// Dependency file: @openzeppelin/contracts/utils/Address.sol



// 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);
    }

    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);
            }
        }
    }
}


// Dependency file: @openzeppelin/contracts/GSN/Context.sol


// 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;
    }
}


// Dependency file: @openzeppelin/contracts/token/ERC20/IERC20.sol


// 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);
}


// Dependency file: @openzeppelin/contracts/math/SafeMath.sol


// 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, reverting on
     * overflow.
     *
     * Counterpart to Solidity's `+` operator.
     *
     * Requirements:
     *
     * - Addition cannot overflow.
     */
    function add(uint256 a, uint256 b) internal pure returns (uint256) {
        uint256 c = a + b;
        require(c >= a, "SafeMath: addition overflow");

        return c;
    }

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

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

        return c;
    }

    /**
     * @dev Returns the multiplication of two unsigned integers, reverting on
     * overflow.
     *
     * Counterpart to Solidity's `*` operator.
     *
     * Requirements:
     *
     * - Multiplication cannot overflow.
     */
    function mul(uint256 a, uint256 b) internal pure returns (uint256) {
        // Gas optimization: this is cheaper than requiring 'a' not being zero, but the
        // benefit is lost if 'b' is also tested.
        // See: https://github.com/OpenZeppelin/openzeppelin-contracts/pull/522
        if (a == 0) {
            return 0;
        }

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

        return c;
    }

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

    /**
     * @dev Returns the integer division of two unsigned integers. Reverts with custom message on
     * division by zero. The result is rounded towards zero.
     *
     * Counterpart to Solidity's `/` operator. Note: this function uses a
     * `revert` opcode (which leaves remaining gas untouched) while Solidity
     * uses an invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function div(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
        require(b > 0, errorMessage);
        uint256 c = a / b;
        // assert(a == b * c + a % b); // There is no case in which this doesn't hold

        return c;
    }

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

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


// Dependency file: @openzeppelin/contracts/token/ERC20/ERC20.sol


// pragma solidity >=0.6.0 <0.8.0;

// import "@openzeppelin/contracts/GSN/Context.sol";
// import "@openzeppelin/contracts/token/ERC20/IERC20.sol";
// import "@openzeppelin/contracts/math/SafeMath.sol";

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

    mapping (address => uint256) private _balances;

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

    uint256 private _totalSupply;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

        _beforeTokenTransfer(sender, recipient, amount);

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

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

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

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

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

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

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

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

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

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

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


// Dependency file: @openzeppelin/contracts/utils/SafeCast.sol


// pragma solidity >=0.6.0 <0.8.0;


/**
 * @dev Wrappers over Solidity's uintXX/intXX casting operators with added overflow
 * checks.
 *
 * Downcasting from uint256/int256 in Solidity does not revert on overflow. This can
 * easily result in undesired exploitation or bugs, since developers usually
 * assume that overflows raise errors. `SafeCast` restores this intuition by
 * reverting the transaction when such 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.
 *
 * Can be combined with {SafeMath} and {SignedSafeMath} to extend it to smaller types, by performing
 * all math on `uint256` and `int256` and then downcasting.
 */
library SafeCast {

    /**
     * @dev Returns the downcasted uint128 from uint256, reverting on
     * overflow (when the input is greater than largest uint128).
     *
     * Counterpart to Solidity's `uint128` operator.
     *
     * Requirements:
     *
     * - input must fit into 128 bits
     */
    function toUint128(uint256 value) internal pure returns (uint128) {
        require(value < 2**128, "SafeCast: value doesn\'t fit in 128 bits");
        return uint128(value);
    }

    /**
     * @dev Returns the downcasted uint64 from uint256, reverting on
     * overflow (when the input is greater than largest uint64).
     *
     * Counterpart to Solidity's `uint64` operator.
     *
     * Requirements:
     *
     * - input must fit into 64 bits
     */
    function toUint64(uint256 value) internal pure returns (uint64) {
        require(value < 2**64, "SafeCast: value doesn\'t fit in 64 bits");
        return uint64(value);
    }

    /**
     * @dev Returns the downcasted uint32 from uint256, reverting on
     * overflow (when the input is greater than largest uint32).
     *
     * Counterpart to Solidity's `uint32` operator.
     *
     * Requirements:
     *
     * - input must fit into 32 bits
     */
    function toUint32(uint256 value) internal pure returns (uint32) {
        require(value < 2**32, "SafeCast: value doesn\'t fit in 32 bits");
        return uint32(value);
    }

    /**
     * @dev Returns the downcasted uint16 from uint256, reverting on
     * overflow (when the input is greater than largest uint16).
     *
     * Counterpart to Solidity's `uint16` operator.
     *
     * Requirements:
     *
     * - input must fit into 16 bits
     */
    function toUint16(uint256 value) internal pure returns (uint16) {
        require(value < 2**16, "SafeCast: value doesn\'t fit in 16 bits");
        return uint16(value);
    }

    /**
     * @dev Returns the downcasted uint8 from uint256, reverting on
     * overflow (when the input is greater than largest uint8).
     *
     * Counterpart to Solidity's `uint8` operator.
     *
     * Requirements:
     *
     * - input must fit into 8 bits.
     */
    function toUint8(uint256 value) internal pure returns (uint8) {
        require(value < 2**8, "SafeCast: value doesn\'t fit in 8 bits");
        return uint8(value);
    }

    /**
     * @dev Converts a signed int256 into an unsigned uint256.
     *
     * Requirements:
     *
     * - input must be greater than or equal to 0.
     */
    function toUint256(int256 value) internal pure returns (uint256) {
        require(value >= 0, "SafeCast: value must be positive");
        return uint256(value);
    }

    /**
     * @dev Returns the downcasted int128 from int256, reverting on
     * overflow (when the input is less than smallest int128 or
     * greater than largest int128).
     *
     * Counterpart to Solidity's `int128` operator.
     *
     * Requirements:
     *
     * - input must fit into 128 bits
     *
     * _Available since v3.1._
     */
    function toInt128(int256 value) internal pure returns (int128) {
        require(value >= -2**127 && value < 2**127, "SafeCast: value doesn\'t fit in 128 bits");
        return int128(value);
    }

    /**
     * @dev Returns the downcasted int64 from int256, reverting on
     * overflow (when the input is less than smallest int64 or
     * greater than largest int64).
     *
     * Counterpart to Solidity's `int64` operator.
     *
     * Requirements:
     *
     * - input must fit into 64 bits
     *
     * _Available since v3.1._
     */
    function toInt64(int256 value) internal pure returns (int64) {
        require(value >= -2**63 && value < 2**63, "SafeCast: value doesn\'t fit in 64 bits");
        return int64(value);
    }

    /**
     * @dev Returns the downcasted int32 from int256, reverting on
     * overflow (when the input is less than smallest int32 or
     * greater than largest int32).
     *
     * Counterpart to Solidity's `int32` operator.
     *
     * Requirements:
     *
     * - input must fit into 32 bits
     *
     * _Available since v3.1._
     */
    function toInt32(int256 value) internal pure returns (int32) {
        require(value >= -2**31 && value < 2**31, "SafeCast: value doesn\'t fit in 32 bits");
        return int32(value);
    }

    /**
     * @dev Returns the downcasted int16 from int256, reverting on
     * overflow (when the input is less than smallest int16 or
     * greater than largest int16).
     *
     * Counterpart to Solidity's `int16` operator.
     *
     * Requirements:
     *
     * - input must fit into 16 bits
     *
     * _Available since v3.1._
     */
    function toInt16(int256 value) internal pure returns (int16) {
        require(value >= -2**15 && value < 2**15, "SafeCast: value doesn\'t fit in 16 bits");
        return int16(value);
    }

    /**
     * @dev Returns the downcasted int8 from int256, reverting on
     * overflow (when the input is less than smallest int8 or
     * greater than largest int8).
     *
     * Counterpart to Solidity's `int8` operator.
     *
     * Requirements:
     *
     * - input must fit into 8 bits.
     *
     * _Available since v3.1._
     */
    function toInt8(int256 value) internal pure returns (int8) {
        require(value >= -2**7 && value < 2**7, "SafeCast: value doesn\'t fit in 8 bits");
        return int8(value);
    }

    /**
     * @dev Converts an unsigned uint256 into a signed int256.
     *
     * Requirements:
     *
     * - input must be less than or equal to maxInt256.
     */
    function toInt256(uint256 value) internal pure returns (int256) {
        require(value < 2**255, "SafeCast: value doesn't fit in an int256");
        return int256(value);
    }
}


// Dependency file: @openzeppelin/contracts/math/SignedSafeMath.sol


// pragma solidity >=0.6.0 <0.8.0;

/**
 * @title SignedSafeMath
 * @dev Signed math operations with safety checks that revert on error.
 */
library SignedSafeMath {
    int256 constant private _INT256_MIN = -2**255;

    /**
     * @dev Returns the multiplication of two signed integers, reverting on
     * overflow.
     *
     * Counterpart to Solidity's `*` operator.
     *
     * Requirements:
     *
     * - Multiplication cannot overflow.
     */
    function mul(int256 a, int256 b) internal pure returns (int256) {
        // Gas optimization: this is cheaper than requiring 'a' not being zero, but the
        // benefit is lost if 'b' is also tested.
        // See: https://github.com/OpenZeppelin/openzeppelin-contracts/pull/522
        if (a == 0) {
            return 0;
        }

        require(!(a == -1 && b == _INT256_MIN), "SignedSafeMath: multiplication overflow");

        int256 c = a * b;
        require(c / a == b, "SignedSafeMath: multiplication overflow");

        return c;
    }

    /**
     * @dev Returns the integer division of two signed integers. Reverts on
     * division by zero. The result is rounded towards zero.
     *
     * Counterpart to Solidity's `/` operator. Note: this function uses a
     * `revert` opcode (which leaves remaining gas untouched) while Solidity
     * uses an invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function div(int256 a, int256 b) internal pure returns (int256) {
        require(b != 0, "SignedSafeMath: division by zero");
        require(!(b == -1 && a == _INT256_MIN), "SignedSafeMath: division overflow");

        int256 c = a / b;

        return c;
    }

    /**
     * @dev Returns the subtraction of two signed integers, reverting on
     * overflow.
     *
     * Counterpart to Solidity's `-` operator.
     *
     * Requirements:
     *
     * - Subtraction cannot overflow.
     */
    function sub(int256 a, int256 b) internal pure returns (int256) {
        int256 c = a - b;
        require((b >= 0 && c <= a) || (b < 0 && c > a), "SignedSafeMath: subtraction overflow");

        return c;
    }

    /**
     * @dev Returns the addition of two signed integers, reverting on
     * overflow.
     *
     * Counterpart to Solidity's `+` operator.
     *
     * Requirements:
     *
     * - Addition cannot overflow.
     */
    function add(int256 a, int256 b) internal pure returns (int256) {
        int256 c = a + b;
        require((b >= 0 && c >= a) || (b < 0 && c < a), "SignedSafeMath: addition overflow");

        return c;
    }
}


// Dependency file: contracts/interfaces/IController.sol

/*
    Copyright 2020 Set Labs Inc.

    Licensed under the Apache License, Version 2.0 (the "License");
    you may not use this file except in compliance with the License.
    You may obtain a copy of the License at

    http://www.apache.org/licenses/LICENSE-2.0

    Unless required by applicable law or agreed to in writing, software
    distributed under the License is distributed on an "AS IS" BASIS,
    WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
    See the License for the specific language governing permissions and
    limitations under the License.


*/
// pragma solidity 0.6.10;

interface IController {
    function addSet(address _setToken) external;
    function feeRecipient() external view returns(address);
    function getModuleFee(address _module, uint256 _feeType) external view returns(uint256);
    function isModule(address _module) external view returns(bool);
    function isSet(address _setToken) external view returns(bool);
    function isSystemContract(address _contractAddress) external view returns (bool);
    function resourceId(uint256 _id) external view returns(address);
}

// Dependency file: contracts/interfaces/IModule.sol

/*
    Copyright 2020 Set Labs Inc.

    Licensed under the Apache License, Version 2.0 (the "License");
    you may not use this file except in compliance with the License.
    You may obtain a copy of the License at

    http://www.apache.org/licenses/LICENSE-2.0

    Unless required by applicable law or agreed to in writing, software
    distributed under the License is distributed on an "AS IS" BASIS,
    WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
    See the License for the specific language governing permissions and
    limitations under the License.


*/
// pragma solidity 0.6.10;


/**
 * @title IModule
 * @author Set Protocol
 *
 * Interface for interacting with Modules.
 */
interface IModule {
    /**
     * Called by a SetToken to notify that this module was removed from the Set token. Any logic can be included
     * in case checks need to be made or state needs to be cleared.
     */
    function removeModule() external;
}

// Dependency file: contracts/interfaces/ISetToken.sol

/*
    Copyright 2020 Set Labs Inc.

    Licensed under the Apache License, Version 2.0 (the "License");
    you may not use this file except in compliance with the License.
    You may obtain a copy of the License at

    http://www.apache.org/licenses/LICENSE-2.0

    Unless required by applicable law or agreed to in writing, software
    distributed under the License is distributed on an "AS IS" BASIS,
    WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
    See the License for the specific language governing permissions and
    limitations under the License.


*/
// pragma solidity 0.6.10;


// import { IERC20 } from "@openzeppelin/contracts/token/ERC20/IERC20.sol";

/**
 * @title ISetToken
 * @author Set Protocol
 *
 * Interface for operating with SetTokens.
 */
interface ISetToken is IERC20 {

    /* ============ Enums ============ */

    enum ModuleState {
        NONE,
        PENDING,
        INITIALIZED
    }

    /* ============ Structs ============ */
    /**
     * The base definition of a SetToken Position
     *
     * @param component           Address of token in the Position
     * @param module              If not in default state, the address of associated module
     * @param unit                Each unit is the # of components per 10^18 of a SetToken
     * @param positionState       Position ENUM. Default is 0; External is 1
     * @param data                Arbitrary data
     */
    struct Position {
        address component;
        address module;
        int256 unit;
        uint8 positionState;
        bytes data;
    }

    /**
     * A struct that stores a component's cash position details and external positions
     * This data structure allows O(1) access to a component's cash position units and 
     * virtual units.
     *
     * @param virtualUnit               Virtual value of a component's DEFAULT position. Stored as virtual for efficiency
     *                                  updating all units at once via the position multiplier. Virtual units are achieved
     *                                  by dividing a "real" value by the "positionMultiplier"
     * @param componentIndex            
     * @param externalPositionModules   List of external modules attached to each external position. Each module
     *                                  maps to an external position
     * @param externalPositions         Mapping of module => ExternalPosition struct for a given component
     */
    struct ComponentPosition {
      int256 virtualUnit;
      address[] externalPositionModules;
      mapping(address => ExternalPosition) externalPositions;
    }

    /**
     * A struct that stores a component's external position details including virtual unit and any
     * auxiliary data.
     *
     * @param virtualUnit       Virtual value of a component's EXTERNAL position.
     * @param data              Arbitrary data
     */
    struct ExternalPosition {
      int256 virtualUnit;
      bytes data;
    }


    /* ============ Functions ============ */
    
    function addComponent(address _component) external;
    function removeComponent(address _component) external;
    function editDefaultPositionUnit(address _component, int256 _realUnit) external;
    function addExternalPositionModule(address _component, address _positionModule) external;
    function removeExternalPositionModule(address _component, address _positionModule) external;
    function editExternalPositionUnit(address _component, address _positionModule, int256 _realUnit) external;
    function editExternalPositionData(address _component, address _positionModule, bytes calldata _data) external;

    function invoke(address _target, uint256 _value, bytes calldata _data) external returns(bytes memory);

    function editPositionMultiplier(int256 _newMultiplier) external;

    function mint(address _account, uint256 _quantity) external;
    function burn(address _account, uint256 _quantity) external;

    function lock() external;
    function unlock() external;

    function addModule(address _module) external;
    function removeModule(address _module) external;
    function initializeModule() external;

    function setManager(address _manager) external;

    function manager() external view returns (address);
    function moduleStates(address _module) external view returns (ModuleState);
    function getModules() external view returns (address[] memory);
    
    function getDefaultPositionRealUnit(address _component) external view returns(int256);
    function getExternalPositionRealUnit(address _component, address _positionModule) external view returns(int256);
    function getComponents() external view returns(address[] memory);
    function getExternalPositionModules(address _component) external view returns(address[] memory);
    function getExternalPositionData(address _component, address _positionModule) external view returns(bytes memory);
    function isExternalPositionModule(address _component, address _module) external view returns(bool);
    function isComponent(address _component) external view returns(bool);
    
    function positionMultiplier() external view returns (int256);
    function getPositions() external view returns (Position[] memory);
    function getTotalComponentRealUnits(address _component) external view returns(int256);

    function isInitializedModule(address _module) external view returns(bool);
    function isPendingModule(address _module) external view returns(bool);
    function isLocked() external view returns (bool);
}

// Dependency file: contracts/lib/PreciseUnitMath.sol

/*
    Copyright 2020 Set Labs Inc.

    Licensed under the Apache License, Version 2.0 (the "License");
    you may not use this file except in compliance with the License.
    You may obtain a copy of the License at

    http://www.apache.org/licenses/LICENSE-2.0

    Unless required by applicable law or agreed to in writing, software
    distributed under the License is distributed on an "AS IS" BASIS,
    WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
    See the License for the specific language governing permissions and
    limitations under the License.


*/

// pragma solidity 0.6.10;
pragma experimental ABIEncoderV2;

// import { SafeMath } from "@openzeppelin/contracts/math/SafeMath.sol";
// import { SignedSafeMath } from "@openzeppelin/contracts/math/SignedSafeMath.sol";


/**
 * @title PreciseUnitMath
 * @author Set Protocol
 *
 * Arithmetic for fixed-point numbers with 18 decimals of precision. Some functions taken from
 * dYdX's BaseMath library.
 *
 * CHANGELOG:
 * - 9/21/20: Added safePower function
 */
library PreciseUnitMath {
    using SafeMath for uint256;
    using SignedSafeMath for int256;

    // The number One in precise units.
    uint256 constant internal PRECISE_UNIT = 10 ** 18;
    int256 constant internal PRECISE_UNIT_INT = 10 ** 18;

    // Max unsigned integer value
    uint256 constant internal MAX_UINT_256 = type(uint256).max;
    // Max and min signed integer value
    int256 constant internal MAX_INT_256 = type(int256).max;
    int256 constant internal MIN_INT_256 = type(int256).min;

    /**
     * @dev Getter function since constants can't be read directly from libraries.
     */
    function preciseUnit() internal pure returns (uint256) {
        return PRECISE_UNIT;
    }

    /**
     * @dev Getter function since constants can't be read directly from libraries.
     */
    function preciseUnitInt() internal pure returns (int256) {
        return PRECISE_UNIT_INT;
    }

    /**
     * @dev Getter function since constants can't be read directly from libraries.
     */
    function maxUint256() internal pure returns (uint256) {
        return MAX_UINT_256;
    }

    /**
     * @dev Getter function since constants can't be read directly from libraries.
     */
    function maxInt256() internal pure returns (int256) {
        return MAX_INT_256;
    }

    /**
     * @dev Getter function since constants can't be read directly from libraries.
     */
    function minInt256() internal pure returns (int256) {
        return MIN_INT_256;
    }

    /**
     * @dev Multiplies value a by value b (result is rounded down). It's assumed that the value b is the significand
     * of a number with 18 decimals precision.
     */
    function preciseMul(uint256 a, uint256 b) internal pure returns (uint256) {
        return a.mul(b).div(PRECISE_UNIT);
    }

    /**
     * @dev Multiplies value a by value b (result is rounded towards zero). It's assumed that the value b is the
     * significand of a number with 18 decimals precision.
     */
    function preciseMul(int256 a, int256 b) internal pure returns (int256) {
        return a.mul(b).div(PRECISE_UNIT_INT);
    }

    /**
     * @dev Multiplies value a by value b (result is rounded up). It's assumed that the value b is the significand
     * of a number with 18 decimals precision.
     */
    function preciseMulCeil(uint256 a, uint256 b) internal pure returns (uint256) {
        if (a == 0 || b == 0) {
            return 0;
        }
        return a.mul(b).sub(1).div(PRECISE_UNIT).add(1);
    }

    /**
     * @dev Divides value a by value b (result is rounded down).
     */
    function preciseDiv(uint256 a, uint256 b) internal pure returns (uint256) {
        return a.mul(PRECISE_UNIT).div(b);
    }


    /**
     * @dev Divides value a by value b (result is rounded towards 0).
     */
    function preciseDiv(int256 a, int256 b) internal pure returns (int256) {
        return a.mul(PRECISE_UNIT_INT).div(b);
    }

    /**
     * @dev Divides value a by value b (result is rounded up or away from 0).
     */
    function preciseDivCeil(uint256 a, uint256 b) internal pure returns (uint256) {
        require(b != 0, "Cant divide by 0");

        return a > 0 ? a.mul(PRECISE_UNIT).sub(1).div(b).add(1) : 0;
    }

    /**
     * @dev Divides value a by value b (result is rounded down - positive numbers toward 0 and negative away from 0).
     */
    function divDown(int256 a, int256 b) internal pure returns (int256) {
        require(b != 0, "Cant divide by 0");
        require(a != MIN_INT_256 || b != -1, "Invalid input");

        int256 result = a.div(b);
        if (a ^ b < 0 && a % b != 0) {
            result -= 1;
        }

        return result;
    }

    /**
     * @dev Multiplies value a by value b where rounding is towards the lesser number. 
     * (positive values are rounded towards zero and negative values are rounded away from 0). 
     */
    function conservativePreciseMul(int256 a, int256 b) internal pure returns (int256) {
        return divDown(a.mul(b), PRECISE_UNIT_INT);
    }

    /**
     * @dev Divides value a by value b where rounding is towards the lesser number. 
     * (positive values are rounded towards zero and negative values are rounded away from 0). 
     */
    function conservativePreciseDiv(int256 a, int256 b) internal pure returns (int256) {
        return divDown(a.mul(PRECISE_UNIT_INT), b);
    }

    /**
    * @dev Performs the power on a specified value, reverts on overflow.
    */
    function safePower(
        uint256 a,
        uint256 pow
    )
        internal
        pure
        returns (uint256)
    {
        require(a > 0, "Value must be positive");

        uint256 result = 1;
        for (uint256 i = 0; i < pow; i++){
            uint256 previousResult = result;

            // Using safemath multiplication prevents overflows
            result = previousResult.mul(a);
        }

        return result;
    }
}

// Dependency file: contracts/protocol/lib/Position.sol

/*
    Copyright 2020 Set Labs Inc.

    Licensed under the Apache License, Version 2.0 (the "License");
    you may not use this file except in compliance with the License.
    You may obtain a copy of the License at

    http://www.apache.org/licenses/LICENSE-2.0

    Unless required by applicable law or agreed to in writing, software
    distributed under the License is distributed on an "AS IS" BASIS,
    WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
    See the License for the specific language governing permissions and
    limitations under the License.


*/

// pragma solidity 0.6.10;


// import { IERC20 } from "@openzeppelin/contracts/token/ERC20/IERC20.sol";
// import { SafeCast } from "@openzeppelin/contracts/utils/SafeCast.sol";
// import { SafeMath } from "@openzeppelin/contracts/math/SafeMath.sol";
// import { SignedSafeMath } from "@openzeppelin/contracts/math/SignedSafeMath.sol";

// import { ISetToken } from "contracts/interfaces/ISetToken.sol";
// import { PreciseUnitMath } from "contracts/lib/PreciseUnitMath.sol";


/**
 * @title Position
 * @author Set Protocol
 *
 * Collection of helper functions for handling and updating SetToken Positions
 *
 * CHANGELOG:
 *  - Updated editExternalPosition to work when no external position is associated with module
 */
library Position {
    using SafeCast for uint256;
    using SafeMath for uint256;
    using SafeCast for int256;
    using SignedSafeMath for int256;
    using PreciseUnitMath for uint256;

    /* ============ Helper ============ */

    /**
     * Returns whether the SetToken has a default position for a given component (if the real unit is > 0)
     */
    function hasDefaultPosition(ISetToken _setToken, address _component) internal view returns(bool) {
        return _setToken.getDefaultPositionRealUnit(_component) > 0;
    }

    /**
     * Returns whether the SetToken has an external position for a given component (if # of position modules is > 0)
     */
    function hasExternalPosition(ISetToken _setToken, address _component) internal view returns(bool) {
        return _setToken.getExternalPositionModules(_component).length > 0;
    }
    
    /**
     * Returns whether the SetToken component default position real unit is greater than or equal to units passed in.
     */
    function hasSufficientDefaultUnits(ISetToken _setToken, address _component, uint256 _unit) internal view returns(bool) {
        return _setToken.getDefaultPositionRealUnit(_component) >= _unit.toInt256();
    }

    /**
     * Returns whether the SetToken component external position is greater than or equal to the real units passed in.
     */
    function hasSufficientExternalUnits(
        ISetToken _setToken,
        address _component,
        address _positionModule,
        uint256 _unit
    )
        internal
        view
        returns(bool)
    {
       return _setToken.getExternalPositionRealUnit(_component, _positionModule) >= _unit.toInt256();    
    }

    /**
     * If the position does not exist, create a new Position and add to the SetToken. If it already exists,
     * then set the position units. If the new units is 0, remove the position. Handles adding/removing of 
     * components where needed (in light of potential external positions).
     *
     * @param _setToken           Address of SetToken being modified
     * @param _component          Address of the component
     * @param _newUnit            Quantity of Position units - must be >= 0
     */
    function editDefaultPosition(ISetToken _setToken, address _component, uint256 _newUnit) internal {
        bool isPositionFound = hasDefaultPosition(_setToken, _component);
        if (!isPositionFound && _newUnit > 0) {
            // If there is no Default Position and no External Modules, then component does not exist
            if (!hasExternalPosition(_setToken, _component)) {
                _setToken.addComponent(_component);
            }
        } else if (isPositionFound && _newUnit == 0) {
            // If there is a Default Position and no external positions, remove the component
            if (!hasExternalPosition(_setToken, _component)) {
                _setToken.removeComponent(_component);
            }
        }

        _setToken.editDefaultPositionUnit(_component, _newUnit.toInt256());
    }

    /**
     * Update an external position and remove and external positions or components if necessary. The logic flows as follows:
     * 1) If component is not already added then add component and external position. 
     * 2) If component is added but no existing external position using the passed module exists then add the external position.
     * 3) If the existing position is being added to then just update the unit and data
     * 4) If the position is being closed and no other external positions or default positions are associated with the component
     *    then untrack the component and remove external position.
     * 5) If the position is being closed and other existing positions still exist for the component then just remove the
     *    external position.
     *
     * @param _setToken         SetToken being updated
     * @param _component        Component position being updated
     * @param _module           Module external position is associated with
     * @param _newUnit          Position units of new external position
     * @param _data             Arbitrary data associated with the position
     */
    function editExternalPosition(
        ISetToken _setToken,
        address _component,
        address _module,
        int256 _newUnit,
        bytes memory _data
    )
        internal
    {
        if (_newUnit != 0) {
            if (!_setToken.isComponent(_component)) {
                _setToken.addComponent(_component);
                _setToken.addExternalPositionModule(_component, _module);
            } else if (!_setToken.isExternalPositionModule(_component, _module)) {
                _setToken.addExternalPositionModule(_component, _module);
            }
            _setToken.editExternalPositionUnit(_component, _module, _newUnit);
            _setToken.editExternalPositionData(_component, _module, _data);
        } else {
            require(_data.length == 0, "Passed data must be null");
            // If no default or external position remaining then remove component from components array
            if (_setToken.getExternalPositionRealUnit(_component, _module) != 0) {
                address[] memory positionModules = _setToken.getExternalPositionModules(_component);
                if (_setToken.getDefaultPositionRealUnit(_component) == 0 && positionModules.length == 1) {
                    require(positionModules[0] == _module, "External positions must be 0 to remove component");
                    _setToken.removeComponent(_component);
                }
                _setToken.removeExternalPositionModule(_component, _module);
            }
        }
    }

    /**
     * Get total notional amount of Default position
     *
     * @param _setTokenSupply     Supply of SetToken in precise units (10^18)
     * @param _positionUnit       Quantity of Position units
     *
     * @return                    Total notional amount of units
     */
    function getDefaultTotalNotional(uint256 _setTokenSupply, uint256 _positionUnit) internal pure returns (uint256) {
        return _setTokenSupply.preciseMul(_positionUnit);
    }

    /**
     * Get position unit from total notional amount
     *
     * @param _setTokenSupply     Supply of SetToken in precise units (10^18)
     * @param _totalNotional      Total notional amount of component prior to
     * @return                    Default position unit
     */
    function getDefaultPositionUnit(uint256 _setTokenSupply, uint256 _totalNotional) internal pure returns (uint256) {
        return _totalNotional.preciseDiv(_setTokenSupply);
    }

    /**
     * Get the total tracked balance - total supply * position unit
     *
     * @param _setToken           Address of the SetToken
     * @param _component          Address of the component
     * @return                    Notional tracked balance
     */
    function getDefaultTrackedBalance(ISetToken _setToken, address _component) internal view returns(uint256) {
        int256 positionUnit = _setToken.getDefaultPositionRealUnit(_component); 
        return _setToken.totalSupply().preciseMul(positionUnit.toUint256());
    }

    /**
     * Calculates the new default position unit and performs the edit with the new unit
     *
     * @param _setToken                 Address of the SetToken
     * @param _component                Address of the component
     * @param _setTotalSupply           Current SetToken supply
     * @param _componentPreviousBalance Pre-action component balance
     * @return                          Current component balance
     * @return                          Previous position unit
     * @return                          New position unit
     */
    function calculateAndEditDefaultPosition(
        ISetToken _setToken,
        address _component,
        uint256 _setTotalSupply,
        uint256 _componentPreviousBalance
    )
        internal
        returns(uint256, uint256, uint256)
    {
        uint256 currentBalance = IERC20(_component).balanceOf(address(_setToken));
        uint256 positionUnit = _setToken.getDefaultPositionRealUnit(_component).toUint256();

        uint256 newTokenUnit;
        if (currentBalance > 0) {
            newTokenUnit = calculateDefaultEditPositionUnit(
                _setTotalSupply,
                _componentPreviousBalance,
                currentBalance,
                positionUnit
            );
        } else {
            newTokenUnit = 0;
        }

        editDefaultPosition(_setToken, _component, newTokenUnit);

        return (currentBalance, positionUnit, newTokenUnit);
    }

    /**
     * Calculate the new position unit given total notional values pre and post executing an action that changes SetToken state
     * The intention is to make updates to the units without accidentally picking up airdropped assets as well.
     *
     * @param _setTokenSupply     Supply of SetToken in precise units (10^18)
     * @param _preTotalNotional   Total notional amount of component prior to executing action
     * @param _postTotalNotional  Total notional amount of component after the executing action
     * @param _prePositionUnit    Position unit of SetToken prior to executing action
     * @return                    New position unit
     */
    function calculateDefaultEditPositionUnit(
        uint256 _setTokenSupply,
        uint256 _preTotalNotional,
        uint256 _postTotalNotional,
        uint256 _prePositionUnit
    )
        internal
        pure
        returns (uint256)
    {
        // If pre action total notional amount is greater then subtract post action total notional and calculate new position units
        uint256 airdroppedAmount = _preTotalNotional.sub(_prePositionUnit.preciseMul(_setTokenSupply));
        return _postTotalNotional.sub(airdroppedAmount).preciseDiv(_setTokenSupply);
    }
}


// Dependency file: contracts/lib/AddressArrayUtils.sol

/*
    Copyright 2020 Set Labs Inc.

    Licensed under the Apache License, Version 2.0 (the "License");
    you may not use this file except in compliance with the License.
    You may obtain a copy of the License at

    http://www.apache.org/licenses/LICENSE-2.0

    Unless required by applicable law or agreed to in writing, software
    distributed under the License is distributed on an "AS IS" BASIS,
    WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
    See the License for the specific language governing permissions and
    limitations under the License.


*/

// pragma solidity 0.6.10;

/**
 * @title AddressArrayUtils
 * @author Set Protocol
 *
 * Utility functions to handle Address Arrays
 */
library AddressArrayUtils {

    /**
     * Finds the index of the first occurrence of the given element.
     * @param A The input array to search
     * @param a The value to find
     * @return Returns (index and isIn) for the first occurrence starting from index 0
     */
    function indexOf(address[] memory A, address a) internal pure returns (uint256, bool) {
        uint256 length = A.length;
        for (uint256 i = 0; i < length; i++) {
            if (A[i] == a) {
                return (i, true);
            }
        }
        return (uint256(-1), false);
    }

    /**
    * Returns true if the value is present in the list. Uses indexOf internally.
    * @param A The input array to search
    * @param a The value to find
    * @return Returns isIn for the first occurrence starting from index 0
    */
    function contains(address[] memory A, address a) internal pure returns (bool) {
        (, bool isIn) = indexOf(A, a);
        return isIn;
    }

    /**
    * Returns true if there are 2 elements that are the same in an array
    * @param A The input array to search
    * @return Returns boolean for the first occurrence of a duplicate
    */
    function hasDuplicate(address[] memory A) internal pure returns(bool) {
        require(A.length > 0, "A is empty");

        for (uint256 i = 0; i < A.length - 1; i++) {
            address current = A[i];
            for (uint256 j = i + 1; j < A.length; j++) {
                if (current == A[j]) {
                    return true;
                }
            }
        }
        return false;
    }

    /**
     * @param A The input array to search
     * @param a The address to remove     
     * @return Returns the array with the object removed.
     */
    function remove(address[] memory A, address a)
        internal
        pure
        returns (address[] memory)
    {
        (uint256 index, bool isIn) = indexOf(A, a);
        if (!isIn) {
            revert("Address not in array.");
        } else {
            (address[] memory _A,) = pop(A, index);
            return _A;
        }
    }

    /**
     * @param A The input array to search
     * @param a The address to remove
     */
    function removeStorage(address[] storage A, address a)
        internal
    {
        (uint256 index, bool isIn) = indexOf(A, a);
        if (!isIn) {
            revert("Address not in array.");
        } else {
            uint256 lastIndex = A.length - 1; // If the array would be empty, the previous line would throw, so no underflow here
            if (index != lastIndex) { A[index] = A[lastIndex]; }
            A.pop();
        }
    }

    /**
    * Removes specified index from array
    * @param A The input array to search
    * @param index The index to remove
    * @return Returns the new array and the removed entry
    */
    function pop(address[] memory A, uint256 index)
        internal
        pure
        returns (address[] memory, address)
    {
        uint256 length = A.length;
        require(index < A.length, "Index must be < A length");
        address[] memory newAddresses = new address[](length - 1);
        for (uint256 i = 0; i < index; i++) {
            newAddresses[i] = A[i];
        }
        for (uint256 j = index + 1; j < length; j++) {
            newAddresses[j - 1] = A[j];
        }
        return (newAddresses, A[index]);
    }

    /**
     * Returns the combination of the two arrays
     * @param A The first array
     * @param B The second array
     * @return Returns A extended by B
     */
    function extend(address[] memory A, address[] memory B) internal pure returns (address[] memory) {
        uint256 aLength = A.length;
        uint256 bLength = B.length;
        address[] memory newAddresses = new address[](aLength + bLength);
        for (uint256 i = 0; i < aLength; i++) {
            newAddresses[i] = A[i];
        }
        for (uint256 j = 0; j < bLength; j++) {
            newAddresses[aLength + j] = B[j];
        }
        return newAddresses;
    }
}

// Root file: contracts/protocol/SetToken.sol

/*
    Copyright 2020 Set Labs Inc.

    Licensed under the Apache License, Version 2.0 (the "License");
    you may not use this file except in compliance with the License.
    You may obtain a copy of the License at

    http://www.apache.org/licenses/LICENSE-2.0

    Unless required by applicable law or agreed to in writing, software
    distributed under the License is distributed on an "AS IS" BASIS,
    WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
    See the License for the specific language governing permissions and
    limitations under the License.


*/

pragma solidity 0.6.10;


// import { Address } from "@openzeppelin/contracts/utils/Address.sol";
// import { ERC20 } from "@openzeppelin/contracts/token/ERC20/ERC20.sol";
// import { SafeCast } from "@openzeppelin/contracts/utils/SafeCast.sol";
// import { SafeMath } from "@openzeppelin/contracts/math/SafeMath.sol";
// import { SignedSafeMath } from "@openzeppelin/contracts/math/SignedSafeMath.sol";

// import { IController } from "contracts/interfaces/IController.sol";
// import { IModule } from "contracts/interfaces/IModule.sol";
// import { ISetToken } from "contracts/interfaces/ISetToken.sol";
// import { Position } from "contracts/protocol/lib/Position.sol";
// import { PreciseUnitMath } from "contracts/lib/PreciseUnitMath.sol";
// import { AddressArrayUtils } from "contracts/lib/AddressArrayUtils.sol";


/**
 * @title SetToken
 * @author Set Protocol
 *
 * ERC20 Token contract that allows privileged modules to make modifications to its positions and invoke function calls
 * from the SetToken. 
 */
contract SetToken is ERC20 {
    using SafeMath for uint256;
    using SafeCast for int256;
    using SafeCast for uint256;
    using SignedSafeMath for int256;
    using PreciseUnitMath for int256;
    using Address for address;
    using AddressArrayUtils for address[];

    /* ============ Constants ============ */

    /*
        The PositionState is the status of the Position, whether it is Default (held on the SetToken)
        or otherwise held on a separate smart contract (whether a module or external source).
        There are issues with cross-usage of enums, so we are defining position states
        as a uint8.
    */
    uint8 internal constant DEFAULT = 0;
    uint8 internal constant EXTERNAL = 1;

    /* ============ Events ============ */

    event Invoked(address indexed _target, uint indexed _value, bytes _data, bytes _returnValue);
    event ModuleAdded(address indexed _module);
    event ModuleRemoved(address indexed _module);    
    event ModuleInitialized(address indexed _module);
    event ManagerEdited(address _newManager, address _oldManager);
    event PendingModuleRemoved(address indexed _module);
    event PositionMultiplierEdited(int256 _newMultiplier);
    event ComponentAdded(address indexed _component);
    event ComponentRemoved(address indexed _component);
    event DefaultPositionUnitEdited(address indexed _component, int256 _realUnit);
    event ExternalPositionUnitEdited(address indexed _component, address indexed _positionModule, int256 _realUnit);
    event ExternalPositionDataEdited(address indexed _component, address indexed _positionModule, bytes _data);
    event PositionModuleAdded(address indexed _component, address indexed _positionModule);
    event PositionModuleRemoved(address indexed _component, address indexed _positionModule);

    /* ============ Modifiers ============ */

    /**
     * Throws if the sender is not a SetToken's module or module not enabled
     */
    modifier onlyModule() {
        // Internal function used to reduce bytecode size
        _validateOnlyModule();
        _;
    }

    /**
     * Throws if the sender is not the SetToken's manager
     */
    modifier onlyManager() {
        _validateOnlyManager();
        _;
    }

    /**
     * Throws if SetToken is locked and called by any account other than the locker.
     */
    modifier whenLockedOnlyLocker() {
        _validateWhenLockedOnlyLocker();
        _;
    }

    /* ============ State Variables ============ */

    // Address of the controller
    IController public controller;

    // The manager has the privelege to add modules, remove, and set a new manager
    address public manager;

    // A module that has locked other modules from privileged functionality, typically required
    // for multi-block module actions such as auctions
    address public locker;

    // List of initialized Modules; Modules extend the functionality of SetTokens
    address[] public modules;

    // Modules are initialized from NONE -> PENDING -> INITIALIZED through the
    // addModule (called by manager) and initialize  (called by module) functions
    mapping(address => ISetToken.ModuleState) public moduleStates;

    // When locked, only the locker (a module) can call privileged functionality
    // Typically utilized if a module (e.g. Auction) needs multiple transactions to complete an action
    // without interruption
    bool public isLocked;

    // List of components
    address[] public components;

    // Mapping that stores all Default and External position information for a given component.
    // Position quantities are represented as virtual units; Default positions are on the top-level,
    // while external positions are stored in a module array and accessed through its externalPositions mapping
    mapping(address => ISetToken.ComponentPosition) private componentPositions;

    // The multiplier applied to the virtual position unit to achieve the real/actual unit.
    // This multiplier is used for efficiently modifying the entire position units (e.g. streaming fee)
    int256 public positionMultiplier;

    /* ============ Constructor ============ */

    /**
     * When a new SetToken is created, initializes Positions in default state and adds modules into pending state.
     * All parameter validations are on the SetTokenCreator contract. Validations are performed already on the 
     * SetTokenCreator. Initiates the positionMultiplier as 1e18 (no adjustments).
     *
     * @param _components             List of addresses of components for initial Positions
     * @param _units                  List of units. Each unit is the # of components per 10^18 of a SetToken
     * @param _modules                List of modules to enable. All modules must be approved by the Controller
     * @param _controller             Address of the controller
     * @param _manager                Address of the manager
     * @param _name                   Name of the SetToken
     * @param _symbol                 Symbol of the SetToken
     */
    constructor(
        address[] memory _components,
        int256[] memory _units,
        address[] memory _modules,
        IController _controller,
        address _manager,
        string memory _name,
        string memory _symbol
    )
        public
        ERC20(_name, _symbol)
    {
        controller = _controller;
        manager = _manager;
        positionMultiplier = PreciseUnitMath.preciseUnitInt();
        components = _components;

        // Modules are put in PENDING state, as they need to be individually initialized by the Module
        for (uint256 i = 0; i < _modules.length; i++) {
            moduleStates[_modules[i]] = ISetToken.ModuleState.PENDING;
        }

        // Positions are put in default state initially
        for (uint256 j = 0; j < _components.length; j++) {
            componentPositions[_components[j]].virtualUnit = _units[j];
        }
    }

    /* ============ External Functions ============ */

    /**
     * PRIVELEGED MODULE FUNCTION. Low level function that allows a module to make an arbitrary function
     * call to any contract.
     *
     * @param _target                 Address of the smart contract to call
     * @param _value                  Quantity of Ether to provide the call (typically 0)
     * @param _data                   Encoded function selector and arguments
     * @return _returnValue           Bytes encoded return value
     */
    function invoke(
        address _target,
        uint256 _value,
        bytes calldata _data
    )
        external
        onlyModule
        whenLockedOnlyLocker
        returns (bytes memory _returnValue)
    {
        _returnValue = _target.functionCallWithValue(_data, _value);

        emit Invoked(_target, _value, _data, _returnValue);

        return _returnValue;
    }

    /**
     * PRIVELEGED MODULE FUNCTION. Low level function that adds a component to the components array.
     */
    function addComponent(address _component) external onlyModule whenLockedOnlyLocker {
        require(!isComponent(_component), "Must not be component");
        
        components.push(_component);

        emit ComponentAdded(_component);
    }

    /**
     * PRIVELEGED MODULE FUNCTION. Low level function that removes a component from the components array.
     */
    function removeComponent(address _component) external onlyModule whenLockedOnlyLocker {
        components.removeStorage(_component);

        emit ComponentRemoved(_component);
    }

    /**
     * PRIVELEGED MODULE FUNCTION. Low level function that edits a component's virtual unit. Takes a real unit
     * and converts it to virtual before committing.
     */
    function editDefaultPositionUnit(address _component, int256 _realUnit) external onlyModule whenLockedOnlyLocker {
        int256 virtualUnit = _convertRealToVirtualUnit(_realUnit);

        componentPositions[_component].virtualUnit = virtualUnit;

        emit DefaultPositionUnitEdited(_component, _realUnit);
    }

    /**
     * PRIVELEGED MODULE FUNCTION. Low level function that adds a module to a component's externalPositionModules array
     */
    function addExternalPositionModule(address _component, address _positionModule) external onlyModule whenLockedOnlyLocker {
        require(!isExternalPositionModule(_component, _positionModule), "Module already added");

        componentPositions[_component].externalPositionModules.push(_positionModule);

        emit PositionModuleAdded(_component, _positionModule);
    }

    /**
     * PRIVELEGED MODULE FUNCTION. Low level function that removes a module from a component's 
     * externalPositionModules array and deletes the associated externalPosition.
     */
    function removeExternalPositionModule(
        address _component,
        address _positionModule
    )
        external
        onlyModule
        whenLockedOnlyLocker
    {
        componentPositions[_component].externalPositionModules.removeStorage(_positionModule);

        delete componentPositions[_component].externalPositions[_positionModule];

        emit PositionModuleRemoved(_component, _positionModule);
    }

    /**
     * PRIVELEGED MODULE FUNCTION. Low level function that edits a component's external position virtual unit. 
     * Takes a real unit and converts it to virtual before committing.
     */
    function editExternalPositionUnit(
        address _component,
        address _positionModule,
        int256 _realUnit
    )
        external
        onlyModule
        whenLockedOnlyLocker
    {
        int256 virtualUnit = _convertRealToVirtualUnit(_realUnit);

        componentPositions[_component].externalPositions[_positionModule].virtualUnit = virtualUnit;

        emit ExternalPositionUnitEdited(_component, _positionModule, _realUnit);
    }

    /**
     * PRIVELEGED MODULE FUNCTION. Low level function that edits a component's external position data
     */
    function editExternalPositionData(
        address _component,
        address _positionModule,
        bytes calldata _data
    )
        external
        onlyModule
        whenLockedOnlyLocker
    {
        componentPositions[_component].externalPositions[_positionModule].data = _data;

        emit ExternalPositionDataEdited(_component, _positionModule, _data);
    }

    /**
     * PRIVELEGED MODULE FUNCTION. Modifies the position multiplier. This is typically used to efficiently
     * update all the Positions' units at once in applications where inflation is awarded (e.g. subscription fees).
     */
    function editPositionMultiplier(int256 _newMultiplier) external onlyModule whenLockedOnlyLocker {        
        _validateNewMultiplier(_newMultiplier);

        positionMultiplier = _newMultiplier;

        emit PositionMultiplierEdited(_newMultiplier);
    }

    /**
     * PRIVELEGED MODULE FUNCTION. Increases the "account" balance by the "quantity".
     */
    function mint(address _account, uint256 _quantity) external onlyModule whenLockedOnlyLocker {
        _mint(_account, _quantity);
    }

    /**
     * PRIVELEGED MODULE FUNCTION. Decreases the "account" balance by the "quantity".
     * _burn checks that the "account" already has the required "quantity".
     */
    function burn(address _account, uint256 _quantity) external onlyModule whenLockedOnlyLocker {
        _burn(_account, _quantity);
    }

    /**
     * PRIVELEGED MODULE FUNCTION. When a SetToken is locked, only the locker can call privileged functions.
     */
    function lock() external onlyModule {
        require(!isLocked, "Must not be locked");
        locker = msg.sender;
        isLocked = true;
    }

    /**
     * PRIVELEGED MODULE FUNCTION. Unlocks the SetToken and clears the locker
     */
    function unlock() external onlyModule {
        require(isLocked, "Must be locked");
        require(locker == msg.sender, "Must be locker");
        delete locker;
        isLocked = false;
    }

    /**
     * MANAGER ONLY. Adds a module into a PENDING state; Module must later be initialized via 
     * module's initialize function
     */
    function addModule(address _module) external onlyManager {
        require(moduleStates[_module] == ISetToken.ModuleState.NONE, "Module must not be added");
        require(controller.isModule(_module), "Must be enabled on Controller");

        moduleStates[_module] = ISetToken.ModuleState.PENDING;

        emit ModuleAdded(_module);
    }

    /**
     * MANAGER ONLY. Removes a module from the SetToken. SetToken calls removeModule on module itself to confirm
     * it is not needed to manage any remaining positions and to remove state.
     */
    function removeModule(address _module) external onlyManager {
        require(!isLocked, "Only when unlocked");
        require(moduleStates[_module] == ISetToken.ModuleState.INITIALIZED, "Module must be added");

        IModule(_module).removeModule();

        moduleStates[_module] = ISetToken.ModuleState.NONE;

        modules.removeStorage(_module);

        emit ModuleRemoved(_module);
    }

    /**
     * MANAGER ONLY. Removes a pending module from the SetToken.
     */
    function removePendingModule(address _module) external onlyManager {
        require(!isLocked, "Only when unlocked");
        require(moduleStates[_module] == ISetToken.ModuleState.PENDING, "Module must be pending");

        moduleStates[_module] = ISetToken.ModuleState.NONE;

        emit PendingModuleRemoved(_module);
    }

    /**
     * Initializes an added module from PENDING to INITIALIZED state. Can only call when unlocked.
     * An address can only enter a PENDING state if it is an enabled module added by the manager.
     * Only callable by the module itself, hence msg.sender is the subject of update.
     */
    function initializeModule() external {
        require(!isLocked, "Only when unlocked");
        require(moduleStates[msg.sender] == ISetToken.ModuleState.PENDING, "Module must be pending");
        
        moduleStates[msg.sender] = ISetToken.ModuleState.INITIALIZED;
        modules.push(msg.sender);

        emit ModuleInitialized(msg.sender);
    }

    /**
     * MANAGER ONLY. Changes manager; We allow null addresses in case the manager wishes to wind down the SetToken.
     * Modules may rely on the manager state, so only changable when unlocked
     */
    function setManager(address _manager) external onlyManager {
        require(!isLocked, "Only when unlocked");
        address oldManager = manager;
        manager = _manager;

        emit ManagerEdited(_manager, oldManager);
    }

    /* ============ External Getter Functions ============ */

    function getComponents() external view returns(address[] memory) {
        return components;
    }

    function getDefaultPositionRealUnit(address _component) public view returns(int256) {
        return _convertVirtualToRealUnit(_defaultPositionVirtualUnit(_component));
    }

    function getExternalPositionRealUnit(address _component, address _positionModule) public view returns(int256) {
        return _convertVirtualToRealUnit(_externalPositionVirtualUnit(_component, _positionModule));
    }

    function getExternalPositionModules(address _component) external view returns(address[] memory) {
        return _externalPositionModules(_component);
    }

    function getExternalPositionData(address _component,address _positionModule) external view returns(bytes memory) {
        return _externalPositionData(_component, _positionModule);
    }

    function getModules() external view returns (address[] memory) {
        return modules;
    }

    function isComponent(address _component) public view returns(bool) {
        return components.contains(_component);
    }

    function isExternalPositionModule(address _component, address _module) public view returns(bool) {
        return _externalPositionModules(_component).contains(_module);
    }

    /**
     * Only ModuleStates of INITIALIZED modules are considered enabled
     */
    function isInitializedModule(address _module) external view returns (bool) {
        return moduleStates[_module] == ISetToken.ModuleState.INITIALIZED;
    }

    /**
     * Returns whether the module is in a pending state
     */
    function isPendingModule(address _module) external view returns (bool) {
        return moduleStates[_module] == ISetToken.ModuleState.PENDING;
    }

    /**
     * Returns a list of Positions, through traversing the components. Each component with a non-zero virtual unit
     * is considered a Default Position, and each externalPositionModule will generate a unique position.
     * Virtual units are converted to real units. This function is typically used off-chain for data presentation purposes.
     */
    function getPositions() external view returns (ISetToken.Position[] memory) {
        ISetToken.Position[] memory positions = new ISetToken.Position[](_getPositionCount());
        uint256 positionCount = 0;

        for (uint256 i = 0; i < components.length; i++) {
            address component = components[i];

            // A default position exists if the default virtual unit is > 0
            if (_defaultPositionVirtualUnit(component) > 0) {
                positions[positionCount] = ISetToken.Position({
                    component: component,
                    module: address(0),
                    unit: getDefaultPositionRealUnit(component),
                    positionState: DEFAULT,
                    data: ""
                });

                positionCount++;
            }

            address[] memory externalModules = _externalPositionModules(component);
            for (uint256 j = 0; j < externalModules.length; j++) {
                address currentModule = externalModules[j];

                positions[positionCount] = ISetToken.Position({
                    component: component,
                    module: currentModule,
                    unit: getExternalPositionRealUnit(component, currentModule),
                    positionState: EXTERNAL,
                    data: _externalPositionData(component, currentModule)
                });

                positionCount++;
            }
        }

        return positions;
    }

    /**
     * Returns the total Real Units for a given component, summing the default and external position units.
     */
    function getTotalComponentRealUnits(address _component) external view returns(int256) {
        int256 totalUnits = getDefaultPositionRealUnit(_component);

        address[] memory externalModules = _externalPositionModules(_component);
        for (uint256 i = 0; i < externalModules.length; i++) {
            // We will perform the summation no matter what, as an external position virtual unit can be negative
            totalUnits = totalUnits.add(getExternalPositionRealUnit(_component, externalModules[i]));
        }

        return totalUnits;
    }


    receive() external payable {} // solium-disable-line quotes

    /* ============ Internal Functions ============ */

    function _defaultPositionVirtualUnit(address _component) internal view returns(int256) {
        return componentPositions[_component].virtualUnit;
    }

    function _externalPositionModules(address _component) internal view returns(address[] memory) {
        return componentPositions[_component].externalPositionModules;
    }

    function _externalPositionVirtualUnit(address _component, address _module) internal view returns(int256) {
        return componentPositions[_component].externalPositions[_module].virtualUnit;
    }

    function _externalPositionData(address _component, address _module) internal view returns(bytes memory) {
        return componentPositions[_component].externalPositions[_module].data;
    }

    /**
     * Takes a real unit and divides by the position multiplier to return the virtual unit
     */
    function _convertRealToVirtualUnit(int256 _realUnit) internal view returns(int256) {
        int256 virtualUnit = _realUnit.conservativePreciseDiv(positionMultiplier);

        // These checks ensure that the virtual unit does not return a result that has rounded down to 0
        if (_realUnit > 0 && virtualUnit == 0) {
            revert("Virtual unit conversion invalid");
        }

        return virtualUnit;
    }

    /**
     * Takes a virtual unit and multiplies by the position multiplier to return the real unit
     */
    function _convertVirtualToRealUnit(int256 _virtualUnit) internal view returns(int256) {
        return _virtualUnit.conservativePreciseMul(positionMultiplier);
    }

    /**
     * To prevent virtual to real unit conversion issues (where real unit may be 0), the 
     * product of the positionMultiplier and the lowest absolute virtualUnit value (across default and
     * external positions) must be greater than 0.
     */
    function _validateNewMultiplier(int256 _newMultiplier) internal view {
        int256 minVirtualUnit = _getPositionsAbsMinimumVirtualUnit();

        require(minVirtualUnit.conservativePreciseMul(_newMultiplier) > 0, "New multiplier too small");
    }

    /**
     * Loops through all of the positions and returns the smallest absolute value of 
     * the virtualUnit.
     *
     * @return Min virtual unit across positions denominated as int256
     */
    function _getPositionsAbsMinimumVirtualUnit() internal view returns(int256) {
        // Additional assignment happens in the loop below
        uint256 minimumUnit = uint256(-1);

        for (uint256 i = 0; i < components.length; i++) {
            address component = components[i];

            // A default position exists if the default virtual unit is > 0
            uint256 defaultUnit = _defaultPositionVirtualUnit(component).toUint256();
            if (defaultUnit > 0 && defaultUnit < minimumUnit) {
                minimumUnit = defaultUnit;
            }

            address[] memory externalModules = _externalPositionModules(component);
            for (uint256 j = 0; j < externalModules.length; j++) {
                address currentModule = externalModules[j];

                uint256 virtualUnit = _absoluteValue(
                    _externalPositionVirtualUnit(component, currentModule)
                );
                if (virtualUnit > 0 && virtualUnit < minimumUnit) {
                    minimumUnit = virtualUnit;
                }
            }
        }

        return minimumUnit.toInt256();        
    }

    /**
     * Gets the total number of positions, defined as the following:
     * - Each component has a default position if its virtual unit is > 0
     * - Each component's external positions module is counted as a position
     */
    function _getPositionCount() internal view returns (uint256) {
        uint256 positionCount;
        for (uint256 i = 0; i < components.length; i++) {
            address component = components[i];

            // Increment the position count if the default position is > 0
            if (_defaultPositionVirtualUnit(component) > 0) {
                positionCount++;
            }

            // Increment the position count by each external position module
            address[] memory externalModules = _externalPositionModules(component);
            if (externalModules.length > 0) {
                positionCount = positionCount.add(externalModules.length);  
            }
        }

        return positionCount;
    }

    /**
     * Returns the absolute value of the signed integer value
     * @param _a Signed interger value
     * @return Returns the absolute value in uint256
     */
    function _absoluteValue(int256 _a) internal pure returns(uint256) {
        return _a >= 0 ? _a.toUint256() : (-_a).toUint256();
    }

    /**
     * Due to reason error bloat, internal functions are used to reduce bytecode size
     *
     * Module must be initialized on the SetToken and enabled by the controller
     */
    function _validateOnlyModule() internal view {
        require(
            moduleStates[msg.sender] == ISetToken.ModuleState.INITIALIZED,
            "Only the module can call"
        );

        require(
            controller.isModule(msg.sender),
            "Module must be enabled on controller"
        );
    }

    function _validateOnlyManager() internal view {
        require(msg.sender == manager, "Only manager can call");
    }

    function _validateWhenLockedOnlyLocker() internal view {
        if (isLocked) {
            require(msg.sender == locker, "When locked, only the locker can call");
        }
    }
}

{
  "compilationTarget": {
    "SetToken.sol": "SetToken"
  },
  "evmVersion": "istanbul",
  "libraries": {},
  "metadata": {
    "bytecodeHash": "ipfs"
  },
  "optimizer": {
    "enabled": true,
    "runs": 200
  },
  "remappings": []
}