// File: contracts/MahinNFT.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.7.0;
pragma experimental ABIEncoderV2;

import "./ERC721.sol";
import "openzeppelin-solidity/contracts/access/Ownable.sol";
import "openzeppelin-solidity/contracts/token/ERC20/IERC20.sol";
import "./Roles.sol";
import "./Randomness.sol";
import "./Fees.sol";


contract MahinNFT is Roles, ERC721("Mahin", "MAHIN"), Randomness, HasFees  {
  event TokenDataStorage(
    uint256 indexed tokenId,
    bytes[] states
  );

  event Diagnosed(
    uint256 indexed tokenId
  );

  struct Piece {
    string name;
    bytes[] imageData;
    string[] ipfsHashes;
    string[] arweaveHashes;
    uint8 currentState;
  }

  // The beneficiary (the charity or someone acting in their name) - receives royalties.
  address public beneficiary;

  mapping(uint256 => Piece) public pieces;

  constructor(VRFConfig memory vrfConfig) Randomness(vrfConfig) {
  }

  function withdraw() public onlyOwner {
    address payable owner = payable(owner());
    owner.transfer(address(this).balance);
  }

  function withdrawToken(address tokenAddress) public onlyOwner {
    IERC20 token = IERC20(tokenAddress);
    token.transfer(owner(), token.balanceOf(address(this)));
  }

  // Returns the current SVG/PNG of the piece.
  function getImageData(uint256 tokenId) public view returns (bytes memory) {
    require(_exists(tokenId), "not a valid token");
    return pieces[tokenId].imageData[0];
  }

  function setImageData(uint256 tokenId, bytes calldata state1, bytes calldata state2) public onlyOwner {
    pieces[tokenId].imageData[0] = state1;
    pieces[tokenId].imageData[1] = state2;
  }

  // Will be used by the owner during setup to create all pieces of the work.
  // ipfsHashes - the ipfs location of each state - needed so provided an off-chain metadata url.
  function initToken(uint256 tokenId, string memory name, string[] memory arweaveHashes, string[] memory ipfsHashes) public onlyOwner {
    require(pieces[tokenId].ipfsHashes.length == 0, "invalid id");

    pieces[tokenId].name = name;
    pieces[tokenId].ipfsHashes = ipfsHashes;
    pieces[tokenId].arweaveHashes = arweaveHashes;
    pieces[tokenId].currentState = 0;
  }

  // Init multiple tokens at once
  function initTokens(uint256[] memory tokenIds, string[] memory names, string[][] memory arweaveHashSets, string[][] memory ipfsHashSets) public onlyOwner {
    for (uint256 i=0; i<tokenIds.length; i++) {
      uint256 tokenId = tokenIds[i];
      require(pieces[tokenId].ipfsHashes.length == 0, "invalid id");

      pieces[tokenId].name = names[i];
      pieces[tokenId].ipfsHashes = ipfsHashSets[i];
      pieces[tokenId].arweaveHashes = arweaveHashSets[i];
      pieces[tokenId].currentState = 0;
    }
  }

  // Allow contract owner&minter to mint a token and assigned to to anyone they please.
  function mintToken(uint256 tokenId, address firstOwner) public onlyMinterOrOwner {
    require(pieces[tokenId].ipfsHashes.length > 0, "invalid id");
    require(!_exists(tokenId), "exists");

    _mint(firstOwner, tokenId);
  }

  // Allow contract owner to set the IPFS host
  function setIPFSHost(string memory baseURI_) public onlyOwner {
    _setBaseURI(baseURI_);
  }

  function setBeneficiary(address _beneficiary) public onlyOwner {
    beneficiary = _beneficiary;
  }

  // Return the current IPFS link based on state
  function tokenURI(uint256 tokenId) public view override returns (string memory) {
    require(pieces[tokenId].ipfsHashes.length > 0, "invalid id");

    Piece memory piece = pieces[tokenId];
    string memory tokenPath = piece.ipfsHashes[piece.currentState];
    return string(abi.encodePacked(baseURI(), tokenPath));
  }

  function onDiagnosed(uint256 tokenId) internal override {
    pieces[tokenId].currentState = 1;
    emit Diagnosed(tokenId);
  }

  function diagnose(uint256 tokenId) public onlyDoctor {
    onDiagnosed(tokenId);
  }

  function getBeneficiary() internal override view returns (address) {
    return beneficiary;
  }

  function getFee(uint256 tokenId) override internal view returns (uint256) {
    if (pieces[tokenId].currentState >= 1) {
      return 15;
    } else {
      return 5;
    }
  }
}


// File: contracts/ERC721.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.7.0;

// Copied from openzeppelin because we want to override the tokenURI() function

import "openzeppelin-solidity/contracts/GSN/Context.sol";
import "openzeppelin-solidity/contracts/token/ERC721/IERC721.sol";
import "openzeppelin-solidity/contracts/token/ERC721/IERC721Metadata.sol";
import "openzeppelin-solidity/contracts/token/ERC721/IERC721Enumerable.sol";
import "openzeppelin-solidity/contracts/token/ERC721/IERC721Receiver.sol";
import "openzeppelin-solidity/contracts/introspection/ERC165.sol";
import "openzeppelin-solidity/contracts/math/SafeMath.sol";
import "openzeppelin-solidity/contracts/utils/Address.sol";
import "openzeppelin-solidity/contracts/utils/EnumerableSet.sol";
import "openzeppelin-solidity/contracts/utils/EnumerableMap.sol";
import "openzeppelin-solidity/contracts/utils/Strings.sol";

/**
 * @title ERC721 Non-Fungible Token Standard basic implementation
 * @dev see https://eips.ethereum.org/EIPS/eip-721
 */
abstract contract ERC721 is Context, ERC165, IERC721, IERC721Metadata, IERC721Enumerable {
  using SafeMath for uint256;
  using Address for address;
  using EnumerableSet for EnumerableSet.UintSet;
  using EnumerableMap for EnumerableMap.UintToAddressMap;
  using Strings for uint256;

  // Equals to `bytes4(keccak256("onERC721Received(address,address,uint256,bytes)"))`
  // which can be also obtained as `IERC721Receiver(0).onERC721Received.selector`
  bytes4 private constant _ERC721_RECEIVED = 0x150b7a02;

  // Mapping from holder address to their (enumerable) set of owned tokens
  mapping (address => EnumerableSet.UintSet) private _holderTokens;

  // Enumerable mapping from token ids to their owners
  EnumerableMap.UintToAddressMap private _tokenOwners;

  // Mapping from token ID to approved address
  mapping (uint256 => address) private _tokenApprovals;

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

  // Token name
  string private _name;

  // Token symbol
  string private _symbol;

  // Optional mapping for token URIs
  mapping (uint256 => string) internal _tokenURIs;

  // Base URI
  string private _baseURI;

  /*
   *     bytes4(keccak256('balanceOf(address)')) == 0x70a08231
   *     bytes4(keccak256('ownerOf(uint256)')) == 0x6352211e
   *     bytes4(keccak256('approve(address,uint256)')) == 0x095ea7b3
   *     bytes4(keccak256('getApproved(uint256)')) == 0x081812fc
   *     bytes4(keccak256('setApprovalForAll(address,bool)')) == 0xa22cb465
   *     bytes4(keccak256('isApprovedForAll(address,address)')) == 0xe985e9c5
   *     bytes4(keccak256('transferFrom(address,address,uint256)')) == 0x23b872dd
   *     bytes4(keccak256('safeTransferFrom(address,address,uint256)')) == 0x42842e0e
   *     bytes4(keccak256('safeTransferFrom(address,address,uint256,bytes)')) == 0xb88d4fde
   *
   *     => 0x70a08231 ^ 0x6352211e ^ 0x095ea7b3 ^ 0x081812fc ^
   *        0xa22cb465 ^ 0xe985e9c5 ^ 0x23b872dd ^ 0x42842e0e ^ 0xb88d4fde == 0x80ac58cd
   */
  bytes4 private constant _INTERFACE_ID_ERC721 = 0x80ac58cd;

  /*
   *     bytes4(keccak256('name()')) == 0x06fdde03
   *     bytes4(keccak256('symbol()')) == 0x95d89b41
   *     bytes4(keccak256('tokenURI(uint256)')) == 0xc87b56dd
   *
   *     => 0x06fdde03 ^ 0x95d89b41 ^ 0xc87b56dd == 0x5b5e139f
   */
  bytes4 private constant _INTERFACE_ID_ERC721_METADATA = 0x5b5e139f;

  /*
   *     bytes4(keccak256('totalSupply()')) == 0x18160ddd
   *     bytes4(keccak256('tokenOfOwnerByIndex(address,uint256)')) == 0x2f745c59
   *     bytes4(keccak256('tokenByIndex(uint256)')) == 0x4f6ccce7
   *
   *     => 0x18160ddd ^ 0x2f745c59 ^ 0x4f6ccce7 == 0x780e9d63
   */
  bytes4 private constant _INTERFACE_ID_ERC721_ENUMERABLE = 0x780e9d63;

  /**
   * @dev Initializes the contract by setting a `name` and a `symbol` to the token collection.
   */
  constructor (string memory name_, string memory symbol_) {
    _name = name_;
    _symbol = symbol_;

    // register the supported interfaces to conform to ERC721 via ERC165
    _registerInterface(_INTERFACE_ID_ERC721);
    _registerInterface(_INTERFACE_ID_ERC721_METADATA);
    _registerInterface(_INTERFACE_ID_ERC721_ENUMERABLE);
  }

  /**
   * @dev See {IERC721-balanceOf}.
   */
  function balanceOf(address owner) public view override returns (uint256) {
    require(owner != address(0), "ERC721: balance query for the zero address");

    return _holderTokens[owner].length();
  }

  /**
   * @dev See {IERC721-ownerOf}.
   */
  function ownerOf(uint256 tokenId) public view override returns (address) {
    return _tokenOwners.get(tokenId, "ERC721: owner query for nonexistent token");
  }

  /**
   * @dev See {IERC721Metadata-name}.
   */
  function name() public view override returns (string memory) {
    return _name;
  }

  /**
   * @dev See {IERC721Metadata-symbol}.
   */
  function symbol() public view override returns (string memory) {
    return _symbol;
  }

  /**
  * @dev Returns the base URI set via {_setBaseURI}. This will be
  * automatically added as a prefix in {tokenURI} to each token's URI, or
  * to the token ID if no specific URI is set for that token ID.
  */
  function baseURI() public view returns (string memory) {
    return _baseURI;
  }

  /**
   * @dev See {IERC721Enumerable-tokenOfOwnerByIndex}.
   */
  function tokenOfOwnerByIndex(address owner, uint256 index) public view override returns (uint256) {
    return _holderTokens[owner].at(index);
  }

  /**
   * @dev See {IERC721Enumerable-totalSupply}.
   */
  function totalSupply() public view override returns (uint256) {
    // _tokenOwners are indexed by tokenIds, so .length() returns the number of tokenIds
    return _tokenOwners.length();
  }

  /**
   * @dev See {IERC721Enumerable-tokenByIndex}.
   */
  function tokenByIndex(uint256 index) public view override returns (uint256) {
    (uint256 tokenId, ) = _tokenOwners.at(index);
    return tokenId;
  }

  /**
   * @dev See {IERC721-approve}.
   */
  function approve(address to, uint256 tokenId) public virtual override {
    address owner = ownerOf(tokenId);
    require(to != owner, "ERC721: approval to current owner");

    require(_msgSender() == owner || isApprovedForAll(owner, _msgSender()),
      "ERC721: approve caller is not owner nor approved for all"
    );

    _approve(to, tokenId);
  }

  /**
   * @dev See {IERC721-getApproved}.
   */
  function getApproved(uint256 tokenId) public view override returns (address) {
    require(_exists(tokenId), "ERC721: approved query for nonexistent token");

    return _tokenApprovals[tokenId];
  }

  /**
   * @dev See {IERC721-setApprovalForAll}.
   */
  function setApprovalForAll(address operator, bool approved) public virtual override {
    require(operator != _msgSender(), "ERC721: approve to caller");

    _operatorApprovals[_msgSender()][operator] = approved;
    emit ApprovalForAll(_msgSender(), operator, approved);
  }

  /**
   * @dev See {IERC721-isApprovedForAll}.
   */
  function isApprovedForAll(address owner, address operator) public view override returns (bool) {
    return _operatorApprovals[owner][operator];
  }

  /**
   * @dev See {IERC721-transferFrom}.
   */
  function transferFrom(address from, address to, uint256 tokenId) public virtual override {
    //solhint-disable-next-line max-line-length
    require(_isApprovedOrOwner(_msgSender(), tokenId), "ERC721: transfer caller is not owner nor approved");

    _transfer(from, to, tokenId);
  }

  /**
   * @dev See {IERC721-safeTransferFrom}.
   */
  function safeTransferFrom(address from, address to, uint256 tokenId) public virtual override {
    safeTransferFrom(from, to, tokenId, "");
  }

  /**
   * @dev See {IERC721-safeTransferFrom}.
   */
  function safeTransferFrom(address from, address to, uint256 tokenId, bytes memory _data) public virtual override {
    require(_isApprovedOrOwner(_msgSender(), tokenId), "ERC721: transfer caller is not owner nor approved");
    _safeTransfer(from, to, tokenId, _data);
  }

  /**
   * @dev Safely transfers `tokenId` token from `from` to `to`, checking first that contract recipients
   * are aware of the ERC721 protocol to prevent tokens from being forever locked.
   *
   * `_data` is additional data, it has no specified format and it is sent in call to `to`.
   *
   * This internal function is equivalent to {safeTransferFrom}, and can be used to e.g.
   * implement alternative mechanisms to perform token transfer, such as signature-based.
   *
   * Requirements:
   *
   * - `from` cannot be the zero address.
   * - `to` cannot be the zero address.
   * - `tokenId` token must exist and be owned by `from`.
   * - If `to` refers to a smart contract, it must implement {IERC721Receiver-onERC721Received}, which is called upon a safe transfer.
   *
   * Emits a {Transfer} event.
   */
  function _safeTransfer(address from, address to, uint256 tokenId, bytes memory _data) internal virtual {
    _transfer(from, to, tokenId);
    require(_checkOnERC721Received(from, to, tokenId, _data), "ERC721: transfer to non ERC721Receiver implementer");
  }

  /**
   * @dev Returns whether `tokenId` exists.
   *
   * Tokens can be managed by their owner or approved accounts via {approve} or {setApprovalForAll}.
   *
   * Tokens start existing when they are minted (`_mint`),
   * and stop existing when they are burned (`_burn`).
   */
  function _exists(uint256 tokenId) internal view returns (bool) {
    return _tokenOwners.contains(tokenId);
  }

  /**
   * @dev Returns whether `spender` is allowed to manage `tokenId`.
   *
   * Requirements:
   *
   * - `tokenId` must exist.
   */
  function _isApprovedOrOwner(address spender, uint256 tokenId) internal view returns (bool) {
    require(_exists(tokenId), "ERC721: operator query for nonexistent token");
    address owner = ownerOf(tokenId);
    return (spender == owner || getApproved(tokenId) == spender || isApprovedForAll(owner, spender));
  }

  /**
   * @dev Safely mints `tokenId` and transfers it to `to`.
   *
   * Requirements:
   d*
   * - `tokenId` must not exist.
   * - If `to` refers to a smart contract, it must implement {IERC721Receiver-onERC721Received}, which is called upon a safe transfer.
   *
   * Emits a {Transfer} event.
   */
  function _safeMint(address to, uint256 tokenId) internal virtual {
    _safeMint(to, tokenId, "");
  }

  /**
   * @dev Same as {xref-ERC721-_safeMint-address-uint256-}[`_safeMint`], with an additional `data` parameter which is
   * forwarded in {IERC721Receiver-onERC721Received} to contract recipients.
   */
  function _safeMint(address to, uint256 tokenId, bytes memory _data) internal virtual {
    _mint(to, tokenId);
    require(_checkOnERC721Received(address(0), to, tokenId, _data), "ERC721: transfer to non ERC721Receiver implementer");
  }

  /**
   * @dev Mints `tokenId` and transfers it to `to`.
   *
   * WARNING: Usage of this method is discouraged, use {_safeMint} whenever possible
   *
   * Requirements:
   *
   * - `tokenId` must not exist.
   * - `to` cannot be the zero address.
   *
   * Emits a {Transfer} event.
   */
  function _mint(address to, uint256 tokenId) internal virtual {
    require(to != address(0), "ERC721: mint to the zero address");
    require(!_exists(tokenId), "ERC721: token already minted");

    _beforeTokenTransfer(address(0), to, tokenId);

    _holderTokens[to].add(tokenId);

    _tokenOwners.set(tokenId, to);

    emit Transfer(address(0), to, tokenId);
  }

  /**
   * @dev Destroys `tokenId`.
   * The approval is cleared when the token is burned.
   *
   * Requirements:
   *
   * - `tokenId` must exist.
   *
   * Emits a {Transfer} event.
   */
  function _burn(uint256 tokenId) internal virtual {
    address owner = ownerOf(tokenId);

    _beforeTokenTransfer(owner, address(0), tokenId);

    // Clear approvals
    _approve(address(0), tokenId);

    // Clear metadata (if any)
    if (bytes(_tokenURIs[tokenId]).length != 0) {
      delete _tokenURIs[tokenId];
    }

    _holderTokens[owner].remove(tokenId);

    _tokenOwners.remove(tokenId);

    emit Transfer(owner, address(0), tokenId);
  }

  /**
   * @dev Transfers `tokenId` from `from` to `to`.
   *  As opposed to {transferFrom}, this imposes no restrictions on msg.sender.
   *
   * Requirements:
   *
   * - `to` cannot be the zero address.
   * - `tokenId` token must be owned by `from`.
   *
   * Emits a {Transfer} event.
   */
  function _transfer(address from, address to, uint256 tokenId) internal virtual {
    require(ownerOf(tokenId) == from, "ERC721: transfer of token that is not own");
    require(to != address(0), "ERC721: transfer to the zero address");

    _beforeTokenTransfer(from, to, tokenId);

    // Clear approvals from the previous owner
    _approve(address(0), tokenId);

    _holderTokens[from].remove(tokenId);
    _holderTokens[to].add(tokenId);

    _tokenOwners.set(tokenId, to);

    emit Transfer(from, to, tokenId);
  }

  /**
   * @dev Sets `_tokenURI` as the tokenURI of `tokenId`.
   *
   * Requirements:
   *
   * - `tokenId` must exist.
   */
  function _setTokenURI(uint256 tokenId, string memory _tokenURI) internal virtual {
    require(_exists(tokenId), "ERC721Metadata: URI set of nonexistent token");
    _tokenURIs[tokenId] = _tokenURI;
  }

  /**
   * @dev Internal function to set the base URI for all token IDs. It is
   * automatically added as a prefix to the value returned in {tokenURI},
   * or to the token ID if {tokenURI} is empty.
   */
  function _setBaseURI(string memory baseURI_) internal virtual {
    _baseURI = baseURI_;
  }

  /**
   * @dev Internal function to invoke {IERC721Receiver-onERC721Received} on a target address.
   * The call is not executed if the target address is not a contract.
   *
   * @param from address representing the previous owner of the given token ID
   * @param to target address that will receive the tokens
   * @param tokenId uint256 ID of the token to be transferred
   * @param _data bytes optional data to send along with the call
   * @return bool whether the call correctly returned the expected magic value
   */
  function _checkOnERC721Received(address from, address to, uint256 tokenId, bytes memory _data)
  private returns (bool)
  {
    if (!to.isContract()) {
      return true;
    }
    bytes memory returndata = to.functionCall(abi.encodeWithSelector(
        IERC721Receiver(to).onERC721Received.selector,
        _msgSender(),
        from,
        tokenId,
        _data
      ), "ERC721: transfer to non ERC721Receiver implementer");
    bytes4 retval = abi.decode(returndata, (bytes4));
    return (retval == _ERC721_RECEIVED);
  }

  function _approve(address to, uint256 tokenId) private {
    _tokenApprovals[tokenId] = to;
    emit Approval(ownerOf(tokenId), to, tokenId);
  }

  /**
   * @dev Hook that is called before any token transfer. This includes minting
   * and burning.
   *
   * Calling conditions:
   *
   * - When `from` and `to` are both non-zero, ``from``'s `tokenId` will be
   * transferred to `to`.
   * - When `from` is zero, `tokenId` will be minted for `to`.
   * - When `to` is zero, ``from``'s `tokenId` will be burned.
   * - `from` cannot be the zero address.
   * - `to` cannot be the zero address.
   *
   * To learn more about hooks, head to xref:ROOT:extending-contracts.adoc#using-hooks[Using Hooks].
   */
  function _beforeTokenTransfer(address from, address to, uint256 tokenId) internal virtual { }
}

// File: openzeppelin-solidity/contracts/access/Ownable.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

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

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

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

// File: openzeppelin-solidity/contracts/token/ERC20/IERC20.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

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

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

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

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

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

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

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

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

// File: contracts/Roles.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

import "openzeppelin-solidity/contracts/access/Ownable.sol";
import "openzeppelin-solidity/contracts/GSN/Context.sol";

/**
 * @dev Uses the Ownable class and adds a second role called the minter.
 *
 * Owner: Can upload tokens, withdraw lost tokens, config ipfs hashes etc. Can also mint tokens.
     Can set the other roles.
 * Minter: Can only mint tokens.
 * Doctor: If set, can diagnose pieces. Replaces the builtin rand gen.
 */
abstract contract Roles is Context, Ownable {
    address private _minter;
    address private _doctor;

    /**
     * @dev Initializes the contract setting the deployer as the initial minter.
     */
    constructor () {
        address msgSender = _msgSender();
        _minter = msgSender;
        emit OwnershipTransferred(address(0), msgSender);
    }

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

    /**
     * @dev Returns the address of the doctor.
     */
    function doctor() public view returns (address) {
        return _doctor;
    }

    /**
     * @dev Throws if called by any account other than the minter.
     */
    modifier onlyMinter() {
        require(_minter == _msgSender(), "not minter");
        _;
    }

    /**
     * @dev Throws if called by any account other than the doctor.
     */
    modifier onlyDoctor() {
        require(_doctor == _msgSender(), "not doctor");
        _;
    }

    /**
     * @dev Throws if called by any account other than the minter or the owner.
     */
    modifier onlyMinterOrOwner() {
        require(_minter == _msgSender() || owner() == _msgSender(), "not minter or owner");
        _;
    }

    /**
     * @dev Transfers the minter role of the contract to a new account (`newMinter`).
     * Can only be called by the owner.
     */
    function setMinter(address newMinter) public virtual onlyOwner {
        require(newMinter != address(0), "zero address");
        _minter = newMinter;
    }

    /**
     * @dev Assigns the doctor role, replacing the builtin rng.
     */
    function setDoctor(address newDoctor) public virtual onlyOwner {
        require(newDoctor != address(0), "zero address");
        _doctor = newDoctor;
    }
}

// File: contracts/Randomness.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.7.0;

//import "hardhat/console.sol";
import "./ABDKMath64x64.sol";
import "./ChainlinkVRF.sol";
import "openzeppelin-solidity/contracts/token/ERC721/IERC721Enumerable.sol";
import "./Roles.sol";


abstract contract Randomness is Roles, ChainlinkVRF, IERC721Enumerable {
    using SafeMath for uint256;

    // Configuration Chainlink VRF
    struct VRFConfig {
        address coordinator;
        address token;
        bytes32 keyHash;
        uint256 price;
    }

    event RollInProgress(
        int128 probability
    );

    event RollComplete();

    uint public constant projectRuntimeSeconds = 365 days * 5;   // Runs for 5 years
    uint public constant targetProbability     = 2000000000000000;  // 0.2% - over the course of the project
    uint public constant denominator           = 10000000000000000; // 100%
    // This has been pre-calculated based on the values above
    uint public constant probabilityPerSecond  = 14151671;        // 0.0000000014151671%

    uint256 randomSeedBlock = 0;
    int128 public rollProbability = 0;
    uint256 public lastRollTime = 0;

    bytes32 chainlinkRequestId = 0;
    uint256 chainlinkRandomNumber = 0;
    bytes32 internal chainlinkKeyHash;
    uint256 internal chainlinkFee;

    constructor(VRFConfig memory config) ChainlinkVRF(config.coordinator, config.token) {
        chainlinkFee = config.price;
        chainlinkKeyHash = config.keyHash;

        lastRollTime = block.timestamp;
    }

    // Will return the probability of a (non-)diagnosis for an individual NFT, assuming the roll will happen at
    // `timestamp`. This will be based on the last time a roll happened, targeting a certain total probability
    // over the period the project is running.
    // Will return 0.80 to indicate that the probability of a diagnosis is 20%.
    function getProbability(uint256 timestamp) public view returns (int128 probability) {
        uint256 secondsSinceLastRoll = timestamp.sub(lastRollTime);

        // Say we want totalProbability = 20% over the course of the project's runtime.
        // If we roll 12 times, what should be the probability of each roll so they compound to 20%?
        //    (1 - x) ** 12 = (1 - 20%)
        // Or generalized:
        //    (1 - x) ** numTries = (1 - totalProbability)
        // Solve by x:
        //     x = 1 - (1 - totalProbability) ** (1/numTries)
        //

        // We use the 64.64 fixed point math library here. More info about this kind of math in Solidity:
        // https://medium.com/hackernoon/10x-better-fixed-point-math-in-solidity-32441fd25d43
        // https://ethereum.stackexchange.com/questions/83785/what-fixed-or-float-point-math-libraries-are-available-in-solidity

        // We already pre-calculated the probability for a 1-second interval
        int128 _denominator = ABDKMath64x64.fromUInt(denominator);
        int128 _probabilityPerSecond = ABDKMath64x64.fromUInt(probabilityPerSecond);

        // From the *probability per second* number, calculate the probability for this dice roll based on
        // the number of seconds since the last roll. randomNumber must be larger than this.
        probability = ABDKMath64x64.pow(
        // Convert from our fraction using our denominator, to a 64.64 fixed point number
            ABDKMath64x64.div(
            // reverse-probability of x: (1-x)
                ABDKMath64x64.sub(
                    _denominator,
                    _probabilityPerSecond
                ),
                _denominator
            ),
            secondsSinceLastRoll
        );

        // `randomNumber / (2**64)` would now give us the random number as a 10-base decimal number.
        // To show it in Solidity, which does not support non-integers, we could multiply to shift the
        // decimal point, for example:
        //    console.log("randomNumber",
        //      uint256(ABDKMath64x64.toUInt(
        //        ABDKMath64x64.mul(randomNumber, ABDKMath64x64.fromUInt(1000000))
        //      ))
        //    );
    }

    // Anyone can roll, but the beneficiary is incentivized to do so.
    //
    // # When using Chainlink VRF:
    // Make sure you have previously funded the contract with LINK. Since anyone can start a request at
    // any time, do not prefund the contract; send the tokens when you want to enable a roll.
    //
    // # When using the blockhash-based fallback method:
    // A future block is picked, whose hash will provide the randomness.
    // We accept as low-impact that a miner mining this block could withhold it. A user seed/reveal system
    // to counteract miner withholding introduces too much complexity (need to penalize users etc).
    function requestRoll(bool useFallback) external {
        require(doctor() == address(0), "rng-disabled");

        // If a roll is already scheduled, do nothing.
        if (isRolling()) { return; }

        if (useFallback) {
            // Two blocks from now, the block hash will provide the randomness to decide the outcome
            randomSeedBlock = block.number + 2;
        }
        else {
            chainlinkRequestId = requestRandomness(chainlinkKeyHash, chainlinkFee, block.timestamp);
        }

        // Calculate the probability for this roll, based on the current lastRollTime, before we update the latter.
        rollProbability = getProbability(block.timestamp);

        // Set the last roll time, which "consumes" parts of the total probability for a diagnosis
        lastRollTime = block.timestamp;

        emit RollInProgress(rollProbability);
    }

    // Callback: randomness is returned from Chainlink VRF
    function fulfillRandomness(bytes32 requestId, uint256 randomness) internal override {
        require(requestId == chainlinkRequestId, "invalid-request");
        chainlinkRandomNumber = randomness;
    }

    // Apply the results of the roll (run the randomness function, update NFTs).
    //
    // When using the block-hash based fallback randomness function:
    // If this is not called within 250 odd blocks, the hash of that block will no longer be accessible to us.
    // The roller thus has a possible reason *not* to call apply(), if the outcome is not as they desire.
    // We counteract this as follows:
    // - We consider an incomplete roll as a completed (which did not cause a state chance) for purposes of the
    //   compound probability. That is, you cannot increase the chance of any of the NFTs being diagnosed, you
    //   can only prevent it from happening. A caller looking to manipulate a roll would presumably desire a
    //   diagnosis, as they otherwise would simply do nothing.
    // - We counteract grieving (the repeated calling of pre-roll without calling apply, thus resetting the
    //   probability of a diagnosis) by letting anyone call `apply`, and emitting an event on `preroll`, to make
    //   it easy to watch for that.
    //
    // When using Chainlink VRF:
    //
    // In case we do not get a response from Chainlink within 2 hours, this can be called.
    //
    function applyRoll() external {
        require(isRolling(), "no-roll");

        bytes32 randomness;

        // Roll was started using the fallback random method based on the block hash
        if (randomSeedBlock > 0) {
            require(block.number > randomSeedBlock, "too-early");
            randomness = blockhash(randomSeedBlock);

            // The seed block is no longer available. We act as if the roll led to zero diagnoses.
            if (randomness <= 0) {
                resetRoll();
                return;
            }
        }

        // Roll was started using Chainlink VRF
        else {
            // No response from Chainlink
            if (chainlinkRandomNumber == 0 && block.timestamp - lastRollTime > 2 hours) {
                resetRoll();
                return;
            }

            require(chainlinkRandomNumber > 0, "too-early");
            randomness = bytes32(chainlinkRandomNumber);
        }

        _applyRandomness(randomness);
        resetRoll();
    }

    function _applyRandomness(bytes32 randomness) internal {
        for (uint i=0; i<this.totalSupply(); i++) {
            uint256 tokenId = this.tokenByIndex(i);

            // For each token, mix in the token id to get a new random number
            bytes32 hash = keccak256(abi.encodePacked(randomness, tokenId));

            // Now we want to convert the token hash to a number between 0 and 1.
            // - 64.64-bit fixed point is a int128  which represents the fraction `{int128}/(64**2)`.
            // - Thus, the lowest 64 bits of the int128 are essentially what is after the decimal point -
            //   the fractional part of the number.
            // - So taking only the lowest 64 bits from a token hash essentially gives us a random number
            //   between 0 and 1.

            // block hash is 256 bits - shift the left-most 64 bits into the right-most position, essentially
            // giving us a 64-bit number. Stored as an int128, this represents a fractional value between 0 and 1
            // in the format used by the 64.64 - fixed point library.
            int128 randomNumber = int128(uint256(hash) >> 192);
            //console.log("RANDOMNUMBER", uint256(randomNumber));

            if (randomNumber > rollProbability) {
                onDiagnosed(tokenId);
            }
        }
    }

    function resetRoll() internal {
        randomSeedBlock = 0;
        rollProbability = 0;
        chainlinkRequestId = 0;
        chainlinkRandomNumber = 0;
        emit RollComplete();
    }

    function isRolling() public view returns (bool) {
        return (randomSeedBlock > 0) || (chainlinkRequestId > 0);
    }

    function onDiagnosed(uint256 tokenId) internal virtual;
}

// File: contracts/Fees.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.7.0;

import "openzeppelin-solidity/contracts/introspection/ERC165.sol";

abstract contract IRoyalities {
    function getBeneficiary() internal virtual view returns (address);
    // Value between 0 and 100 (0% to 100%).
    function getFee(uint256 tokenId) virtual internal view returns (uint256);
}

interface IRaribleFees is IERC165 {
    // Rarible emits this when minting, we don't bother.
    //event SecondarySaleFees(uint256 tokenId, address[] recipients, uint[] bps);

    function getFeeRecipients(uint256 id) external view returns (address payable[] memory);
    // 1000 = 10%
    function getFeeBps(uint256 id) external view returns (uint[] memory);
}

/**
 * @dev Implementation of royalties for 721s
 *
 */
interface IERC2981 is IERC165 {
    /*
     * ERC165 bytes to add to interface array - set in parent contract implementing this standard
     *
     * bytes4(keccak256('royaltyInfo()')) == 0x46e80720
     * bytes4 private constant _INTERFACE_ID_ERC721ROYALTIES = 0x46e80720;
     * _registerInterface(_INTERFACE_ID_ERC721ROYALTIES);
     */
    /**

    /**
     * @notice Called to return both the creator's address and the royalty percentage - this would be the main
     *   function called by marketplaces unless they specifically need just the royaltyAmount
     * @notice Percentage is calculated as a fixed point with a scaling factor of 10,000, such that 100% would be
     *   the value (1.000.000) where, 1.000.000/10.000 = 100. 1% would be the value 10.000/10.000 = 1
     */
    function royaltyInfo(uint256 _tokenId) external returns (address receiver, uint256 amount);
}

abstract contract HasFees is ERC165, IRaribleFees, IRoyalities, IERC2981 {
    /*
     * bytes4(keccak256('getFeeBps(uint256)')) == 0x0ebd4c7f
     * bytes4(keccak256('getFeeRecipients(uint256)')) == 0xb9c4d9fb
     *
     * => 0x0ebd4c7f ^ 0xb9c4d9fb == 0xb7799584
     */
    bytes4 private constant _INTERFACE_ID_RARIBLE_FEES = 0xb7799584;

    /*
     * ERC165 bytes to add to interface array - set in parent contract implementing this standard
     *
     * bytes4(keccak256('royaltyInfo()')) == 0x46e80720
     */
    bytes4 private constant _INTERFACE_ID_ERC721ROYALTIES = 0x46e80720;

    constructor() {
        _registerInterface(_INTERFACE_ID_RARIBLE_FEES);
        _registerInterface(_INTERFACE_ID_ERC721ROYALTIES);
    }

    function getFeeRecipients(uint256) public override view returns (address payable[] memory) {
        address payable[] memory recipients = new address payable[](1);
        recipients[0] = payable(address(this));
        return recipients;
    }
    function getFeeBps(uint256 id) public override view returns (uint[] memory) {
        uint[] memory fees = new uint[](1);
        fees[0] = getFee(id) * 100;
        return fees;
    }

    // Implements the current version of https://eips.ethereum.org/EIPS/eip-2981
    function royaltyInfo(uint256 _tokenId) external view override returns (address receiver, uint256 amount) {
        return (address(this), getFee(_tokenId) * 10000);
    }
}

// File: openzeppelin-solidity/contracts/GSN/Context.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

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

// File: openzeppelin-solidity/contracts/token/ERC721/IERC721.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.2 <0.8.0;

import "../../introspection/IERC165.sol";

/**
 * @dev Required interface of an ERC721 compliant contract.
 */
interface IERC721 is IERC165 {
    /**
     * @dev Emitted when `tokenId` token is transferred from `from` to `to`.
     */
    event Transfer(address indexed from, address indexed to, uint256 indexed tokenId);

    /**
     * @dev Emitted when `owner` enables `approved` to manage the `tokenId` token.
     */
    event Approval(address indexed owner, address indexed approved, uint256 indexed tokenId);

    /**
     * @dev Emitted when `owner` enables or disables (`approved`) `operator` to manage all of its assets.
     */
    event ApprovalForAll(address indexed owner, address indexed operator, bool approved);

    /**
     * @dev Returns the number of tokens in ``owner``'s account.
     */
    function balanceOf(address owner) external view returns (uint256 balance);

    /**
     * @dev Returns the owner of the `tokenId` token.
     *
     * Requirements:
     *
     * - `tokenId` must exist.
     */
    function ownerOf(uint256 tokenId) external view returns (address owner);

    /**
     * @dev Safely transfers `tokenId` token from `from` to `to`, checking first that contract recipients
     * are aware of the ERC721 protocol to prevent tokens from being forever locked.
     *
     * Requirements:
     *
     * - `from` cannot be the zero address.
     * - `to` cannot be the zero address.
     * - `tokenId` token must exist and be owned by `from`.
     * - If the caller is not `from`, it must be have been allowed to move this token by either {approve} or {setApprovalForAll}.
     * - If `to` refers to a smart contract, it must implement {IERC721Receiver-onERC721Received}, which is called upon a safe transfer.
     *
     * Emits a {Transfer} event.
     */
    function safeTransferFrom(address from, address to, uint256 tokenId) external;

    /**
     * @dev Transfers `tokenId` token from `from` to `to`.
     *
     * WARNING: Usage of this method is discouraged, use {safeTransferFrom} whenever possible.
     *
     * Requirements:
     *
     * - `from` cannot be the zero address.
     * - `to` cannot be the zero address.
     * - `tokenId` token must be owned by `from`.
     * - If the caller is not `from`, it must be approved to move this token by either {approve} or {setApprovalForAll}.
     *
     * Emits a {Transfer} event.
     */
    function transferFrom(address from, address to, uint256 tokenId) external;

    /**
     * @dev Gives permission to `to` to transfer `tokenId` token to another account.
     * The approval is cleared when the token is transferred.
     *
     * Only a single account can be approved at a time, so approving the zero address clears previous approvals.
     *
     * Requirements:
     *
     * - The caller must own the token or be an approved operator.
     * - `tokenId` must exist.
     *
     * Emits an {Approval} event.
     */
    function approve(address to, uint256 tokenId) external;

    /**
     * @dev Returns the account approved for `tokenId` token.
     *
     * Requirements:
     *
     * - `tokenId` must exist.
     */
    function getApproved(uint256 tokenId) external view returns (address operator);

    /**
     * @dev Approve or remove `operator` as an operator for the caller.
     * Operators can call {transferFrom} or {safeTransferFrom} for any token owned by the caller.
     *
     * Requirements:
     *
     * - The `operator` cannot be the caller.
     *
     * Emits an {ApprovalForAll} event.
     */
    function setApprovalForAll(address operator, bool _approved) external;

    /**
     * @dev Returns if the `operator` is allowed to manage all of the assets of `owner`.
     *
     * See {setApprovalForAll}
     */
    function isApprovedForAll(address owner, address operator) external view returns (bool);

    /**
      * @dev Safely transfers `tokenId` token from `from` to `to`.
      *
      * Requirements:
      *
      * - `from` cannot be the zero address.
      * - `to` cannot be the zero address.
      * - `tokenId` token must exist and be owned by `from`.
      * - If the caller is not `from`, it must be approved to move this token by either {approve} or {setApprovalForAll}.
      * - If `to` refers to a smart contract, it must implement {IERC721Receiver-onERC721Received}, which is called upon a safe transfer.
      *
      * Emits a {Transfer} event.
      */
    function safeTransferFrom(address from, address to, uint256 tokenId, bytes calldata data) external;
}

// File: openzeppelin-solidity/contracts/token/ERC721/IERC721Metadata.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.2 <0.8.0;

import "./IERC721.sol";

/**
 * @title ERC-721 Non-Fungible Token Standard, optional metadata extension
 * @dev See https://eips.ethereum.org/EIPS/eip-721
 */
interface IERC721Metadata is IERC721 {

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

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

    /**
     * @dev Returns the Uniform Resource Identifier (URI) for `tokenId` token.
     */
    function tokenURI(uint256 tokenId) external view returns (string memory);
}

// File: openzeppelin-solidity/contracts/token/ERC721/IERC721Enumerable.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.2 <0.8.0;

import "./IERC721.sol";

/**
 * @title ERC-721 Non-Fungible Token Standard, optional enumeration extension
 * @dev See https://eips.ethereum.org/EIPS/eip-721
 */
interface IERC721Enumerable is IERC721 {

    /**
     * @dev Returns the total amount of tokens stored by the contract.
     */
    function totalSupply() external view returns (uint256);

    /**
     * @dev Returns a token ID owned by `owner` at a given `index` of its token list.
     * Use along with {balanceOf} to enumerate all of ``owner``'s tokens.
     */
    function tokenOfOwnerByIndex(address owner, uint256 index) external view returns (uint256 tokenId);

    /**
     * @dev Returns a token ID at a given `index` of all the tokens stored by the contract.
     * Use along with {totalSupply} to enumerate all tokens.
     */
    function tokenByIndex(uint256 index) external view returns (uint256);
}

// File: openzeppelin-solidity/contracts/token/ERC721/IERC721Receiver.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

/**
 * @title ERC721 token receiver interface
 * @dev Interface for any contract that wants to support safeTransfers
 * from ERC721 asset contracts.
 */
interface IERC721Receiver {
    /**
     * @dev Whenever an {IERC721} `tokenId` token is transferred to this contract via {IERC721-safeTransferFrom}
     * by `operator` from `from`, this function is called.
     *
     * It must return its Solidity selector to confirm the token transfer.
     * If any other value is returned or the interface is not implemented by the recipient, the transfer will be reverted.
     *
     * The selector can be obtained in Solidity with `IERC721.onERC721Received.selector`.
     */
    function onERC721Received(address operator, address from, uint256 tokenId, bytes calldata data) external returns (bytes4);
}

// File: openzeppelin-solidity/contracts/introspection/ERC165.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

import "./IERC165.sol";

/**
 * @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;
    }
}

// File: openzeppelin-solidity/contracts/math/SafeMath.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

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

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

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

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

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

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

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

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

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

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

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

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

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

// File: openzeppelin-solidity/contracts/utils/Address.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.2 <0.8.0;

/**
 * @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 v3.4._
     */
    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);
            }
        }
    }
}

// File: openzeppelin-solidity/contracts/utils/EnumerableSet.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

/**
 * @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 v3.3.0, sets of type `bytes32` (`Bytes32Set`), `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];
    }

    // Bytes32Set

    struct Bytes32Set {
        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(Bytes32Set storage set, bytes32 value) internal returns (bool) {
        return _add(set._inner, 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(Bytes32Set storage set, bytes32 value) internal returns (bool) {
        return _remove(set._inner, value);
    }

    /**
     * @dev Returns true if the value is in the set. O(1).
     */
    function contains(Bytes32Set storage set, bytes32 value) internal view returns (bool) {
        return _contains(set._inner, value);
    }

    /**
     * @dev Returns the number of values in the set. O(1).
     */
    function length(Bytes32Set 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(Bytes32Set storage set, uint256 index) internal view returns (bytes32) {
        return _at(set._inner, 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(uint160(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(uint160(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(uint160(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(uint160(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));
    }
}

// File: openzeppelin-solidity/contracts/utils/EnumerableMap.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

/**
 * @dev Library for managing an enumerable variant of Solidity's
 * https://solidity.readthedocs.io/en/latest/types.html#mapping-types[`mapping`]
 * type.
 *
 * Maps have the following properties:
 *
 * - Entries are added, removed, and checked for existence in constant time
 * (O(1)).
 * - Entries are enumerated in O(n). No guarantees are made on the ordering.
 *
 * ```
 * contract Example {
 *     // Add the library methods
 *     using EnumerableMap for EnumerableMap.UintToAddressMap;
 *
 *     // Declare a set state variable
 *     EnumerableMap.UintToAddressMap private myMap;
 * }
 * ```
 *
 * As of v3.0.0, only maps of type `uint256 -> address` (`UintToAddressMap`) are
 * supported.
 */
library EnumerableMap {
    // To implement this library for multiple types with as little code
    // repetition as possible, we write it in terms of a generic Map type with
    // bytes32 keys and values.
    // The Map implementation uses private functions, and user-facing
    // implementations (such as Uint256ToAddressMap) are just wrappers around
    // the underlying Map.
    // This means that we can only create new EnumerableMaps for types that fit
    // in bytes32.

    struct MapEntry {
        bytes32 _key;
        bytes32 _value;
    }

    struct Map {
        // Storage of map keys and values
        MapEntry[] _entries;

        // Position of the entry defined by a key in the `entries` array, plus 1
        // because index 0 means a key is not in the map.
        mapping (bytes32 => uint256) _indexes;
    }

    /**
     * @dev Adds a key-value pair to a map, or updates the value for an existing
     * key. O(1).
     *
     * Returns true if the key was added to the map, that is if it was not
     * already present.
     */
    function _set(Map storage map, bytes32 key, bytes32 value) private returns (bool) {
        // We read and store the key's index to prevent multiple reads from the same storage slot
        uint256 keyIndex = map._indexes[key];

        if (keyIndex == 0) { // Equivalent to !contains(map, key)
            map._entries.push(MapEntry({ _key: key, _value: value }));
            // The entry is stored at length-1, but we add 1 to all indexes
            // and use 0 as a sentinel value
            map._indexes[key] = map._entries.length;
            return true;
        } else {
            map._entries[keyIndex - 1]._value = value;
            return false;
        }
    }

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

        if (keyIndex != 0) { // Equivalent to contains(map, key)
            // To delete a key-value pair from the _entries array in O(1), we swap the entry to delete with the last one
            // in the array, and then remove the last entry (sometimes called as 'swap and pop').
            // This modifies the order of the array, as noted in {at}.

            uint256 toDeleteIndex = keyIndex - 1;
            uint256 lastIndex = map._entries.length - 1;

            // When the entry 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.

            MapEntry storage lastEntry = map._entries[lastIndex];

            // Move the last entry to the index where the entry to delete is
            map._entries[toDeleteIndex] = lastEntry;
            // Update the index for the moved entry
            map._indexes[lastEntry._key] = toDeleteIndex + 1; // All indexes are 1-based

            // Delete the slot where the moved entry was stored
            map._entries.pop();

            // Delete the index for the deleted slot
            delete map._indexes[key];

            return true;
        } else {
            return false;
        }
    }

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

    /**
     * @dev Returns the number of key-value pairs in the map. O(1).
     */
    function _length(Map storage map) private view returns (uint256) {
        return map._entries.length;
    }

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

        MapEntry storage entry = map._entries[index];
        return (entry._key, entry._value);
    }

    /**
     * @dev Tries to returns the value associated with `key`.  O(1).
     * Does not revert if `key` is not in the map.
     */
    function _tryGet(Map storage map, bytes32 key) private view returns (bool, bytes32) {
        uint256 keyIndex = map._indexes[key];
        if (keyIndex == 0) return (false, 0); // Equivalent to contains(map, key)
        return (true, map._entries[keyIndex - 1]._value); // All indexes are 1-based
    }

    /**
     * @dev Returns the value associated with `key`.  O(1).
     *
     * Requirements:
     *
     * - `key` must be in the map.
     */
    function _get(Map storage map, bytes32 key) private view returns (bytes32) {
        uint256 keyIndex = map._indexes[key];
        require(keyIndex != 0, "EnumerableMap: nonexistent key"); // Equivalent to contains(map, key)
        return map._entries[keyIndex - 1]._value; // All indexes are 1-based
    }

    /**
     * @dev Same as {_get}, with a custom error message when `key` is not in the map.
     *
     * CAUTION: This function is deprecated because it requires allocating memory for the error
     * message unnecessarily. For custom revert reasons use {_tryGet}.
     */
    function _get(Map storage map, bytes32 key, string memory errorMessage) private view returns (bytes32) {
        uint256 keyIndex = map._indexes[key];
        require(keyIndex != 0, errorMessage); // Equivalent to contains(map, key)
        return map._entries[keyIndex - 1]._value; // All indexes are 1-based
    }

    // UintToAddressMap

    struct UintToAddressMap {
        Map _inner;
    }

    /**
     * @dev Adds a key-value pair to a map, or updates the value for an existing
     * key. O(1).
     *
     * Returns true if the key was added to the map, that is if it was not
     * already present.
     */
    function set(UintToAddressMap storage map, uint256 key, address value) internal returns (bool) {
        return _set(map._inner, bytes32(key), bytes32(uint256(uint160(value))));
    }

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

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

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

   /**
    * @dev Returns the element 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(UintToAddressMap storage map, uint256 index) internal view returns (uint256, address) {
        (bytes32 key, bytes32 value) = _at(map._inner, index);
        return (uint256(key), address(uint160(uint256(value))));
    }

    /**
     * @dev Tries to returns the value associated with `key`.  O(1).
     * Does not revert if `key` is not in the map.
     *
     * _Available since v3.4._
     */
    function tryGet(UintToAddressMap storage map, uint256 key) internal view returns (bool, address) {
        (bool success, bytes32 value) = _tryGet(map._inner, bytes32(key));
        return (success, address(uint160(uint256(value))));
    }

    /**
     * @dev Returns the value associated with `key`.  O(1).
     *
     * Requirements:
     *
     * - `key` must be in the map.
     */
    function get(UintToAddressMap storage map, uint256 key) internal view returns (address) {
        return address(uint160(uint256(_get(map._inner, bytes32(key)))));
    }

    /**
     * @dev Same as {get}, with a custom error message when `key` is not in the map.
     *
     * CAUTION: This function is deprecated because it requires allocating memory for the error
     * message unnecessarily. For custom revert reasons use {tryGet}.
     */
    function get(UintToAddressMap storage map, uint256 key, string memory errorMessage) internal view returns (address) {
        return address(uint160(uint256(_get(map._inner, bytes32(key), errorMessage))));
    }
}

// File: openzeppelin-solidity/contracts/utils/Strings.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

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

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

// File: openzeppelin-solidity/contracts/utils/Context.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

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

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

// File: openzeppelin-solidity/contracts/introspection/IERC165.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

/**
 * @dev Interface of the ERC165 standard, as defined in the
 * https://eips.ethereum.org/EIPS/eip-165[EIP].
 *
 * Implementers can declare support of contract interfaces, which can then be
 * queried by others ({ERC165Checker}).
 *
 * For an implementation, see {ERC165}.
 */
interface 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);
}

// File: contracts/ABDKMath64x64.sol



// SPDX-License-Identifier: BSD-4-Clause
/*
 * ABDK Math 64.64 Smart Contract Library.  Copyright © 2019 by ABDK Consulting.
 * Author: Mikhail Vladimirov <mikhail.vladimirov@gmail.com>
 */
pragma solidity ^0.7.0;

/**
 * Smart contract library of mathematical functions operating with signed
 * 64.64-bit fixed point numbers.  Signed 64.64-bit fixed point number is
 * basically a simple fraction whose numerator is signed 128-bit integer and
 * denominator is 2^64.  As long as denominator is always the same, there is no
 * need to store it, thus in Solidity signed 64.64-bit fixed point numbers are
 * represented by int128 type holding only the numerator.
 */
library ABDKMath64x64 {
    /*
     * Minimum value signed 64.64-bit fixed point number may have.
     */
    int128 private constant MIN_64x64 = -0x80000000000000000000000000000000;

    /*
     * Maximum value signed 64.64-bit fixed point number may have.
     */
    int128 private constant MAX_64x64 = 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF;

    /**
     * Convert signed 256-bit integer number into signed 64.64-bit fixed point
     * number.  Revert on overflow.
     *
     * @param x signed 256-bit integer number
     * @return signed 64.64-bit fixed point number
     */
    function fromInt (int256 x) internal pure returns (int128) {
        require (x >= -0x8000000000000000 && x <= 0x7FFFFFFFFFFFFFFF);
        return int128 (x << 64);
    }

    /**
     * Convert signed 64.64 fixed point number into signed 64-bit integer number
     * rounding down.
     *
     * @param x signed 64.64-bit fixed point number
     * @return signed 64-bit integer number
     */
    function toInt (int128 x) internal pure returns (int64) {
        return int64 (x >> 64);
    }

    /**
     * Convert unsigned 256-bit integer number into signed 64.64-bit fixed point
     * number.  Revert on overflow.
     *
     * @param x unsigned 256-bit integer number
     * @return signed 64.64-bit fixed point number
     */
    function fromUInt (uint256 x) internal pure returns (int128) {
        require (x <= 0x7FFFFFFFFFFFFFFF);
        return int128 (x << 64);
    }

    /**
     * Convert signed 64.64 fixed point number into unsigned 64-bit integer
     * number rounding down.  Revert on underflow.
     *
     * @param x signed 64.64-bit fixed point number
     * @return unsigned 64-bit integer number
     */
    function toUInt (int128 x) internal pure returns (uint64) {
        require (x >= 0);
        return uint64 (x >> 64);
    }

    /**
     * Convert signed 128.128 fixed point number into signed 64.64-bit fixed point
     * number rounding down.  Revert on overflow.
     *
     * @param x signed 128.128-bin fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function from128x128 (int256 x) internal pure returns (int128) {
        int256 result = x >> 64;
        require (result >= MIN_64x64 && result <= MAX_64x64);
        return int128 (result);
    }

    /**
     * Convert signed 64.64 fixed point number into signed 128.128 fixed point
     * number.
     *
     * @param x signed 64.64-bit fixed point number
     * @return signed 128.128 fixed point number
     */
    function to128x128 (int128 x) internal pure returns (int256) {
        return int256 (x) << 64;
    }

    /**
     * Calculate x + y.  Revert on overflow.
     *
     * @param x signed 64.64-bit fixed point number
     * @param y signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function add (int128 x, int128 y) internal pure returns (int128) {
        int256 result = int256(x) + y;
        require (result >= MIN_64x64 && result <= MAX_64x64);
        return int128 (result);
    }

    /**
     * Calculate x - y.  Revert on overflow.
     *
     * @param x signed 64.64-bit fixed point number
     * @param y signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function sub (int128 x, int128 y) internal pure returns (int128) {
        int256 result = int256(x) - y;
        require (result >= MIN_64x64 && result <= MAX_64x64);
        return int128 (result);
    }

    /**
     * Calculate x * y rounding down.  Revert on overflow.
     *
     * @param x signed 64.64-bit fixed point number
     * @param y signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function mul (int128 x, int128 y) internal pure returns (int128) {
        int256 result = int256(x) * y >> 64;
        require (result >= MIN_64x64 && result <= MAX_64x64);
        return int128 (result);
    }

    /**
     * Calculate x * y rounding towards zero, where x is signed 64.64 fixed point
     * number and y is signed 256-bit integer number.  Revert on overflow.
     *
     * @param x signed 64.64 fixed point number
     * @param y signed 256-bit integer number
     * @return signed 256-bit integer number
     */
    function muli (int128 x, int256 y) internal pure returns (int256) {
        if (x == MIN_64x64) {
            require (y >= -0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF &&
            y <= 0x1000000000000000000000000000000000000000000000000);
            return -y << 63;
        } else {
            bool negativeResult = false;
            if (x < 0) {
                x = -x;
                negativeResult = true;
            }
            if (y < 0) {
                y = -y; // We rely on overflow behavior here
                negativeResult = !negativeResult;
            }
            uint256 absoluteResult = mulu (x, uint256 (y));
            if (negativeResult) {
                require (absoluteResult <=
                    0x8000000000000000000000000000000000000000000000000000000000000000);
                return -int256 (absoluteResult); // We rely on overflow behavior here
            } else {
                require (absoluteResult <=
                    0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);
                return int256 (absoluteResult);
            }
        }
    }

    /**
     * Calculate x * y rounding down, where x is signed 64.64 fixed point number
     * and y is unsigned 256-bit integer number.  Revert on overflow.
     *
     * @param x signed 64.64 fixed point number
     * @param y unsigned 256-bit integer number
     * @return unsigned 256-bit integer number
     */
    function mulu (int128 x, uint256 y) internal pure returns (uint256) {
        if (y == 0) return 0;

        require (x >= 0);

        uint256 lo = (uint256 (x) * (y & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF)) >> 64;
        uint256 hi = uint256 (x) * (y >> 128);

        require (hi <= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);
        hi <<= 64;

        require (hi <=
            0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF - lo);
        return hi + lo;
    }

    /**
     * Calculate x / y rounding towards zero.  Revert on overflow or when y is
     * zero.
     *
     * @param x signed 64.64-bit fixed point number
     * @param y signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function div (int128 x, int128 y) internal pure returns (int128) {
        require (y != 0);
        int256 result = (int256 (x) << 64) / y;
        require (result >= MIN_64x64 && result <= MAX_64x64);
        return int128 (result);
    }

    /**
     * Calculate x / y rounding towards zero, where x and y are signed 256-bit
     * integer numbers.  Revert on overflow or when y is zero.
     *
     * @param x signed 256-bit integer number
     * @param y signed 256-bit integer number
     * @return signed 64.64-bit fixed point number
     */
    function divi (int256 x, int256 y) internal pure returns (int128) {
        require (y != 0);

        bool negativeResult = false;
        if (x < 0) {
            x = -x; // We rely on overflow behavior here
            negativeResult = true;
        }
        if (y < 0) {
            y = -y; // We rely on overflow behavior here
            negativeResult = !negativeResult;
        }
        uint128 absoluteResult = divuu (uint256 (x), uint256 (y));
        if (negativeResult) {
            require (absoluteResult <= 0x80000000000000000000000000000000);
            return -int128 (absoluteResult); // We rely on overflow behavior here
        } else {
            require (absoluteResult <= 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);
            return int128 (absoluteResult); // We rely on overflow behavior here
        }
    }

    /**
     * Calculate x / y rounding towards zero, where x and y are unsigned 256-bit
     * integer numbers.  Revert on overflow or when y is zero.
     *
     * @param x unsigned 256-bit integer number
     * @param y unsigned 256-bit integer number
     * @return signed 64.64-bit fixed point number
     */
    function divu (uint256 x, uint256 y) internal pure returns (int128) {
        require (y != 0);
        uint128 result = divuu (x, y);
        require (result <= uint128 (MAX_64x64));
        return int128 (result);
    }

    /**
     * Calculate -x.  Revert on overflow.
     *
     * @param x signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function neg (int128 x) internal pure returns (int128) {
        require (x != MIN_64x64);
        return -x;
    }

    /**
     * Calculate |x|.  Revert on overflow.
     *
     * @param x signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function abs (int128 x) internal pure returns (int128) {
        require (x != MIN_64x64);
        return x < 0 ? -x : x;
    }

    /**
     * Calculate 1 / x rounding towards zero.  Revert on overflow or when x is
     * zero.
     *
     * @param x signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function inv (int128 x) internal pure returns (int128) {
        require (x != 0);
        int256 result = int256 (0x100000000000000000000000000000000) / x;
        require (result >= MIN_64x64 && result <= MAX_64x64);
        return int128 (result);
    }

    /**
     * Calculate arithmetics average of x and y, i.e. (x + y) / 2 rounding down.
     *
     * @param x signed 64.64-bit fixed point number
     * @param y signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function avg (int128 x, int128 y) internal pure returns (int128) {
        return int128 ((int256 (x) + int256 (y)) >> 1);
    }

    /**
     * Calculate geometric average of x and y, i.e. sqrt (x * y) rounding down.
     * Revert on overflow or in case x * y is negative.
     *
     * @param x signed 64.64-bit fixed point number
     * @param y signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function gavg (int128 x, int128 y) internal pure returns (int128) {
        int256 m = int256 (x) * int256 (y);
        require (m >= 0);
        require (m <
            0x4000000000000000000000000000000000000000000000000000000000000000);
        return int128 (sqrtu (uint256 (m)));
    }

    /**
     * Calculate x^y assuming 0^0 is 1, where x is signed 64.64 fixed point number
     * and y is unsigned 256-bit integer number.  Revert on overflow.
     *
     * @param x signed 64.64-bit fixed point number
     * @param y uint256 value
     * @return signed 64.64-bit fixed point number
     */
    function pow (int128 x, uint256 y) internal pure returns (int128) {
        uint256 absoluteResult;
        bool negativeResult = false;
        if (x >= 0) {
            absoluteResult = powu (uint256 (x) << 63, y);
        } else {
            // We rely on overflow behavior here
            absoluteResult = powu (uint256 (uint128 (-x)) << 63, y);
            negativeResult = y & 1 > 0;
        }

        absoluteResult >>= 63;

        if (negativeResult) {
            require (absoluteResult <= 0x80000000000000000000000000000000);
            return -int128 (absoluteResult); // We rely on overflow behavior here
        } else {
            require (absoluteResult <= 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);
            return int128 (absoluteResult); // We rely on overflow behavior here
        }
    }

    /**
     * Calculate sqrt (x) rounding down.  Revert if x < 0.
     *
     * @param x signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function sqrt (int128 x) internal pure returns (int128) {
        require (x >= 0);
        return int128 (sqrtu (uint256 (x) << 64));
    }

    /**
     * Calculate binary logarithm of x.  Revert if x <= 0.
     *
     * @param x signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function log_2 (int128 x) internal pure returns (int128) {
        require (x > 0);

        int256 msb = 0;
        int256 xc = x;
        if (xc >= 0x10000000000000000) { xc >>= 64; msb += 64; }
        if (xc >= 0x100000000) { xc >>= 32; msb += 32; }
        if (xc >= 0x10000) { xc >>= 16; msb += 16; }
        if (xc >= 0x100) { xc >>= 8; msb += 8; }
        if (xc >= 0x10) { xc >>= 4; msb += 4; }
        if (xc >= 0x4) { xc >>= 2; msb += 2; }
        if (xc >= 0x2) msb += 1;  // No need to shift xc anymore

        int256 result = msb - 64 << 64;
        uint256 ux = uint256 (x) << uint256 (127 - msb);
        for (int256 bit = 0x8000000000000000; bit > 0; bit >>= 1) {
            ux *= ux;
            uint256 b = ux >> 255;
            ux >>= 127 + b;
            result += bit * int256 (b);
        }

        return int128 (result);
    }

    /**
     * Calculate natural logarithm of x.  Revert if x <= 0.
     *
     * @param x signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function ln (int128 x) internal pure returns (int128) {
        require (x > 0);

        return int128 (
            uint256 (log_2 (x)) * 0xB17217F7D1CF79ABC9E3B39803F2F6AF >> 128);
    }

    /**
     * Calculate binary exponent of x.  Revert on overflow.
     *
     * @param x signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function exp_2 (int128 x) internal pure returns (int128) {
        require (x < 0x400000000000000000); // Overflow

        if (x < -0x400000000000000000) return 0; // Underflow

        uint256 result = 0x80000000000000000000000000000000;

        if (x & 0x8000000000000000 > 0)
            result = result * 0x16A09E667F3BCC908B2FB1366EA957D3E >> 128;
        if (x & 0x4000000000000000 > 0)
            result = result * 0x1306FE0A31B7152DE8D5A46305C85EDEC >> 128;
        if (x & 0x2000000000000000 > 0)
            result = result * 0x1172B83C7D517ADCDF7C8C50EB14A791F >> 128;
        if (x & 0x1000000000000000 > 0)
            result = result * 0x10B5586CF9890F6298B92B71842A98363 >> 128;
        if (x & 0x800000000000000 > 0)
            result = result * 0x1059B0D31585743AE7C548EB68CA417FD >> 128;
        if (x & 0x400000000000000 > 0)
            result = result * 0x102C9A3E778060EE6F7CACA4F7A29BDE8 >> 128;
        if (x & 0x200000000000000 > 0)
            result = result * 0x10163DA9FB33356D84A66AE336DCDFA3F >> 128;
        if (x & 0x100000000000000 > 0)
            result = result * 0x100B1AFA5ABCBED6129AB13EC11DC9543 >> 128;
        if (x & 0x80000000000000 > 0)
            result = result * 0x10058C86DA1C09EA1FF19D294CF2F679B >> 128;
        if (x & 0x40000000000000 > 0)
            result = result * 0x1002C605E2E8CEC506D21BFC89A23A00F >> 128;
        if (x & 0x20000000000000 > 0)
            result = result * 0x100162F3904051FA128BCA9C55C31E5DF >> 128;
        if (x & 0x10000000000000 > 0)
            result = result * 0x1000B175EFFDC76BA38E31671CA939725 >> 128;
        if (x & 0x8000000000000 > 0)
            result = result * 0x100058BA01FB9F96D6CACD4B180917C3D >> 128;
        if (x & 0x4000000000000 > 0)
            result = result * 0x10002C5CC37DA9491D0985C348C68E7B3 >> 128;
        if (x & 0x2000000000000 > 0)
            result = result * 0x1000162E525EE054754457D5995292026 >> 128;
        if (x & 0x1000000000000 > 0)
            result = result * 0x10000B17255775C040618BF4A4ADE83FC >> 128;
        if (x & 0x800000000000 > 0)
            result = result * 0x1000058B91B5BC9AE2EED81E9B7D4CFAB >> 128;
        if (x & 0x400000000000 > 0)
            result = result * 0x100002C5C89D5EC6CA4D7C8ACC017B7C9 >> 128;
        if (x & 0x200000000000 > 0)
            result = result * 0x10000162E43F4F831060E02D839A9D16D >> 128;
        if (x & 0x100000000000 > 0)
            result = result * 0x100000B1721BCFC99D9F890EA06911763 >> 128;
        if (x & 0x80000000000 > 0)
            result = result * 0x10000058B90CF1E6D97F9CA14DBCC1628 >> 128;
        if (x & 0x40000000000 > 0)
            result = result * 0x1000002C5C863B73F016468F6BAC5CA2B >> 128;
        if (x & 0x20000000000 > 0)
            result = result * 0x100000162E430E5A18F6119E3C02282A5 >> 128;
        if (x & 0x10000000000 > 0)
            result = result * 0x1000000B1721835514B86E6D96EFD1BFE >> 128;
        if (x & 0x8000000000 > 0)
            result = result * 0x100000058B90C0B48C6BE5DF846C5B2EF >> 128;
        if (x & 0x4000000000 > 0)
            result = result * 0x10000002C5C8601CC6B9E94213C72737A >> 128;
        if (x & 0x2000000000 > 0)
            result = result * 0x1000000162E42FFF037DF38AA2B219F06 >> 128;
        if (x & 0x1000000000 > 0)
            result = result * 0x10000000B17217FBA9C739AA5819F44F9 >> 128;
        if (x & 0x800000000 > 0)
            result = result * 0x1000000058B90BFCDEE5ACD3C1CEDC823 >> 128;
        if (x & 0x400000000 > 0)
            result = result * 0x100000002C5C85FE31F35A6A30DA1BE50 >> 128;
        if (x & 0x200000000 > 0)
            result = result * 0x10000000162E42FF0999CE3541B9FFFCF >> 128;
        if (x & 0x100000000 > 0)
            result = result * 0x100000000B17217F80F4EF5AADDA45554 >> 128;
        if (x & 0x80000000 > 0)
            result = result * 0x10000000058B90BFBF8479BD5A81B51AD >> 128;
        if (x & 0x40000000 > 0)
            result = result * 0x1000000002C5C85FDF84BD62AE30A74CC >> 128;
        if (x & 0x20000000 > 0)
            result = result * 0x100000000162E42FEFB2FED257559BDAA >> 128;
        if (x & 0x10000000 > 0)
            result = result * 0x1000000000B17217F7D5A7716BBA4A9AE >> 128;
        if (x & 0x8000000 > 0)
            result = result * 0x100000000058B90BFBE9DDBAC5E109CCE >> 128;
        if (x & 0x4000000 > 0)
            result = result * 0x10000000002C5C85FDF4B15DE6F17EB0D >> 128;
        if (x & 0x2000000 > 0)
            result = result * 0x1000000000162E42FEFA494F1478FDE05 >> 128;
        if (x & 0x1000000 > 0)
            result = result * 0x10000000000B17217F7D20CF927C8E94C >> 128;
        if (x & 0x800000 > 0)
            result = result * 0x1000000000058B90BFBE8F71CB4E4B33D >> 128;
        if (x & 0x400000 > 0)
            result = result * 0x100000000002C5C85FDF477B662B26945 >> 128;
        if (x & 0x200000 > 0)
            result = result * 0x10000000000162E42FEFA3AE53369388C >> 128;
        if (x & 0x100000 > 0)
            result = result * 0x100000000000B17217F7D1D351A389D40 >> 128;
        if (x & 0x80000 > 0)
            result = result * 0x10000000000058B90BFBE8E8B2D3D4EDE >> 128;
        if (x & 0x40000 > 0)
            result = result * 0x1000000000002C5C85FDF4741BEA6E77E >> 128;
        if (x & 0x20000 > 0)
            result = result * 0x100000000000162E42FEFA39FE95583C2 >> 128;
        if (x & 0x10000 > 0)
            result = result * 0x1000000000000B17217F7D1CFB72B45E1 >> 128;
        if (x & 0x8000 > 0)
            result = result * 0x100000000000058B90BFBE8E7CC35C3F0 >> 128;
        if (x & 0x4000 > 0)
            result = result * 0x10000000000002C5C85FDF473E242EA38 >> 128;
        if (x & 0x2000 > 0)
            result = result * 0x1000000000000162E42FEFA39F02B772C >> 128;
        if (x & 0x1000 > 0)
            result = result * 0x10000000000000B17217F7D1CF7D83C1A >> 128;
        if (x & 0x800 > 0)
            result = result * 0x1000000000000058B90BFBE8E7BDCBE2E >> 128;
        if (x & 0x400 > 0)
            result = result * 0x100000000000002C5C85FDF473DEA871F >> 128;
        if (x & 0x200 > 0)
            result = result * 0x10000000000000162E42FEFA39EF44D91 >> 128;
        if (x & 0x100 > 0)
            result = result * 0x100000000000000B17217F7D1CF79E949 >> 128;
        if (x & 0x80 > 0)
            result = result * 0x10000000000000058B90BFBE8E7BCE544 >> 128;
        if (x & 0x40 > 0)
            result = result * 0x1000000000000002C5C85FDF473DE6ECA >> 128;
        if (x & 0x20 > 0)
            result = result * 0x100000000000000162E42FEFA39EF366F >> 128;
        if (x & 0x10 > 0)
            result = result * 0x1000000000000000B17217F7D1CF79AFA >> 128;
        if (x & 0x8 > 0)
            result = result * 0x100000000000000058B90BFBE8E7BCD6D >> 128;
        if (x & 0x4 > 0)
            result = result * 0x10000000000000002C5C85FDF473DE6B2 >> 128;
        if (x & 0x2 > 0)
            result = result * 0x1000000000000000162E42FEFA39EF358 >> 128;
        if (x & 0x1 > 0)
            result = result * 0x10000000000000000B17217F7D1CF79AB >> 128;

        result >>= uint256 (63 - (x >> 64));
        require (result <= uint256 (MAX_64x64));

        return int128 (result);
    }

    /**
     * Calculate natural exponent of x.  Revert on overflow.
     *
     * @param x signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function exp (int128 x) internal pure returns (int128) {
        require (x < 0x400000000000000000); // Overflow

        if (x < -0x400000000000000000) return 0; // Underflow

        return exp_2 (
            int128 (int256 (x) * 0x171547652B82FE1777D0FFDA0D23A7D12 >> 128));
    }

    /**
     * Calculate x / y rounding towards zero, where x and y are unsigned 256-bit
     * integer numbers.  Revert on overflow or when y is zero.
     *
     * @param x unsigned 256-bit integer number
     * @param y unsigned 256-bit integer number
     * @return unsigned 64.64-bit fixed point number
     */
    function divuu (uint256 x, uint256 y) private pure returns (uint128) {
        require (y != 0);

        uint256 result;

        if (x <= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF)
            result = (x << 64) / y;
        else {
            uint256 msb = 192;
            uint256 xc = x >> 192;
            if (xc >= 0x100000000) { xc >>= 32; msb += 32; }
            if (xc >= 0x10000) { xc >>= 16; msb += 16; }
            if (xc >= 0x100) { xc >>= 8; msb += 8; }
            if (xc >= 0x10) { xc >>= 4; msb += 4; }
            if (xc >= 0x4) { xc >>= 2; msb += 2; }
            if (xc >= 0x2) msb += 1;  // No need to shift xc anymore

            result = (x << 255 - msb) / ((y - 1 >> msb - 191) + 1);
            require (result <= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);

            uint256 hi = result * (y >> 128);
            uint256 lo = result * (y & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);

            uint256 xh = x >> 192;
            uint256 xl = x << 64;

            if (xl < lo) xh -= 1;
            xl -= lo; // We rely on overflow behavior here
            lo = hi << 128;
            if (xl < lo) xh -= 1;
            xl -= lo; // We rely on overflow behavior here

            assert (xh == hi >> 128);

            result += xl / y;
        }

        require (result <= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);
        return uint128 (result);
    }

    /**
     * Calculate x^y assuming 0^0 is 1, where x is unsigned 129.127 fixed point
     * number and y is unsigned 256-bit integer number.  Revert on overflow.
     *
     * @param x unsigned 129.127-bit fixed point number
     * @param y uint256 value
     * @return unsigned 129.127-bit fixed point number
     */
    function powu (uint256 x, uint256 y) private pure returns (uint256) {
        if (y == 0) return 0x80000000000000000000000000000000;
        else if (x == 0) return 0;
        else {
            int256 msb = 0;
            uint256 xc = x;
            if (xc >= 0x100000000000000000000000000000000) { xc >>= 128; msb += 128; }
            if (xc >= 0x10000000000000000) { xc >>= 64; msb += 64; }
            if (xc >= 0x100000000) { xc >>= 32; msb += 32; }
            if (xc >= 0x10000) { xc >>= 16; msb += 16; }
            if (xc >= 0x100) { xc >>= 8; msb += 8; }
            if (xc >= 0x10) { xc >>= 4; msb += 4; }
            if (xc >= 0x4) { xc >>= 2; msb += 2; }
            if (xc >= 0x2) msb += 1;  // No need to shift xc anymore

            int256 xe = msb - 127;
            if (xe > 0) x >>= uint256 (xe);
            else x <<= uint256 (-xe);

            uint256 result = 0x80000000000000000000000000000000;
            int256 re = 0;

            while (y > 0) {
                if (y & 1 > 0) {
                    result = result * x;
                    y -= 1;
                    re += xe;
                    if (result >=
                        0x8000000000000000000000000000000000000000000000000000000000000000) {
                        result >>= 128;
                        re += 1;
                    } else result >>= 127;
                    if (re < -127) return 0; // Underflow
                    require (re < 128); // Overflow
                } else {
                    x = x * x;
                    y >>= 1;
                    xe <<= 1;
                    if (x >=
                        0x8000000000000000000000000000000000000000000000000000000000000000) {
                        x >>= 128;
                        xe += 1;
                    } else x >>= 127;
                    if (xe < -127) return 0; // Underflow
                    require (xe < 128); // Overflow
                }
            }

            if (re > 0) result <<= uint256 (re);
            else if (re < 0) result >>= uint256 (-re);

            return result;
        }
    }

    /**
     * Calculate sqrt (x) rounding down, where x is unsigned 256-bit integer
     * number.
     *
     * @param x unsigned 256-bit integer number
     * @return unsigned 128-bit integer number
     */
    function sqrtu (uint256 x) private pure returns (uint128) {
        if (x == 0) return 0;
        else {
            uint256 xx = x;
            uint256 r = 1;
            if (xx >= 0x100000000000000000000000000000000) { xx >>= 128; r <<= 64; }
            if (xx >= 0x10000000000000000) { xx >>= 64; r <<= 32; }
            if (xx >= 0x100000000) { xx >>= 32; r <<= 16; }
            if (xx >= 0x10000) { xx >>= 16; r <<= 8; }
            if (xx >= 0x100) { xx >>= 8; r <<= 4; }
            if (xx >= 0x10) { xx >>= 4; r <<= 2; }
            if (xx >= 0x8) { r <<= 1; }
            r = (r + x / r) >> 1;
            r = (r + x / r) >> 1;
            r = (r + x / r) >> 1;
            r = (r + x / r) >> 1;
            r = (r + x / r) >> 1;
            r = (r + x / r) >> 1;
            r = (r + x / r) >> 1; // Seven iterations should be enough
            uint256 r1 = x / r;
            return uint128 (r < r1 ? r : r1);
        }
    }
}
// File: contracts/ChainlinkVRF.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.7.0;

import "./LinkTokenInterface.sol";
import "openzeppelin-solidity/contracts/math/SafeMath.sol";


// See VRFConsumerBase.sol and VRFRequestIDBase.sol from Chainlink.
abstract contract ChainlinkVRF {
    using SafeMath for uint256;

    /**
     * @notice fulfillRandomness handles the VRF response.
     */
    function fulfillRandomness(bytes32 requestId, uint256 randomness) internal virtual;

    /**
     * @notice requestRandomness initiates a request for VRF output given _seed
     */
    function requestRandomness(bytes32 _keyHash, uint256 _fee, uint256 _seed)  internal returns (bytes32 requestId)
    {
        LINK.transferAndCall(vrfCoordinator, _fee, abi.encode(_keyHash, _seed));
        // This is the seed passed to VRFCoordinator. The oracle will mix this with
        // the hash of the block containing this request to obtain the seed/input
        // which is finally passed to the VRF cryptographic machinery.
        uint256 vRFSeed  = makeVRFInputSeed(_keyHash, _seed, address(this), nonces[_keyHash]);
        // nonces[_keyHash] must stay in sync with
        // VRFCoordinator.nonces[_keyHash][this], which was incremented by the above
        // successful LINK.transferAndCall (in VRFCoordinator.randomnessRequest).
        // This provides protection against the user repeating their input seed,
        // which would result in a predictable/duplicate output, if multiple such
        // requests appeared in the same block.
        nonces[_keyHash] = nonces[_keyHash].add(1);
        return makeRequestId(_keyHash, vRFSeed);
    }

    LinkTokenInterface immutable internal LINK;
    address immutable private vrfCoordinator;

    // Nonces for each VRF key from which randomness has been requested.
    //
    // Must stay in sync with VRFCoordinator[_keyHash][this]
    mapping(bytes32 /* keyHash */ => uint256 /* nonce */) private nonces;

    /**
     * @param _vrfCoordinator address of VRFCoordinator contract
     * @param _link address of LINK token contract
     *
     * @dev https://docs.chain.link/docs/link-token-contracts
     */
    constructor(address _vrfCoordinator, address _link) {
        vrfCoordinator = _vrfCoordinator;
        LINK = LinkTokenInterface(_link);
    }

    // rawFulfillRandomness is called by VRFCoordinator when it receives a valid VRF
    // proof. rawFulfillRandomness then calls fulfillRandomness, after validating
    // the origin of the call
    function rawFulfillRandomness(bytes32 requestId, uint256 randomness) external {
        require(msg.sender == vrfCoordinator, "Only VRFCoordinator can fulfill");
        fulfillRandomness(requestId, randomness);
    }

    /**
   * @notice returns the seed which is actually input to the VRF coordinator
   */
    function makeVRFInputSeed(bytes32 _keyHash, uint256 _userSeed, address _requester, uint256 _nonce) internal pure returns (uint256)
    {
        return  uint256(keccak256(abi.encode(_keyHash, _userSeed, _requester, _nonce)));
    }

    /**
     * @notice Returns the id for this request
     */
    function makeRequestId(bytes32 _keyHash, uint256 _vRFInputSeed) internal pure returns (bytes32) {
        return keccak256(abi.encodePacked(_keyHash, _vRFInputSeed));
    }
}

// File: contracts/LinkTokenInterface.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.7.0;

interface LinkTokenInterface {
    function allowance(address owner, address spender) external view returns (uint256 remaining);
    function approve(address spender, uint256 value) external returns (bool success);
    function balanceOf(address owner) external view returns (uint256 balance);
    function decimals() external view returns (uint8 decimalPlaces);
    function decreaseApproval(address spender, uint256 addedValue) external returns (bool success);
    function increaseApproval(address spender, uint256 subtractedValue) external;
    function name() external view returns (string memory tokenName);
    function symbol() external view returns (string memory tokenSymbol);
    function totalSupply() external view returns (uint256 totalTokensIssued);
    function transfer(address to, uint256 value) external returns (bool success);
    function transferAndCall(address to, uint256 value, bytes calldata data) external returns (bool success);
    function transferFrom(address from, address to, uint256 value) external returns (bool success);
}