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 main(input){
  const lines = input.split('\n');
  const K = lines.shift().split(' ').map(x => parseInt(x))[0];

  var result = Infinity;
  for(var i=1;i<=100000;i++){
    var current = 0;
    var nums = (K*i).toString().split('').map(x => parseInt(x));
    for(var j=0;j<nums.length;j++){
      current += nums[j];
    }
    if(current < result){
      result = current;
    }
    current=0;
  }

  console.log(result);

}

main(require('fs').readFileSync('/dev/stdin', 'utf8'));