Problem:
Score : 700 points

Problem Statement

Find the smallest possible sum of the digits in the decimal notation of a positive multiple of K.

Constraints

2 \leq K \leq 10^5

K is an integer.

Input

Input is given from Standard Input in the following format:

K

Output

Print the smallest possible sum of the digits in the decimal notation of a positive multiple of K.

Sample Input 1

6

Sample Output 1

3

12=6×2 yields the smallest sum.

Sample Input 2

41

Sample Output 2

5

11111=41×271 yields the smallest sum.

Sample Input 3

79992

Sample Output 3

36

Solution in JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

(function() {
    'use strict';

    var lines = [];
    require('readline').createInterface({
      input: process.stdin,
      output: process.stdout
    }).on('line', function(line) {
      lines.push(line);
    });
    process.stdin.on('end', function() {
      //lines.forEach(function(line) {
        //var tokens = line.split(' ').map(Number);
        //    console.log(tokens[0] + ' ' + tokens[1]);
      //}
      //)
      ;

    // ToDo start
      var N = parseInt(lines[0])
      var Minsum = 999999999
      for (var i=1;i<10;i++){
        var nm = i*N
        var cnm = nm.toString()
        var hnm = cnm.split('')
        var sum = 0
        for (var j=0; j< cnm.length ; j++) {
            sum += parseInt(hnm[j])
        }
//        console.log("nm:"+  nm + "  sum:" + sum )
        if ( sum < Minsum) {
            Minsum = sum
        }
      }
      console.log(Minsum)
      
//      console.log( Math.pow(parseInt(lines[0]),2) - parseInt(lines[1])  )
    // ToDo end

    });


})();