Problem: Little X used to play a card game called "24 Game", but recently he has found it too easy. So he invented a new game.

Initially you have a sequence of n integers: 1, 2, ..., n. In a single step, you can pick two of them, let's denote them a and b, erase them from the sequence, and append to the sequence either a + b, or a - b, or a × b.

After n - 1 steps there is only one number left. Can you make this number equal to 24?

Input

The first line contains a single integer n (1 ≤ n ≤ 105).

Output

If it's possible, print "YES" in the first line. Otherwise, print "NO" (without the quotes).

If there is a way to obtain 24 as the result number, in the following n - 1 lines print the required operations an operation per line. Each operation should be in form: "a op b = c". Where a and b are the numbers you've picked at this operation; op is either "+", or "-", or "*"; c is the result of corresponding operation. Note, that the absolute value of c mustn't be greater than 1018. The result of the last operation must be equal to 24. Separate operator sign and equality sign from numbers with spaces.

If there are multiple valid answers, you may print any of them.

Examples

Input

1


Output

NO


Input

8


Output

YES
8 * 7 = 56
6 * 5 = 30
3 - 4 = -1
1 - 2 = -1
30 - -1 = 31
56 - 31 = 25
25 + -1 = 24

Solution (in JAVA):

Solution:
function ProblemSolver() {

    this.rec = function( arr , callCounter ) {
        var i , sz , j , k , newArr , a , b , c , d , res , r1 , newCallCounter;
        res = false;
        sz = arr.length;
        newCallCounter = callCounter + 1;
        if( callCounter > this.n - 1 ) {
            return res;
        }
        if( callCounter == this.n - 1 && sz > 1 ) {
            return res;
        }
        if( sz == 1 ) {
            if( arr[ 0 ] == 24 && callCounter == this.n - 1 ) {
                res = true;
            }
            return res;
        }
        for( i = 0 ; i < sz ; i++ ) {
            for( j = i + 1 ; j < sz ; j++ ) {
                a = arr[ i ] * arr[ j ];
                b = arr[ i ] + arr[ j ];
                c = arr[ i ] - arr[ j ];
                d = arr[ j ] - arr[ i ];
                newArr = new Array();
                for( k = 0 ; k < sz ; k++ ) {
                    if( k != i && k != j ) {
                        newArr.push( arr[ k ] );
                    }
                }
                newArr.push( a );
                r1 = this.rec( newArr , newCallCounter );
                if( r1 == true ) {
                    this.arr[ this.cn ] = arr[ i ];
                    this.brr[ this.cn ] = arr[ j ];
                    this.crr[ this.cn ] = a;
                    this.srr[ this.cn ] = "*";
                    this.cn++;
                    res = true;
                    return res;
                }
                newArr.splice( newArr.length - 1 , 1 );
                newArr.push( b );
                r1 = this.rec( newArr , newCallCounter );
                if( r1 == true ) {
                    this.arr[ this.cn ] = arr[ i ];
                    this.brr[ this.cn ] = arr[ j ];
                    this.crr[ this.cn ] = b;
                    this.srr[ this.cn ] = "+";
                    this.cn++;
                    res = true;
                    return res;
                }
                newArr.splice( newArr.length - 1 , 1 );
                newArr.push( c );
                r1 = this.rec( newArr , newCallCounter );
                if( r1 == true ) {
                    this.arr[ this.cn ] = arr[ i ];
                    this.brr[ this.cn ] = arr[ j ];
                    this.crr[ this.cn ] = c;
                    this.srr[ this.cn ] = "-";
                    this.cn++;
                    res = true;
                    return res;
                }
                newArr.splice( newArr.length - 1 , 1 );
                if( c != d ) {
                    newArr.push( d );
                    r1 = this.rec( newArr , newCallCounter );
                    if( r1 == true ) {
                        this.arr[ this.cn ] = arr[ j ];
                        this.brr[ this.cn ] = arr[ i ];
                        this.crr[ this.cn ] = d;
                        this.srr[ this.cn ] = "-";
                        this.cn++;
                        res = true;
                        return res;
                    }
                }
            }
        }
        return res;
    };

    this.solveCase = function() {
        var res , i , j , arr;
        arr = new Array();
        if( this.n < 4 ) {
            print( "NO" );
            return;
        }
        print( "YES" );
        if( this.n > 8 ) {
            print( "1 * 2 = 2" );
            print( "3 * 4 = 12" );
            print( "2 * 12 = 24" );
            print( "5 - 6 = -1" );
            print( "7 - 8 = -1" );
            print( "-1 - -1 = 0" );
            for( i = 9 ; i <= this.n ; i++ ) {
                print( "0 * " + i + " = 0" );
            }
            print( "24 + 0 = 24" );
            return;
        }
        for( i = 1 ; i <= this.n ; i++ ) {
            arr.push( i );
        }
        this.cn = 0;
        res = this.rec( arr , 0 );
        for( i = this.cn - 1 ; i >= 0 ; i-- ) {
            print( this.arr[ i ] + " " + this.srr[ i ] + " " + this.brr[ i ] + " = " + this.crr[ i ] );
        }
    };

    this.getInput = function( irObj ) {
        var hasMoreInput , i;
        hasMoreInput = true;
        try {
            this.n = irObj.nextInt();
        }
        catch( ex ) {
            hasMoreInput = false;
        }
        return hasMoreInput;
    };

    this.clearArraysPerCase = function() {
        var i;
        this.arr = new Array();
        this.brr = new Array();
        this.adj_list = new Array();
        for( i = 0 ; i < this.lim1 ; i++ ) {
            this.arr.push( 0 );
            this.brr.push( 0 );
            this.adj_list.push( new Array() );
        }
    };

    this.clearPerCase = function() {
        this.cn = 0;
        this.cc++;
        //this.clearArraysPerCase() ;
    };

    this.HAS_TEST_CASES = false;
    this.INPUT_FILE_NAME = "test.in";
    this.OUTPUT_FILE_NAME = "out.txt";
    this.DO_OUTPUT_TO_FILE = false;

    this.declareAndFillArrays = function() {
        var i , j;
        this.srr = new Array();
        this.vis = new Array();
        this.arr = new Array();
        this.brr = new Array();
        this.crr = new Array();
        this.memo = new Array();
        this.done = new Array();
        this.adj_list = new Array();
        for( i = 0 ; i < this.lim1 ; i++ ) {
            this.srr.push( "" );
            this.vis.push( 0 );
            this.arr.push( 0 );
            this.brr.push( 0 );
            this.crr.push( 0 );
            this.adj_list.push( new Array() );
        }
        for( i = 0 ; i < this.lim2 ; i++ ) {
            this.memo.push( new Array() );
            this.done.push( new Array() );
            for( j = 0 ; j < this.lim2 ; j++ ) {
                this.memo[ i ].push( -1 );
                this.done[ i ].push( 0 );
            }
        }
    };

    this.init = function() {
        this.lim1 = 100010;
        this.lim2 = 110;
        this.cc = 1;
        this.ind = 1;
        this.n = 0;
        this.cn = 0;
        this.declareAndFillArrays();
    };

    this.memsetArray1D = function( arrParam , val ) {
        var i;
        if( arrParam == null ) {
            throw new Error( "No array supplied in the parameter!" );
        }
        if( val == null ) {
            throw new Error( "No value for memset has been supplied in the parameter!" );
        }
        arrParam = new Array();
        for( i = 0 ; i < this.lim1 ; i++ ) {
            arrParam.push( val );
        }
        return arrParam;
    };

    this.getStringLength = function( stringData ) {
        var len , lengthType;
        len = stringData.length;
        lengthType = typeof len;
        if( lengthType == "function" ) {
            len = stringData.length();
        }
        else {
            len = stringData.length;
        }
        return len;
    };

    this.init();
}

function InputReader() {
    this.allLines = new Array();
    this.currrentLineNumber = 0;
    this.currrentCharacterIndex = 0;

    this.readAllLines = function() {
        var singleLine;
        while( true ) {
            try {
                singleLine = readline();
                if( singleLine == null ) {
                    break;
                }
            }
            catch( ex ) {
                break;
            }
            this.allLines.push( singleLine );
        }
    };

    this.readAllLinesFromRhinoStdin = function() {
        importPackage( java.io );
        importPackage( java.lang );
        var singleLine , reader;
        reader = new BufferedReader( new InputStreamReader( System[ "in" ] ) );
        this.allLines = [];
        while( true ) {
            singleLine = reader.readLine();
            if( singleLine != null ) {
                this.allLines.push( singleLine );
            }
            else {
                break;
            }
        }
    };

    this.readAllLinesFromNodeStdin = function() {
        var fsObj , size , rawData;
        process.stdin.setEncoding( 'ascii' );
        fsObj = require( 'fs' );
        size = fsObj.fstatSync( process.stdin.fd ).size;
        rawData = fsObj.readSync( process.stdin.fd , size )[ 0 ];
        this.parseRawData( rawData );
    };

    this.parseRawData = function( data ) {
        var len , i , currentString;
        len = data.length;
        currentString = "";
        for( i = 0 ; i < len ; i++ ) {
            if( data[ i ] == '\r' ) {
            }
            else if( data[ i ] == '\n' ) {
                this.allLines.push( currentString );
                currentString = "";
            }
            else {
                currentString += data[ i ];
            }
        }
        if( currentString != "" ) {
            this.allLines.push( currentString );
        }
    };

    this.readAllLinesFromFile = function( inputFileName ) {
        var currentDirectory , fsObj , inputFilePath , rawData;
        fsObj = require( 'fs' );
        currentDirectory = __dirname;
        inputFilePath = currentDirectory + "\\" + inputFileName;
        rawData = fsObj.readFileSync( inputFilePath , "utf8" );
        this.parseRawData( rawData );
    };

    this.next = function( flag ) {
        var len , i , startIdx , res , endIdx , lengthType;
        len = this.allLines[ this.currrentLineNumber ].length;
        lengthType = typeof len;
        if( lengthType == "function" ) {
            len = this.allLines[ this.currrentLineNumber ].length();
        }
        if( flag == 0 ) {
            res = "";
            for( i = this.currrentCharacterIndex ; i < len ; i++ ) {
                res += String.fromCharCode( this.allLines[ this.currrentLineNumber ].charCodeAt( i ) );
            }
            this.currrentLineNumber++;
            this.currrentCharacterIndex = 0;
            return res;
        }
        while( true ) {
            if( this.currrentLineNumber >= this.allLines.length ) {
                throw new Error( "No more tokens available!" );
            }
            startIdx = -1;
            for( i = this.currrentCharacterIndex ; i < len ; i++ ) {
                if( this.allLines[ this.currrentLineNumber ].charCodeAt( i ) != ' '.charCodeAt( 0 ) && this.allLines[ this.currrentLineNumber ].charCodeAt( i ) != '\t'.charCodeAt( 0 ) ) {
                    startIdx = i;
                    break;
                }
            }
            if( startIdx == -1 ) {
                this.currrentLineNumber++;
                this.currrentCharacterIndex = 0;
                continue;
            }
            res = "";
            endIdx = -1;
            for( i = startIdx ; i < len ; i++ ) {
                if( this.allLines[ this.currrentLineNumber ].charCodeAt( i ) == ' '.charCodeAt( 0 ) || this.allLines[ this.currrentLineNumber ].charCodeAt( i ) == '\t'.charCodeAt( 0 ) ) {
                    endIdx = i;
                    break;
                }
                res += String.fromCharCode( this.allLines[ this.currrentLineNumber ].charCodeAt( i ) );
            }
            if( endIdx == -1 ) {
                this.currrentLineNumber++;
                this.currrentCharacterIndex = 0;
            }
            else {
                this.currrentCharacterIndex = endIdx;
            }
            return res;
        }
    };

    this.nextInt = function() {
        return parseInt( this.next( 1 ) );
    };

    this.nextDouble = function() {
        return parseFloat( this.next( 1 ) );
    };

    this.nextString = function() {
        return this.next( 1 );
    };

    this.nextLine = function() {
        this.next( 0 );
    };
}

function FileOutputHandler() {
    this.resultantStringArray = new Array();

    this.addNewLine = function( newString ) {
        this.resultantStringArray.push( newString );
    };

    this.clearPercase = function() {
        this.resultantStringArray = new Array();
    };

    this.flushOutOutputToFile = function( outputFileName ) {
        var i , sz , res , currentDirectory , fsObj , outputFilePath;
        res = "";
        sz = this.resultantStringArray.length;
        for( i = 0 ; i < sz ; i++ ) {
            if( i != 0 ) {
                res += "\n";
            }
            res += this.resultantStringArray[ i ];
        }
        fsObj = require( 'fs' );
        currentDirectory = __dirname;
        outputFilePath = currentDirectory + "\\" + outputFileName;
        if( currentDirectory.charAt( 1 ) != ":" ) {
            //not local machine/windows
            outputFilePath = outputFileName;
        }
        fsObj.writeFileSync( outputFilePath , res );
        this.clearPercase();
    };
}

function CodeExecutioner() {
    this.irObj = new InputReader();
    this.psObj = new ProblemSolver();
    this.fohObj = new FileOutputHandler();

    this.runCode = function() {
        var testCases , i , hasMoreTestCases , isLocalMachine , localContext;
        isLocalMachine = false;
        try {
            if( __dirname != null && __dirname.charAt( 1 ) == ':' ) {
                //only on windows
                isLocalMachine = true;
            }
        }
        catch( ex ) {
            isLocalMachine = false;
        }
        if( isLocalMachine == true ) {
            //local machine runs on node and relies on file i/o
            print = console.log;
            if( this.psObj.DO_OUTPUT_TO_FILE == true ) {
                localContext = this.fohObj;
                print = function() {
                    localContext.addNewLine.apply( localContext , arguments );
                }
            }
            this.irObj.readAllLinesFromFile( this.psObj.INPUT_FILE_NAME );
        }
        else {
            //server machine
            try {
                var rlObj = readline;
                //server runs on javasctipt v8 distribution and has readline method on global context
                this.irObj.readAllLines();
            }
            catch( ex ) {
                try {
                    var pObj = process;
                    //server runs on node
                    print = console.log;
                    this.irObj.readAllLinesFromNodeStdin();
                }
                catch( ex ) {
                    try {
                        var ipObj = importPackage;
                        //server runs on rhino
                        this.irObj.readAllLinesFromRhinoStdin();
                    }
                    catch( ex ) {
                        throw new Error( "Unknown javasctipt distribution!" );
                    }
                }
            }
        }
        if( this.psObj.HAS_TEST_CASES == true ) {
            testCases = this.irObj.nextInt();
            for( i = 0 ; i < testCases ; i++ ) {
                this.psObj.clearPerCase();
                this.psObj.getInput( this.irObj );
                this.psObj.solveCase();
            }
        }
        else {
            while( true ) {
                this.psObj.clearPerCase();
                hasMoreTestCases = this.psObj.getInput( this.irObj );
                if( hasMoreTestCases == false ) {
                    break;
                }
                this.psObj.solveCase();
            }
        }
        if( this.psObj.DO_OUTPUT_TO_FILE == true ) {
            //only works for local machine(tested)
            this.fohObj.flushOutOutputToFile( this.psObj.OUTPUT_FILE_NAME );
        }
    };

    this.runCode();
}

new CodeExecutioner();