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•  contract Hourglass *
•    - function buy(address _referredBy)
•    - function reinvest()
•    - function exit()
•    - function withdraw()
•    - function sell(uint256 _amountOfTokens ...
•    - function transfer(address _toAddress, ...
•    - function changeAdmin(address _newAdmi ...
•    - function setStakingRequirement(uint25 ...
•    - function setName(string _name)
•    - function setSymbol(string _symbol)
•    - function totalEthereumBalance()
•    - function totalSupply()
•    - function myTokens()
•    - function myDividends(bool _includeRef ...
•    - function balanceOf(address _customerA ...
•    - function dividendsOf(address _custome ...
•    - function sellPrice()
•    - function buyPrice()
•    - function calculateTokensReceived(uint ...
•    - function calculateEthereumReceived(ui ...
•    - function purchaseTokens(uint256 _inco ...
•    - function calculateReferralBonus(uint2 ...
•    - function ethereumToTokens_(uint256 _e ...
•    - function tokensToEthereum_(uint256 _t ...
•    - function sqrt(uint x)
• library SafeMath
•    - function mul(uint256 a, uint256 b)
•    - function div(uint256 a, uint256 b)
•    - function sub(uint256 a, uint256 b)
•    - function add(uint256 a, uint256 b)

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/**
 *Submitted for verification at Etherscan.io on 2018-11-22
*/

pragma solidity ^0.4.25;


contract Hourglass {
    /*=================================
    =            MODIFIERS            =
    =================================*/
    // only people with tokens
    modifier onlyBagholders() {
        require(myTokens() > 0);
        _;
    }
    
    // only people with profits
    modifier onlyStronghands() {
        require(myDividends(true) > 0);
        _;
    }
    
    // administrator can:
    // -> change the name of the contract
    // -> change the name of the token
    // -> change the PoS difficulty (How many tokens it costs to be a referrer, in case it gets crazy high later)
    // they CANNOT:
    // -> take funds
    // -> disable withdrawals
    // -> kill the contract
    // -> change the price of tokens
    modifier onlyAdministrator(){
        address _customerAddress = msg.sender;
        require(admin_ == _customerAddress);
        _;
    }
    
    
    
    /*==============================
    =            EVENTS            =
    ==============================*/
    event onTokenPurchase(
        address indexed customerAddress,
        uint256 incomingEthereum,
        uint256 tokensMinted,
        address indexed referredBy
    );
    
    event onTokenSell(
        address indexed customerAddress,
        uint256 tokensBurned,
        uint256 ethereumEarned
    );
    
    event onReinvestment(
        address indexed customerAddress,
        uint256 ethereumReinvested,
        uint256 tokensMinted
    );
    
    event onWithdraw(
        address indexed customerAddress,
        uint256 ethereumWithdrawn
    );
    
    // ERC20
    event Transfer(
        address indexed from,
        address indexed to,
        uint256 tokens
    );
    
    
    /*=====================================
    =            CONFIGURABLES            =
    =====================================*/
    string public name = "E3D";
    string public symbol = "E3D";
    uint8 constant public decimals = 18;
    uint8 constant internal dividendFee_ = 30;
    uint256 constant internal tokenPriceInitial_ = 0.0000001 ether;
    uint256 constant internal tokenPriceIncremental_ = 0.000000001 ether;
    uint256 constant internal magnitude = 2**64;
    
    // proof of stake (defaults at 100 tokens)
    uint256 public stakingRequirement = 100e18;
   
   //admin details
    address private admin_;
    
    
    
   /*================================
    =            DATASETS            =
    ================================*/
    // amount of shares for each address (scaled number)
    mapping(address => uint256) internal tokenBalanceLedger_;
    mapping(address => uint256) internal referralBalance_;
    mapping(address => int256) internal payoutsTo_;
    mapping(address => address) internal firstReferrer;
    uint256 internal tokenSupply_ = 0;
    uint256 internal profitPerShare_;
    
    /*=======================================
    =            PUBLIC FUNCTIONS            =
    =======================================*/
    /*
    * -- APPLICATION ENTRY POINTS --  
    */
    constructor()
        public
    {
        // add administrator here
        admin_ = msg.sender;
        
    }

    
     
    /**
     * Converts all incoming ethereum to tokens for the caller, and passes down the referral addy (if any)
     */
    function buy(address _referredBy)
        public
        payable
        returns(uint256)
    {
        purchaseTokens(msg.value, _referredBy);
    }
    
    /**
     * Fallback function to handle ethereum that was send straight to the contract
     * Unfortunately we cannot use a referral address this way.
     */
    function()
        payable
        public
    {
        purchaseTokens(msg.value, 0x0);
    }
    
    /**
     * Converts all of caller's dividends to tokens.
     */
    function reinvest()
        onlyStronghands()
        public
    {
        // fetch dividends
        uint256 _dividends = myDividends(false); // retrieve ref. bonus later in the code
        
        // pay out the dividends virtually
        address _customerAddress = msg.sender;
        payoutsTo_[_customerAddress] +=  (int256) (_dividends * magnitude);
        
        // retrieve ref. bonus
        _dividends += referralBalance_[_customerAddress];
        referralBalance_[_customerAddress] = 0;
        
        // dispatch a buy order with the virtualized "withdrawn dividends"
        uint256 _tokens = purchaseTokens(_dividends, 0x0);
        
        // fire event
        emit onReinvestment(_customerAddress, _dividends, _tokens);
    }
    
    /**
     * Alias of sell() and withdraw().
     */
    function exit()
        public
    {
        // get token count for caller & sell them all
        address _customerAddress = msg.sender;
        uint256 _tokens = tokenBalanceLedger_[_customerAddress];
        if(_tokens > 0) sell(_tokens);
        
        // lambo delivery service
        withdraw();
    }

    /**
     * Withdraws all of the callers earnings.
     */
    function withdraw()
        onlyStronghands()
        public
    {
        // setup data
        address _customerAddress = msg.sender;
        uint256 _dividends = myDividends(false); // get ref. bonus later in the code
        
        // update dividend tracker
        payoutsTo_[_customerAddress] +=  (int256) (_dividends * magnitude);
        
        // add ref. bonus
        _dividends += referralBalance_[_customerAddress];
        referralBalance_[_customerAddress] = 0;
        
        // lambo delivery service
        _customerAddress.transfer(_dividends);
        
        // fire event
        emit onWithdraw(_customerAddress, _dividends);
    }
    
    /**
     * Liquifies tokens to ethereum.
     */
    function sell(uint256 _amountOfTokens)
        onlyBagholders()
        public
    {
        // setup data
        address _customerAddress = msg.sender;
       //should have the balance to sell
        require(_amountOfTokens <= tokenBalanceLedger_[_customerAddress]);
        uint256 _tokens = _amountOfTokens;
        uint256 _ethereum = tokensToEthereum_(_tokens);
        uint256 _dividends = SafeMath.div(_ethereum, 10);
        uint256 _taxedEthereum = SafeMath.sub(_ethereum, _dividends);
        uint256 _adminFees = SafeMath.div(SafeMath.mul(_dividends,3),100);
        uint256 _finalDividends = SafeMath.sub(_dividends,_adminFees);
        
        // burn the sold tokens
        tokenSupply_ = SafeMath.sub(tokenSupply_, _tokens);
        tokenBalanceLedger_[_customerAddress] = SafeMath.sub(tokenBalanceLedger_[_customerAddress], _tokens);

        //Transfer admin fees
        admin_.transfer(_adminFees);
        
        
        // update dividends tracker
        int256 _updatedPayouts = (int256) (profitPerShare_ * _tokens + (_taxedEthereum * magnitude));
        payoutsTo_[_customerAddress] -= _updatedPayouts;       
        
        // dividing by zero is a bad idea
        if (tokenSupply_ > 0) {
            // update the amount of dividends per token
            profitPerShare_ = SafeMath.add(profitPerShare_, (_finalDividends * magnitude) / tokenSupply_);
        }
        
        // fire event
        emit onTokenSell(_customerAddress, _tokens, _taxedEthereum);
    }
    
    
    /**
     * Transfer tokens from the caller to a new holder.
     * Remember, there's a 10% fee here as well.
     */
    function transfer(address _toAddress, uint256 _amountOfTokens)
        onlyBagholders()
        public
        returns(bool)
    {
        // setup
        address _customerAddress = msg.sender;
        
        // make sure we have the requested tokens
        // ( we dont want whale premines )
        require(_amountOfTokens <= tokenBalanceLedger_[_customerAddress]);
        
        // withdraw all outstanding dividends first
        if(myDividends(true) > 0) withdraw();
        
        // liquify 10% of the tokens that are transfered
        // these are dispersed to shareholders
        uint256 _tokenFee = SafeMath.div(_amountOfTokens, 10);
        uint256 _taxedTokens = SafeMath.sub(_amountOfTokens, _tokenFee);
        uint256 _dividends = tokensToEthereum_(_tokenFee);
  
        // burn the fee tokens
        tokenSupply_ = SafeMath.sub(tokenSupply_, _tokenFee);

        // exchange tokens
        tokenBalanceLedger_[_customerAddress] = SafeMath.sub(tokenBalanceLedger_[_customerAddress], _amountOfTokens);
        tokenBalanceLedger_[_toAddress] = SafeMath.add(tokenBalanceLedger_[_toAddress], _taxedTokens);
        
        // update dividend trackers
        payoutsTo_[_customerAddress] -= (int256) (profitPerShare_ * _amountOfTokens);
        payoutsTo_[_toAddress] += (int256) (profitPerShare_ * _taxedTokens);
        
        // disperse dividends among holders
        profitPerShare_ = SafeMath.add(profitPerShare_, (_dividends * magnitude) / tokenSupply_);
        
        // fire event
        emit Transfer(_customerAddress, _toAddress, _taxedTokens);
        
        // ERC20
        return true;
       
    }
    
    /*----------  ADMINISTRATOR ONLY FUNCTIONS  ----------*/
    
    /**
     * Admin can change the admin
    */
    
    function changeAdmin(address _newAdmin) 
    onlyAdministrator() 
    public 
    {
        require(_newAdmin != address(0));
        admin_ = _newAdmin;
    }
    
    /**
     * Precautionary measures in case we need to adjust the masternode rate.
     */
    function setStakingRequirement(uint256 _amountOfTokens)
        onlyAdministrator()
        public
    {
        stakingRequirement = _amountOfTokens;
    }
    
    /**
     * If we want to rebrand, we can.
     */
    function setName(string _name)
        onlyAdministrator()
        public
    {
        name = _name;
    }
    
    /**
     * If we want to rebrand, we can.
     */
    function setSymbol(string _symbol)
        onlyAdministrator()
        public
    {
        symbol = _symbol;
    }

    
    /*----------  HELPERS AND CALCULATORS  ----------*/
    /**
     * Method to view the current Ethereum stored in the contract
     * Example: totalEthereumBalance()
     */
    function totalEthereumBalance()
        public
        view
        returns(uint)
    {
        return address(this).balance;
    }
    
    /**
     * Retrieve the total token supply.
     */
    function totalSupply()
        public
        view
        returns(uint256)
    {
        return tokenSupply_;
    }
    
    /**
     * Retrieve the tokens owned by the caller.
     */
    function myTokens()
        public
        view
        returns(uint256)
    {
        address _customerAddress = msg.sender;
        return balanceOf(_customerAddress);
    }
    
    /**
     * Retrieve the dividends owned by the caller.
     * If `_includeReferralBonus` is to to 1/true, the referral bonus will be included in the calculations.
     * The reason for this, is that in the frontend, we will want to get the total divs (global + ref)
     * But in the internal calculations, we want them separate. 
     */ 
    function myDividends(bool _includeReferralBonus) 
        public 
        view 
        returns(uint256)
    {
        address _customerAddress = msg.sender;
        return _includeReferralBonus ? dividendsOf(_customerAddress) + referralBalance_[_customerAddress] : dividendsOf(_customerAddress) ;
    }
    
    /**
     * Retrieve the token balance of any single address.
     */
    function balanceOf(address _customerAddress)
        view
        public
        returns(uint256)
    {
        return tokenBalanceLedger_[_customerAddress];
    }
    
    /**
     * Retrieve the dividend balance of any single address.
     */
    function dividendsOf(address _customerAddress)
        view
        public
        returns(uint256)
    {
        return (uint256) ((int256)(profitPerShare_ * tokenBalanceLedger_[_customerAddress]) - payoutsTo_[_customerAddress]) / magnitude;
    }
    
    /**
     * Return the buy price of 1 individual token.
     */
    function sellPrice() 
        public 
        view 
        returns(uint256)
    {
        // our calculation relies on the token supply, so we need supply. Doh.
        if(tokenSupply_ == 0){
            return tokenPriceInitial_ - tokenPriceIncremental_;
        } else {
            uint256 _ethereum = tokensToEthereum_(1e18);
            uint256 _dividends = SafeMath.div(_ethereum, dividendFee_  );
            uint256 _taxedEthereum = SafeMath.sub(_ethereum, _dividends);
            return _taxedEthereum;
        }
    }
    
    /**
     * Return the sell price of 1 individual token.
     */
    function buyPrice() 
        public 
        view 
        returns(uint256)
    {
        // our calculation relies on the token supply, so we need supply. Doh.
        if(tokenSupply_ == 0){
            return tokenPriceInitial_ + tokenPriceIncremental_;
        } else {
            uint256 _ethereum = tokensToEthereum_(1e18);
            uint256 _dividends = SafeMath.div(_ethereum, dividendFee_  );
            uint256 _taxedEthereum = SafeMath.add(_ethereum, _dividends);
            return _taxedEthereum;
        }
    }
    
    /**
     * Function for the frontend to dynamically retrieve the price scaling of buy orders.
     */
    function calculateTokensReceived(uint256 _ethereumToSpend) 
        public 
        view 
        returns(uint256)
    {
        uint256 _dividends = SafeMath.div(_ethereumToSpend, dividendFee_);
        uint256 _taxedEthereum = SafeMath.sub(_ethereumToSpend, _dividends);
        uint256 _amountOfTokens = ethereumToTokens_(_taxedEthereum);
        
        return _amountOfTokens;
    }
    
    /**
     * Function for the frontend to dynamically retrieve the price scaling of sell orders.
     */
    function calculateEthereumReceived(uint256 _tokensToSell) 
        public 
        view 
        returns(uint256)
    {
        require(_tokensToSell <= tokenSupply_);
        uint256 _ethereum = tokensToEthereum_(_tokensToSell);
        uint256 _dividends = SafeMath.div(_ethereum, dividendFee_);
        uint256 _taxedEthereum = SafeMath.sub(_ethereum, _dividends);
        return _taxedEthereum;
    }
    
    
    /*==========================================
    =            INTERNAL FUNCTIONS            =
    ==========================================*/
    function purchaseTokens(uint256 _incomingEthereum, address _referredBy)
        internal
        returns(uint256)
    {
        // data setup
        uint256 _undividedDividends = SafeMath.div(SafeMath.mul(_incomingEthereum,dividendFee_),100); //this is the taxed amount as 30% of total investment
        uint256 _referralBonus = SafeMath.div(SafeMath.mul(_undividedDividends, 40),100); //To be given to the referrers
        uint256 _dividends = SafeMath.div(_undividedDividends, 2); //To be distributed among current holders
        uint256 adminFees = SafeMath.div(_undividedDividends,10); //To be transferred to admin
        uint256 _taxedEthereum = SafeMath.sub(_incomingEthereum, _undividedDividends); //Amount for which the user will get the tokens
        uint256 _amountOfTokens = ethereumToTokens_(_taxedEthereum); //number of tokens as per current rate
        uint256 _fee = _dividends * magnitude;
 
        // and yes we know that the safemath function automatically rules out the "greater then" equasion.
        require(_amountOfTokens > 0 && (SafeMath.add(_amountOfTokens,tokenSupply_) > tokenSupply_));
       
        if(!calculateReferralBonus(_referralBonus, _referredBy)) {
            // no ref purchase
            // add the referral bonus back to the global dividends cake
            _dividends = SafeMath.add(_dividends, _referralBonus);
            _fee = _dividends * magnitude;
        }
               
        // we can't give people infinite ethereum
        if(tokenSupply_ > 0){
            
            // add tokens to the pool
            tokenSupply_ = SafeMath.add(tokenSupply_, _amountOfTokens);
 
            // take the amount of dividends gained through this transaction, and allocates them evenly to each shareholder
            profitPerShare_ += (_dividends * magnitude / (tokenSupply_));
            
            // calculate the amount of tokens the customer receives over his purchase 
            _fee = _fee - (_fee-(_amountOfTokens * (_dividends * magnitude / (tokenSupply_))));
        
        } else {
            // add tokens to the pool
            tokenSupply_ = _amountOfTokens;
        }
        
        // update circulating supply & the ledger address for the customer
        tokenBalanceLedger_[msg.sender] = SafeMath.add(tokenBalanceLedger_[msg.sender], _amountOfTokens);
        
        // Tells the contract that the buyer doesn't deserve dividends for the tokens before they owned them;
        //really i know you think you do but you don't
        int256 _updatedPayouts = (int256) ((profitPerShare_ * _amountOfTokens) - _fee);
        payoutsTo_[msg.sender] += _updatedPayouts;
        admin_.transfer(adminFees);
        
        // fire event
        emit onTokenPurchase(msg.sender, _incomingEthereum, _amountOfTokens, _referredBy);
        
        return _amountOfTokens;
    }
    
    
     function calculateReferralBonus(uint256 _referralBonus, address _referredBy) private returns(bool) {

         if(
            // is this a referred purchase?
            _referredBy != 0x0000000000000000000000000000000000000000 &&

            // Ohoo noo, you can't refer yourself buddy :P
            _referredBy != msg.sender &&
            
            // does the referrer fulfill the staking requirement for referrals
            
            tokenBalanceLedger_[_referredBy] >= stakingRequirement
        ) {
            //If the user has already been referred by someone previously, can't be referred by someone else
            if(firstReferrer[msg.sender] != 0x0000000000000000000000000000000000000000) {
                    _referredBy  = firstReferrer[msg.sender];
            }  
            else {
                firstReferrer[msg.sender] = _referredBy;
            }  
                
        //check for second referrer
            if(firstReferrer[_referredBy] != 0x0000000000000000000000000000000000000000)
            { 
                address _secondReferrer = firstReferrer[_referredBy];
                //check for third referrer
                if(firstReferrer[_secondReferrer] != 0x0000000000000000000000000000000000000000) {
                    address _thirdReferrer = firstReferrer[_secondReferrer];

                    //transfer 20% to third referrer
                    referralBalance_[_thirdReferrer] = SafeMath.add(referralBalance_[_thirdReferrer], SafeMath.div(SafeMath.mul(_referralBonus,20),100));
                    //transfer 30% to second referrer
                    referralBalance_[_secondReferrer] = SafeMath.add(referralBalance_[_secondReferrer], SafeMath.div(SafeMath.mul(_referralBonus,30),100));
                    //transfer 50% to first referrer
                    referralBalance_[_referredBy] = SafeMath.add(referralBalance_[_referredBy], SafeMath.div(_referralBonus,2));
                }
                //No Third Referrer then transfer to first and second referrer
                else {
                    //transfer 40% to second referrer
                    referralBalance_[_secondReferrer] = SafeMath.add(referralBalance_[_secondReferrer], SafeMath.div(SafeMath.mul(_referralBonus,40),100));
                    //transfer 60% to first referrer
                    referralBalance_[_referredBy] = SafeMath.add(referralBalance_[_referredBy], SafeMath.div(SafeMath.mul(_referralBonus,60),100));
                }
            } //no second referrer then transfer all to the first referrer
            else {
                referralBalance_[_referredBy] = SafeMath.add(referralBalance_[_referredBy], _referralBonus);
            }
            return true;
    }
    //might be possible that the referrer is 0x0 but previously someone has referred the user
    else if(
            //0x0 coming from the UI
            _referredBy == 0x0000000000000000000000000000000000000000 &&
            
            //check if the somone has previously referred the user
            firstReferrer[msg.sender] != 0x0000000000000000000000000000000000000000 &&

            //The referrer should always has the staking requirement for referring
            tokenBalanceLedger_[firstReferrer[msg.sender]] >= stakingRequirement

        ) {
           //check for second referrer
            if(firstReferrer[_referredBy] != 0x0000000000000000000000000000000000000000)
            { 
                address _secondReferrer1 = firstReferrer[_referredBy];
                //check for third referrer
                if(firstReferrer[_secondReferrer1] != 0x0000000000000000000000000000000000000000) {
                    address _thirdReferrer1 = firstReferrer[_secondReferrer1];

                    //transfer 20% to third referrer
                    referralBalance_[_thirdReferrer1] = SafeMath.add(referralBalance_[_thirdReferrer1], SafeMath.div(SafeMath.mul(_referralBonus,20),100));
                    //transfer 30% to second referrer
                    referralBalance_[_secondReferrer1] = SafeMath.add(referralBalance_[_secondReferrer1], SafeMath.div(SafeMath.mul(_referralBonus,30),100));
                    //transfer 50% to first referrer
                    referralBalance_[_referredBy] = SafeMath.add(referralBalance_[_referredBy], SafeMath.div(_referralBonus,2));
                }
                //No Third Referrer then transfer to first and second referrer
                else {
                    //transfer 40% to second referrer
                    referralBalance_[_secondReferrer1] = SafeMath.add(referralBalance_[_secondReferrer1], SafeMath.div(SafeMath.mul(_referralBonus,40),100));
                    //transfer 60% to first referrer
                    referralBalance_[_referredBy] = SafeMath.add(referralBalance_[_referredBy], SafeMath.div(SafeMath.mul(_referralBonus,40),100));
                }
            } //no second referrer then transfer all to the first referrer
            else {
                referralBalance_[_referredBy] = SafeMath.add(referralBalance_[_referredBy], _referralBonus);
            }
            return true;
        }
        return false;
     }

    /**
     * Calculate Token price based on an amount of incoming ethereum
     * It's an algorithm, hopefully we gave you the whitepaper with it in scientific notation;
     * Some conversions occurred to prevent decimal errors or underflows / overflows in solidity code.
     */
    function ethereumToTokens_(uint256 _ethereum)
        internal
        view
        returns(uint256)
    {
        uint256 _tokenPriceInitial = tokenPriceInitial_ * 1e18;
        uint256 _tokensReceived = 
         (
            (
                // underflow attempts BTFO
                SafeMath.sub(
                    (sqrt
                        (
                            (_tokenPriceInitial**2)
                            +
                            (2*(tokenPriceIncremental_ * 1e18)*(_ethereum * 1e18))
                            +
                            (((tokenPriceIncremental_)**2)*(tokenSupply_**2))
                            +
                            (2*(tokenPriceIncremental_)*_tokenPriceInitial*tokenSupply_)
                        )
                    ), _tokenPriceInitial
                )
            )/(tokenPriceIncremental_)
        )-(tokenSupply_)
        ;
  
        return _tokensReceived;
    }
    
    /**
     * Calculate token sell value.
     * Some conversions occurred to prevent decimal errors or underflows / overflows in solidity code.
     */
     function tokensToEthereum_(uint256 _tokens)
        internal
        view
        returns(uint256)
    {

        uint256 tokens_ = (_tokens + 1e18);
        uint256 _tokenSupply = (tokenSupply_ + 1e18);
        uint256 _etherReceived =
        (
            // underflow attempts BTFO
            SafeMath.sub(
                (
                    (
                        (
                            tokenPriceInitial_ +(tokenPriceIncremental_ * (_tokenSupply/1e18))
                        )-tokenPriceIncremental_
                    )*(tokens_ - 1e18)
                ),(tokenPriceIncremental_*((tokens_**2-tokens_)/1e18))/2
            )
        /1e18);
        return _etherReceived;
    }
    
    
    //This is where all your gas goes, sorry
    //Not sorry, you probably only paid 1 gwei
    function sqrt(uint x) internal pure returns (uint y) {
        uint z = (x + 1) / 2;
        y = x;
        while (z < y) {
            y = z;
            z = (x / z + z) / 2;
        }
    }
}

/**
 * @title SafeMath
 * @dev Math operations with safety checks that throw on error
 */
library SafeMath {

    /**
    * @dev Multiplies two numbers, throws on overflow.
    */
    function mul(uint256 a, uint256 b) internal pure returns (uint256) {
        if (a == 0) {
            return 0;
        }
        uint256 c = a * b;
        assert(c / a == b);
        return c;
    }

    /**
    * @dev Integer division of two numbers, truncating the quotient.
    */
    function div(uint256 a, uint256 b) internal pure returns (uint256) {
        // assert(b > 0); // Solidity automatically throws when dividing by 0
        uint256 c = a / b;
        // assert(a == b * c + a % b); // There is no case in which this doesn't hold
        return c;
    }

    /**
    * @dev Substracts two numbers, throws on overflow (i.e. if subtrahend is greater than minuend).
    */
    function sub(uint256 a, uint256 b) internal pure returns (uint256) {
        assert(b <= a);
        return a - b;
    }

    /**
    * @dev Adds two numbers, throws on overflow.
    */
    function add(uint256 a, uint256 b) internal pure returns (uint256) {
        uint256 c = a + b;
        assert(c >= a);
        return c;
    }
}

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