / 2**112
    struct uq144x112 {
        uint _x;
    }

    uint8 private constant RESOLUTION = 112;
    uint private constant Q112 = uint(1) << RESOLUTION;
    uint private constant Q224 = Q112 << RESOLUTION;

    // encode a uint112 as a UQ112x112
    function encode(uint112 x) internal pure returns (uq112x112 memory) {
        return uq112x112(uint224(x) << RESOLUTION);
    }

    // encodes a uint144 as a UQ144x112
    function encode144(uint144 x) internal pure returns (uq144x112 memory) {
        return uq144x112(uint256(x) << RESOLUTION);
    }

    // divide a UQ112x112 by a uint112, returning a UQ112x112
    function div(uq112x112 memory self, uint112 x) internal pure returns (uq112x112 memory) {
        require(x != 0, 'FixedPoint: DIV_BY_ZERO');
        return uq112x112(self._x / uint224(x));
    }

    // multiply a UQ112x112 by a uint, returning a UQ144x112
    // reverts on overflow
    function mul(uq112x112 memory self, uint y) internal pure returns (uq144x112 memory) {
        uint z;
        require(y == 0 || (z = uint(self._x) * y) / y == uint(self._x), "FixedPoint: MULTIPLICATION_OVERFLOW");
        return uq144x112(z);
    }

    // returns a UQ112x112 which represents the ratio of the numerator to the denominator
    // equivalent to encode(numerator).div(denominator)
    function fraction(uint112 numerator, uint112 denominator) internal pure returns (uq112x112 memory) {
        require(denominator > 0, "FixedPoint: DIV_BY_ZERO");
        return uq112x112((uint224(numerator) << RESOLUTION) / denominator);
    }

    // decode a UQ112x112 into a uint112 by truncating after the radix point
    function decode(uq112x112 memory self) internal pure returns (uint112) {
        return uint112(self._x >> RESOLUTION);
    }

    // decode a UQ144x112 into a uint144 by truncating after the radix point
    function decode144(uq144x112 memory self) internal pure returns (uint144) {
        return uint144(self._x >> RESOLUTION);
    }

    // take the reciprocal of a UQ112x112
    function reciprocal(uq112x112 memory self) internal pure returns (uq112x112 memory) {
        require(self._x != 0, 'FixedPoint: ZERO_RECIPROCAL');
        return uq112x112(uint224(Q224 / self._x));
    }

    // square root of a UQ112x112
    function sqrt(uq112x112 memory self) internal pure returns (uq112x112 memory) {
        return uq112x112(uint224(Babylonian.sqrt(uint256(self._x)) << 56));
    }
}

// 
// library with helper methods for oracles that are concerned with computing average prices
library UniswapV2OracleLibrary {
    using FixedPoint for *;

    // helper function that returns the current block timestamp within the range of uint32, i.e. [0, 2**32 - 1]
    function currentBlockTimestamp() internal view returns (uint32) {
        return uint32(block.timestamp % 2 ** 32);
    }

    // produces the cumulative price using counterfactuals to save gas and avoid a call to sync.
    function currentCumulativePrices(
        address pair,
        bool isToken0
    ) internal view returns (uint priceCumulative, uint32 blockTimestamp) {
        blockTimestamp = currentBlockTimestamp();
        (uint112 reserve0, uint112 reserve1, uint32 blockTimestampLast) = IUniswapV2Pair(pair).getReserves();
        if (isToken0) {
          priceCumulative = IUniswapV2Pair(pair).price0CumulativeLast();

          // if time has elapsed since the last update on the pair, mock the accumulated price values
          if (blockTimestampLast != blockTimestamp) {
              // subtraction overflow is desired
              uint32 timeElapsed = blockTimestamp - blockTimestampLast;
              // addition overflow is desired
              // counterfactual
              priceCumulative += uint(FixedPoint.fraction(reserve1, reserve0)._x) * timeElapsed;
          }
        } else {
          priceCumulative = IUniswapV2Pair(pair).price1CumulativeLast();
          // if time has elapsed since the last update on the pair, mock the accumulated price values
          if (blockTimestampLast != blockTimestamp) {
              // subtraction overflow is desired
              uint32 timeElapsed = blockTimestamp - blockTimestampLast;
              // addition overflow is desired
              // counterfactual
              priceCumulative += uint(FixedPoint.fraction(reserve1, reserve0)._x) * timeElapsed;
          }
        }

    }
    function getUniswapV2Pair(address _token0, address _token1) internal pure returns (address uni_pair, bool isToken0) {
        
        (address token0, address token1) = UniswapV2OracleLibrary.sortTokens(
            _token0,
            _token1
        );
        //bool _isToken0;
        // used for interacting with uniswap
        if (token0 == _token0) {
            isToken0 = true;
        } else {
            isToken0 = false;
        }

        uni_pair = UniswapV2OracleLibrary.pairFor(address(0x5C69bEe701ef814a2B6a3EDD4B1652CB9cc5aA6f), token0, token1);

        return (uni_pair, isToken0);

    }
    /* - Constructor Helpers - */

    // calculates the CREATE2 address for a pair without making any external calls
    function pairFor(
        address factory,
        address token0,
        address token1
    ) internal pure returns (address pair) {
        pair = address(
            uint256(
                keccak256(
                    abi.encodePacked(
                        hex"ff",
                        factory,
                        keccak256(abi.encodePacked(token0, token1)),
                        hex"96e8ac4277198ff8b6f785478aa9a39f403cb768dd02cbee326c3e7da348845f" // init code hash
                    )
                )
            )
        );
    }

    // returns sorted token addresses, used to handle return values from pairs sorted in this order
    function sortTokens(address tokenA, address tokenB)
        internal
        pure
        returns (address token0, address token1)
    {
        require(tokenA != tokenB, "UniswapV2Library: IDENTICAL_ADDRESSES");
        (token0, token1) = tokenA < tokenB
            ? (tokenA, tokenB)
            : (tokenB, tokenA);
        require(token0 != address(0), "UniswapV2Library: ZERO_ADDRESS");
    }
}

// 
interface IMakerPriceFeed {
  function read() external view returns (bytes32);
}

// 
/// math.sol -- mixin for inline numerical wizardry
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.
// You should have received a copy of the GNU General Public License
// along with this program.  If not, see <http://www.gnu.org/licenses/>.
library DSMath {
    function add(uint256 x, uint256 y) internal pure returns (uint256 z) {
        require((z = x + y) >= x, "ds-math-add-overflow");
    }

    function sub(uint256 x, uint256 y) internal pure returns (uint256 z) {
        require((z = x - y) <= x, "ds-math-sub-underflow");
    }

    function mul(uint256 x, uint256 y) internal pure returns (uint256 z) {
        require(y == 0 || (z = x * y) / y == x, "ds-math-mul-overflow");
    }

    function div(uint256 x, uint256 y) internal pure returns (uint256 z) {
        require(y > 0, "ds-math-division-by-zero");
        return x / y;
    }

    function add(
        uint256 x,
        uint256 y,
        string memory errorMessage
    ) internal pure returns (uint256 z) {
        require((z = x + y) >= x, errorMessage);
    }

    function sub(
        uint256 x,
        uint256 y,
        string memory errorMessage
    ) internal pure returns (uint256 z) {
        require((z = x - y) <= x, errorMessage);
    }

    function mul(
        uint256 x,
        uint256 y,
        string memory errorMessage
    ) internal pure returns (uint256 z) {
        require(y == 0 || (z = x * y) / y == x, errorMessage);
    }

    function div(
        uint256 x,
        uint256 y,
        string memory errorMessage
    ) internal pure returns (uint256 z) {
        require(y > 0, errorMessage);
        return x / y;
    }

    function min(uint256 x, uint256 y) internal pure returns (uint256 z) {
        return x <= y ? x : y;
    }

    function max(uint256 x, uint256 y) internal pure returns (uint256 z) {
        return x >= y ? x : y;
    }

    function imin(int256 x, int256 y) internal pure returns (int256 z) {
        return x <= y ? x : y;
    }

    function imax(int256 x, int256 y) internal pure returns (int256 z) {
        return x >= y ? x : y;
    }

    uint256 constant WAD = 10**18;
    uint256 constant RAY = 10**27;

    //rounds to zero if x*y < WAD / 2
    function wmul(uint256 x, uint256 y) internal pure returns (uint256 z) {
        z = add(mul(x, y), WAD / 2) / WAD;
    }

    //rounds to zero if x*y < WAD / 2
    function rmul(uint256 x, uint256 y) internal pure returns (uint256 z) {
        z = add(mul(x, y), RAY / 2) / RAY;
    }

    //rounds to zero if x*y < WAD / 2
    function wdiv(uint256 x, uint256 y) internal pure returns (uint256 z) {
        z = add(mul(x, WAD), y / 2) / y;
    }
    /*
    function wdivM(uint256 x, uint256 y) internal pure returns (uint256 z) {
        x = toWAD18(x);
        y = toWAD18(y);
        z = add(mul(x, WAD), y / 2) / y;
    }
   */
    //rounds to zero if x*y < RAY / 2
    function rdiv(uint256 x, uint256 y) internal pure returns (uint256 z) {
        z = add(mul(x, RAY), y / 2) / y;
    }

    function toWAD18(uint256 x) internal pure returns (uint256 z) {
        z = mul(x, WAD);
    }

    function toRAY27(uint256 x) internal pure returns (uint256 z) {
        z = mul(x, RAY);
    }

    // computes square roots using the babylonian method
    // https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method

    function sqrt(uint256 y) internal pure returns (uint256 z) {
        if (y > 3) {
            z = y;
            uint256 x = y / 2 + 1;
            while (x < z) {
                z = x;
                x = (y / x + x) / 2;
            }
        } else if (y != 0) {
            z = 1;
        }
        // else z = 0
    }

    // This famous algorithm is called "exponentiation by squaring"
    // and calculates x^n with x as fixed-point and n as regular unsigned.
    //
    // It's O(log n), instead of O(n) for naive repeated multiplication.
    //
    // These facts are why it works:
    //
    //  If n is even, then x^n = (x^2)^(n/2).
    //  If n is odd,  then x^n = x * x^(n-1),
    //   and applying the equation for even x gives
    //    x^n = x * (x^2)^((n-1) / 2).
    //
    //  Also, EVM division is flooring and
    //    floor[(n-1) / 2] = floor[n / 2].
    //
    function rpow(uint256 x, uint256 n) internal pure returns (uint256 z) {
        z = n % 2 != 0 ? x : RAY;

        for (n /= 2; n != 0; n /= 2) {
            x = rmul(x, x);

            if (n % 2 != 0) {
                z = rmul(z, x);
            }
        }
    }
}

// 
// Grand Master is the wisest and oldest Wizard of lumos. He now governs over LUMOS. He's wise and helpful so he lets adventurers
//craft LMS while they learn casting spells. He will guide you all in all fairness.
//
// Note that it's ownable and the owner wields tremendous power. The ownership
// will be transferred to a governance smart contract once the key ingredient LMS is sufficiently
// distributed and the community can show to govern itself in peace.
//
// Have fun reading it. Hopefully it's bug-free. May the magic be with you.
contract MasterWizard is Ownable {
    using DSMath for uint;
    using SafeERC20 for IERC20;

    // Info of each adventurer.
    struct UserInfo {
        uint amount; // How many LP tokens the adventurer has provided.
        uint rewardDebt; // Reward debt. See explanation below.
        uint lastHarvestBlock;
        uint totalHarvestReward;
        //
        // We do some fancy math here. Basically, any point in time, the amount of LMS
        // entitled to an adventurer but is pending to be distributed is:
        //
        //   pending reward = (user.amount * pool.accLumosPerShare) - user.rewardDebt
        //
        // Whenever an adventurer deposits or withdraws LP tokens to a pool. Here's what happens:
        //   1. The pool's `accLumosPerShare` (and `lastRewardBlock`) gets updated.
        //   2. Adventurer receives the pending reward sent to his/her address.
        //   3. Adventurer's `amount` gets updated.
        //   4. Adventurer's `rewardDebt` gets updated.
    }

    // Info of each pool.
    struct PoolInfo {
        IERC20 lpToken; // Address of LP token contract.
        uint allocPoint; // How many allocation points assigned to this pool. LMS to distribute per block.
        uint lastRewardBlock; // Last block number that LMS distribution occurs.
        uint accLumosPerShare; // Accumulated LMS per share, times 1e6. See below.
    }

    // The LUMOS TOKEN!
    LumosToken public lumos;
    // Dev fund (2%, initially)
    uint public devFundDivRate = 50 * 1e18; //Wizards casting spells while teaching so some LMS is created. These will be used wisely to develop Lumos. 
    // Dev address.
    address public devaddr;
    // LUMOS tokens created per block.
    uint public lumosPerBlock;

    // Info of each pool.
    PoolInfo[] public poolInfo;

    mapping(address => uint256) public poolId1; // poolId1 count from 1, subtraction 1 before using with poolInfo

    // Info of each user that stakes LP tokens.
    mapping(uint => mapping(address => UserInfo)) public userInfo;
    // Total allocation points. Must be the sum of all allocation points in all pools.
    uint public totalAllocPoint = 0;
    // The block number when LMS mining starts.
    uint public startBlock;

    uint public endBlock;
    //uint public endBlock;
    uint public startBlockTime;

    /// @notice pair for reserveToken <> LMS
    address public uniswap_pair;

    /// @notice last TWAP update time
    uint public blockTimestampLast;

    /// @notice last TWAP cumulative price;
    uint public priceCumulativeLast;

    /// @notice Whether or not this token is first in uniswap LMS<>Reserve pair
    bool public isToken0;

    uint public lmsPriceMultiplier;

    uint public minLMSTWAPIntervalSec;

    address public makerEthPriceFeed;

    uint public timeOfInitTWAP;

    //bool public testMode;

    bool public craftingEnded;

    // Events
    event Recovered(address token, uint amount);
    event Deposit(address indexed user, uint indexed pid, uint amount);
    event Withdraw(address indexed user, uint indexed pid, uint amount);
    event EmergencyWithdraw(
        address indexed user,
        uint indexed pid,
        uint amount
    );

    constructor(
        LumosToken _lumos,
        address reserveToken_,//WETH
        address _devaddr
        //,bool _testMode
    ) public {
        lumos = _lumos;
        devaddr = _devaddr;
        //startBlock = _startBlock;

        (address _uniswap_pair, bool _isToken0) = UniswapV2OracleLibrary.getUniswapV2Pair(address(lumos),reserveToken_);

        uniswap_pair = _uniswap_pair;
        isToken0 = _isToken0;

        makerEthPriceFeed = 0x729D19f657BD0614b4985Cf1D82531c67569197B;
        /*
        testMode = _testMode;
        
         if(testMode == true) {
            minLMSTWAPIntervalSec = 1 minutes;
         }
         else {
        */          
        minLMSTWAPIntervalSec = 24 hours;
        // }

         //init_TWAP();
    }

    function poolLength() external view returns (uint) {
        return poolInfo.length;
    }

    function start_crafting() external onlyOwner {
        require(startBlock > 0 && block.number > startBlock, "not this time.!");
        require(startBlockTime == 0, "crafting already started.!");

        startBlockTime = block.timestamp;

        lumosPerBlock = getLumosPerBlock();
        lmsPriceMultiplier = 1e18;

        massUpdatePools();
    }
   function end_crafting() external 
    {
        require(startBlockTime > 0, "crafting not started.!");

        if(lumos.totalSupply() > (1e18 * 2000000)) {

            massUpdatePools();

            craftingEnded = true;
            endBlock = block.number;
        }

    }
    function init_TWAP() public onlyOwner {
        require(timeOfInitTWAP == 0,"already initialized.!");
        (uint priceCumulative, uint32 blockTimestamp) = UniswapV2OracleLibrary.currentCumulativePrices(uniswap_pair, isToken0);

        require(blockTimestamp > 0, "no trades");

        blockTimestampLast = blockTimestamp;
        priceCumulativeLast = priceCumulative;
        timeOfInitTWAP = blockTimestamp;
    }

    // Add a new lp to the pool. Can only be called by the owner.
    function add(
        uint _allocPoint,
        IERC20 _lpToken,
        bool _withUpdate
    ) public onlyOwner {
        require(poolId1[address(_lpToken)] == 0, "add: lp is already in pool");

        if (_withUpdate) {
            massUpdatePools();
        }
        _allocPoint = _allocPoint.toWAD18();

        uint lastRewardBlock = block.number > startBlock
            ? block.number
            : startBlock;
        totalAllocPoint = totalAllocPoint.add(_allocPoint);
        poolId1[address(_lpToken)] = poolInfo.length + 1;
        poolInfo.push(
            PoolInfo({
                lpToken: _lpToken,
                allocPoint: _allocPoint,
                lastRewardBlock: lastRewardBlock,
                accLumosPerShare: 0
            })
        );
    }

    // Update the given pool's LMS allocation point. Can only be called by the owner.
    function set(
        uint _pid,
        uint _allocPoint,
        bool _withUpdate
    ) public onlyOwner {
        if (_withUpdate) {
            massUpdatePools();
        }

        _allocPoint = _allocPoint.toWAD18();

        totalAllocPoint = totalAllocPoint.sub(poolInfo[_pid].allocPoint).add(
            _allocPoint
        );
        poolInfo[_pid].allocPoint = _allocPoint;
    }
     //Updates the price of LMS token
    function getTWAP() private returns (uint) {

        (uint priceCumulative,uint blockTimestamp) = UniswapV2OracleLibrary.currentCumulativePrices(uniswap_pair, isToken0);
        
        uint timeElapsed = blockTimestamp - blockTimestampLast; // overflow is desired

        // overflow is desired, casting never truncates
        // cumulative price is in (uq112x112 price * seconds) units so we simply wrap it after division by time elapsed
        FixedPoint.uq112x112 memory priceAverage = FixedPoint.uq112x112(
            uint224((priceCumulative - priceCumulativeLast) / timeElapsed)
        );

        priceCumulativeLast = priceCumulative;
        blockTimestampLast = blockTimestamp;

        return FixedPoint.decode144(FixedPoint.mul(priceAverage, 10**18));
    }
    function getCurrentTWAP() public view returns (uint) {

        (uint priceCumulative,uint blockTimestamp) = UniswapV2OracleLibrary.currentCumulativePrices(uniswap_pair, isToken0);
        
        uint timeElapsed = blockTimestamp - blockTimestampLast; // overflow is desired

        // overflow is desired, casting never truncates
        // cumulative price is in (uq112x112 price * seconds) units so we simply wrap it after division by time elapsed
        FixedPoint.uq112x112 memory priceAverage = FixedPoint.uq112x112(
            uint224((priceCumulative - priceCumulativeLast) / timeElapsed)
        );

        return FixedPoint.decode144(FixedPoint.mul(priceAverage, 10**18));
    }
    //Updates the ETHUSD price to calculate LMS price in USD. 
    function getETHUSDPrice() public view returns(uint) {
        /*if(testMode){
            return 384.2e18;
        }*/
        return uint(IMakerPriceFeed(makerEthPriceFeed).read());
    }
    // Return reward multiplier over the given _from to _to block.
    function getMultiplier(uint _from, uint _to) private view returns (uint) {
        //require(startBlockTime > 0, "farming not activated yet.!");
        uint _blockCount = _to.sub(_from);

        return lumosPerBlock.wmul(lmsPriceMultiplier).mul(_blockCount);//.wdiv(1 ether);
    }

    // View function to see pending LMS on frontend.
    function pendingLumos(uint _pid, address _user)
        external
        view
        returns (uint)
    {
        PoolInfo storage pool = poolInfo[_pid];
        UserInfo storage user = userInfo[_pid][_user];
        uint accLumosPerShare = pool.accLumosPerShare;
        uint lpSupply = pool.lpToken.balanceOf(address(this));
        if (block.number > pool.lastRewardBlock && lpSupply != 0 && craftingEnded == false) {
            uint multiplier = getMultiplier(
                pool.lastRewardBlock,
                block.number
            );
            uint lumosReward = multiplier
            //.mul(lumosPerBlock)
                .wmul(pool.allocPoint)
                .wdiv(totalAllocPoint);
                //.wdiv(1e18);
            accLumosPerShare = accLumosPerShare.add(
                lumosReward
                .mul(1e6)
                .wdiv(lpSupply)
            );
        }
        return user.amount.wmul(accLumosPerShare)
        .div(1e6)
        .sub(user.rewardDebt);
    }

    // Update reward vairables for all pools. Be careful of gas spending!
    function massUpdatePools() public {
        uint length = poolInfo.length;
        for (uint pid = 0; pid < length; ++pid) {
            updatePool(pid);
        }
    }

    // Update reward variables of the given pool to be up-to-date.
    function updatePool(uint _pid) public {
        if(startBlock == 0) {
            return;
        }

        PoolInfo storage pool = poolInfo[_pid];
        if (block.number <= pool.lastRewardBlock) {
            return;
        }
        uint lpSupply = pool.lpToken.balanceOf(address(this));
        if (lpSupply == 0) {
            pool.lastRewardBlock = block.number;
            return;
        }
        
        if(craftingEnded){
            return;
        }

        uint multiplier = getMultiplier(pool.lastRewardBlock, block.number);
        uint lmsReward = multiplier
        //.mul(lumosPerBlock)
            .wmul(pool.allocPoint)
            .wdiv(totalAllocPoint);
            //.wdiv(1e18);
        lumos.mint(devaddr, lmsReward.wdiv(devFundDivRate));
        lumos.mint(address(this), lmsReward);
        pool.accLumosPerShare = pool.accLumosPerShare.add(
            lmsReward
            .mul(1e6)
            .wdiv(lpSupply)
        );
        pool.lastRewardBlock = block.number;
    }

    // Deposit LP tokens to MasterWizard for LMS allocation.
    function deposit(uint _pid, uint _amount) public {
        require(startBlockTime > 0, "crafting not activated yet.!");
        
        PoolInfo storage pool = poolInfo[_pid];
        UserInfo storage user = userInfo[_pid][msg.sender];
        updatePool(_pid);
        if (user.amount > 0) {
            uint pending = user
                .amount
                .wmul(pool.accLumosPerShare)
                .div(1e6)
                .sub(user.rewardDebt);
            if (pending > 0) {
                uint _harvestMultiplier = getLumosHarvestMultiplier(
                    user.lastHarvestBlock
                );

                uint _harvestBonus = pending.wmul(_harvestMultiplier);

                // With magic, Grand Master rewards adventurer if she chooses to let their rewards stays in the Crafting Pool.    
                if (_harvestBonus > 1e18) {
                    lumos.mint(msg.sender, _harvestBonus);
                    user.totalHarvestReward = user.totalHarvestReward.add(
                        _harvestBonus
                    );
                }
                safeLMSTransfer(msg.sender, pending);
            }
        }
        if (_amount > 0) {
            pool.lpToken.safeTransferFrom(
                address(msg.sender),
                address(this),
                _amount
            );
            user.amount = user.amount.add(_amount);
        }
        user.lastHarvestBlock = block.number;
        user.rewardDebt = user.amount.wmul(pool.accLumosPerShare).div(1e6);

        emit Deposit(msg.sender, _pid, _amount);
    }

    // Withdraw LP tokens from MasterWizard.
    function withdraw(uint _pid, uint _amount) public {
        PoolInfo storage pool = poolInfo[_pid];
        UserInfo storage user = userInfo[_pid][msg.sender];
        require(user.amount >= _amount, "withdraw: not good");

        updatePool(_pid);
        uint pending = user.amount.wmul(pool.accLumosPerShare)
        .div(1e6)
        .sub(user.rewardDebt);

        if (pending > 0) {
            safeLMSTransfer(msg.sender, pending);
        }
        if (_amount > 0) {
            user.amount = user.amount.sub(_amount);
            pool.lpToken.safeTransfer(address(msg.sender), _amount);
        }
        user.rewardDebt = user.amount.wmul(pool.accLumosPerShare).div(1e6);

        user.lastHarvestBlock = block.number;

        emit Withdraw(msg.sender, _pid, _amount);
    }

    // Withdraw without caring about rewards. EMERGENCY ONLY.
    function emergencyWithdraw(uint _pid) public {
        PoolInfo storage pool = poolInfo[_pid];
        UserInfo storage user = userInfo[_pid][msg.sender];
        pool.lpToken.safeTransfer(address(msg.sender), user.amount);
        emit EmergencyWithdraw(msg.sender, _pid, user.amount);
        user.amount = 0;
        user.rewardDebt = 0;
        user.lastHarvestBlock = block.number;
        // user.withdrawalCount++;
    }

    // Safe lumos transfer function, just in case if rounding error causes pool to not have enough LMS.
    function safeLMSTransfer(address _to, uint _amount) private {
        uint lmsBalance = lumos.balanceOf(address(this));
        if (_amount > lmsBalance) {
            lumos.transfer(_to, lmsBalance);
        } else {
            lumos.transfer(_to, _amount);
        }
    }

    // Update dev address by the previous dev.
    //function dev(address _devaddr) public {
    //    require(msg.sender == devaddr, "dev: wut?");
    //    devaddr = _devaddr;
    //}
    /*
    function setStartBlockTime(uint _startBlockTime) external {
        require(testMode, "testing or not ?");

        startBlockTime = _startBlockTime;
    }
    */
    function setLumosPerBlock() external {
        require(startBlockTime > 0, "crafting not activated yet.!");

        uint _lumosPerBlock = getLumosPerBlock();
        if(_lumosPerBlock != lumosPerBlock){
            massUpdatePools();
            
            lumosPerBlock = _lumosPerBlock;
        }
    }
    /*
    function getLumosTotalSupply() external view returns(uint) {
        require(testMode, "testing or not ?");

        return lumos.totalSupply();
    }
*/
    // Community casting this spell every day and decides the daily bonus multiplier for the next day. This spell can be cast only once in every day. 
    function setLMSPriceMultiplier() external {
        require(startBlockTime > 0 && blockTimestampLast.add(minLMSTWAPIntervalSec) < now, "not this time.!");
        require(timeOfInitTWAP > 0, "crafting not initialized.!");
        require(craftingEnded == false, "crafting ended :(");
        
        massUpdatePools();
        
        setLMSPriceMultiplierInt();
    }
    function getCurrentPriceMultiplier() external view returns(uint){

        uint _lmsPriceETH = getCurrentTWAP();
        uint _ethPriceUSD = getETHUSDPrice();
        uint _price = _lmsPriceETH.wmul(_ethPriceUSD);

        if (_price < 3e18) 
            return 1e18;
        else if (_price >= 3e18 && _price < 5e18)
            return 2e18; 
        else if (_price >= 5e18 && _price < 8e18)
            return 3e18;
        else return 4e18;
    }
    function setLMSPriceMultiplierInt() private {
        if(startBlockTime == 0 || blockTimestampLast.add(minLMSTWAPIntervalSec) > now || timeOfInitTWAP == 0 || craftingEnded == true) {
            return;
        }
        uint _lmsPriceETH = getTWAP();
        uint _ethPriceUSD = getETHUSDPrice();
        uint _price = _lmsPriceETH.wmul(_ethPriceUSD);

        if (_price < 3e18) 
            lmsPriceMultiplier = 1e18;
        else if (_price >= 3e18 && _price < 5e18)
            lmsPriceMultiplier = 2e18; 
        else if (_price >= 5e18 && _price < 8e18)
            lmsPriceMultiplier = 3e18;
        else lmsPriceMultiplier = 4e18;

        lumosPerBlock = getLumosPerBlock();
    }

    // lumos per block multiplier
    function getLumosPerBlock() private view returns (uint) {
        uint elapsedDays = ((now - startBlockTime).div(86400) + 1) * 1e6;
        return elapsedDays.sqrt().wdiv(6363);
    }

    // harvest multiplier
    function getLumosHarvestMultiplier(uint _lastHarvestBlock) private view returns (uint) {
        return
            (block.number - _lastHarvestBlock).wdiv(67000).min(1e18);
    }

    function setStartBlock(uint _startBlock) external onlyOwner {
        require(startBlock == 0 && _startBlock > 0, " startBlock > 0 ?");
        startBlock = _startBlock;
    }

    function setDevFundDivRate(uint _devFundDivRate) external onlyOwner {
        require(_devFundDivRate > 0, "dev fund rate 0 ?");
        devFundDivRate = _devFundDivRate;
    }

    function setminLMSTWAPIntervalSec(uint _interval) external onlyOwner {
        require(_interval > 0, "minLMSTWAPIntervalSec 0 ?");
        minLMSTWAPIntervalSec = _interval;
    }    
}