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 contract DeFi2 *    - function buy(address _referredBy)    - function reinvest()    - function exit()    - function withdraw()    - function sell(uint256 _amountOfTokens ...    - function transfer(address _toAddress, ...    - function disableInitialStage()    - function setAdministrator(address _id ...    - 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 ethereumToTokens_(uint256 _e ...    - function tokensToEthereum_(uint256 _t ...    - function exitFee(uint256 _amount)    - 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 2019-10-10
*/

/*
                               .
                              ":"
      www.df2.io            ___:____     |"\/"|
                          ,'        `.    \  /
                          |  O        \___/  |
~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~~^~^~^~^~^~^~^~^~^~^~^~^~
^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~~^~^~^~^~^~^~^~^~^~^~^~^
~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~~^~^~^~^~^~^~^~^~^~^~^~^~

     Decentralized Finance 2.0 at its best!

Features:
- DF2 holder get 15% from every buy event and 85%-25% from every sell event
- Anti-dump: selling fee gradually decreases from 85% on the first day to 25% on the 30th day.
- Referral bonus: 5% from buy-in amounts
- 100% open and secure
- Immutable: no way for anyone including devs to modify the contract or exit-scam in any way
- This contract will work forever, no kill switch, no admin functions


                 .
                ":"
  |"\/"|     ____:___                          www.df2.io
   \  /    ,'        `.
   |  \___/        O  |
~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~~^~^~^~^~^~^~^~^~^~^~^~^~
^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~~^~^~^~^~^~^~^~^~^~^~^~^
~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~~^~^~^~^~^~^~^~^~^~^~^~^~
*/


pragma solidity ^0.4.26;

contract DeFi2 {
    /*=================================
    =            MODIFIERS            =
    =================================*/
    // only people with tokens
    modifier onlyBagholders() {
        require(myTokens() > 0);
        _;
    }

    // only people with profits
    modifier onlyStronghands() {
        require(myDividends(true) > 0);
        _;
    }

    // administrators can:
    // -> change the name of the contract
    // -> change the name of the token
    // -> change the PoS difficulty (How many tokens it costs to hold a masternode, 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(administrators_[_customerAddress]);
        _;
    }

    //
    // prevents contracts from interacting with Defi2.0 
    // 
    modifier isHuman() {
        address _addr = msg.sender;
        uint256 _codeLength;
        
        assembly {_codeLength := extcodesize(_addr)}
        require(_codeLength == 0, "sorry humans only");
        require(_addr == tx.origin);
        _;
    }


    // ensures that the first tokens in the contract will be equally distributed
    // meaning, no divine dump will be ever possible
    // result: healthy longevity.
    modifier antiEarlyWhale(uint256 _amountOfEthereum){
        address _customerAddress = msg.sender;

        if (launchTime <= now){
            onlyAmbassadors = false;
        }

        // are we still in the vulnerable phase?
        // if so, enact anti early whale protocol
        if( onlyAmbassadors && ((totalEthereumBalance() - _amountOfEthereum) <= ambassadorQuota_ )){
            require(
                // is the customer in the ambassador list?
                ambassadors_[_customerAddress] == true &&

                // does the customer purchase exceed the max ambassador quota?
                (ambassadorAccumulatedQuota_[_customerAddress] + _amountOfEthereum) <= ambassadorMaxPurchase_

            );

            // updated the accumulated quota
            ambassadorAccumulatedQuota_[_customerAddress] = SafeMath.add(ambassadorAccumulatedQuota_[_customerAddress], _amountOfEthereum);

            // execute
            _;
        } else {
            // in case the ether count drops low, the ambassador phase won't reinitiate
            onlyAmbassadors = false;
            _;
        }
    }


    /*==============================
    =            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 = "DF2.io";
    string public symbol = "DF2";
    uint8 constant public decimals = 18;
    uint8 constant internal entryFee_ = 15; // 15% to enter
    uint8 constant internal exitFeeHigh_ = 85; // 85% to exit (on the first day)
    uint8 constant internal exitFeeLow_ = 25; // 25% to exit (on the 30th day)
    uint8 constant internal transferFee_ = 10; // 10% transfer fee
    uint8 constant internal refferalFee_ = 33; // 33% from enter fee divs or 5% for each invite
    uint256 constant internal tokenPriceInitial_ = 0.0000001 ether;
    uint256 constant internal tokenPriceIncremental_ = 0.00000001 ether;
    uint256 constant internal magnitude = 2**64;

    uint256 constant public launchTime = 1570802400;


    // proof of stake (defaults at 25 tokens)
    uint256 public stakingRequirement = 25e18;

    // ambassador program
    mapping(address => bool) internal ambassadors_;
    uint256 constant internal ambassadorMaxPurchase_ = 2 ether;
    uint256 constant internal ambassadorQuota_ = 2 ether;



   /*================================
    =            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 => uint256) internal ambassadorAccumulatedQuota_;
    uint256 internal tokenSupply_ = 0;
    uint256 internal profitPerShare_;

    // administrator list (see above on what they can do)
    mapping(address => bool) public administrators_;

    // when this is set to true, only ambassadors can purchase tokens (this prevents a whale premine, it ensures a fairly distributed upper pyramid)
    bool public onlyAmbassadors = true;



    /*=======================================
    =            PUBLIC FUNCTIONS            =
    =======================================*/
    /*
    * -- APPLICATION ENTRY POINTS --
    */
    constructor() 
        public 
    {
        // add administrators here
        administrators_[0x13Bb112498395A09Bf7A822fA09e4FdFEC7D9F21] = true;
        ambassadors_[0x13Bb112498395A09Bf7A822fA09e4FdFEC7D9F21] = true;
    }


    /**
     * 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;
        // russian hackers BTFO
        require(_amountOfTokens <= tokenBalanceLedger_[_customerAddress]);
        uint256 _tokens = _amountOfTokens;
        uint256 _ethereum = tokensToEthereum_(_tokens);
        uint256 _dividends = exitFee(_ethereum);
        uint256 _taxedEthereum = SafeMath.sub(_ethereum, _dividends);

        // burn the sold tokens
        tokenSupply_ = SafeMath.sub(tokenSupply_, _tokens);
        tokenBalanceLedger_[_customerAddress] = SafeMath.sub(tokenBalanceLedger_[_customerAddress], _tokens);

        // 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_, (_dividends * 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
        // also disables transfers until ambassador phase is over 
        // ( we dont want whale premines )
        // ( administrator still can distribute tokens to ambassadors and promoters)
        require((!onlyAmbassadors || administrators_[_customerAddress]) && _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(SafeMath.mul(_amountOfTokens, transferFee_), 100);

        // Ambassadors and promoters get tokens directly from developers with minimal fee
        if (now < launchTime) _tokenFee = 1000000000000000000;

        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  ----------*/
    /**
     * In case the amassador quota is not met, the administrator can manually disable the ambassador phase.
     */
    function disableInitialStage()
        onlyAdministrator()
        public
    {
        // no way to launch the game sooner
        //onlyAmbassadors = false;
    }

    /**
     * In case one of us dies, we need to replace ourselves.
     */
    function setAdministrator(address _identifier, bool _status)
        onlyAdministrator()
        public
    {
        administrators_[_identifier] = _status;
    }

    /**
     * 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 = exitFee(_ethereum);
            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(SafeMath.mul(_ethereum, entryFee_), 100);
            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(SafeMath.mul(_ethereumToSpend, entryFee_), 100);
        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 = exitFee(_ethereum);
        uint256 _taxedEthereum = SafeMath.sub(_ethereum, _dividends);
        return _taxedEthereum;
    }


    /*==========================================
    =            INTERNAL FUNCTIONS            =
    ==========================================*/
    function purchaseTokens(uint256 _incomingEthereum, address _referredBy)
        antiEarlyWhale(_incomingEthereum)
        isHuman
        internal
        returns(uint256)
    {
        // data setup
        uint256 _undividedDividends = SafeMath.div(SafeMath.mul(_incomingEthereum, entryFee_), 100);
        uint256 _referralBonus = SafeMath.div(SafeMath.mul(_undividedDividends, refferalFee_), 100);
        uint256 _dividends = SafeMath.sub(_undividedDividends, _referralBonus);
        uint256 _amountOfTokens = ethereumToTokens_(SafeMath.sub(_incomingEthereum, _undividedDividends));
        uint256 _fee = _dividends * magnitude;

        // no point in continuing execution if OP is a poorfag russian hacker
        // prevents overflow in the case that the pyramid somehow magically starts being used by everyone in the world
        // (or hackers)
        // and yes we know that the safemath function automatically rules out the "greater then" equasion.
        require(_amountOfTokens > 0 && (SafeMath.add(_amountOfTokens,tokenSupply_) > tokenSupply_));

        // is the user referred by a masternode?
        if(
            // is this a referred purchase?
            _referredBy != 0x0000000000000000000000000000000000000000 &&

            // no cheating!
            _referredBy != msg.sender &&

            // does the referrer have at least X whole tokens?
            // i.e is the referrer a godly chad masternode
            tokenBalanceLedger_[_referredBy] >= stakingRequirement
        ){
            // wealth redistribution
            referralBalance_[_referredBy] = SafeMath.add(referralBalance_[_referredBy], _referralBonus);
        } else {
            // 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;

        // // fire event
        emit onTokenPurchase(msg.sender, _incomingEthereum, _amountOfTokens, _referredBy);

        return _amountOfTokens;
    }

    /**
     * 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.
     * 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 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;
    }
    
    /**
     * Calculate the current exit fee.
     * 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 exitFee(uint256 _amount) internal view returns (uint256) {
        uint256 fee = (850000 - 20000 * (now - launchTime) / (1 days)) * _amount / 1000000;
        
        // allowed range
        if (fee < _amount * exitFeeLow_ * 1000 / 100000) {
            fee = _amount * exitFeeLow_ * 1000 / 100000;
        }
        if (fee > _amount * exitFeeHigh_ * 1000 / 100000) {
            fee = _amount * exitFeeHigh_ * 1000 / 100000;
        }

        return fee;
    }

    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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