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 myout(text){console.log(text);}//standard output
function Main(input) {
	input = parseInt(input);
	//input = input.trim().split(" ");
	//input = input.trim().split("\n");
	//input = input.trim().split(" ").map((a)=>Number(a));
	//input = input.trim().split("\n").map((a)=>Number(a));
  var output = 1000000000;
  for(var i = 1; i <= 100000; i ++){
    var tmp = (input * i).toString().split("").map((a)=>Number(a));
    var check = 0;
    for(var j = 0; j < tmp.length; j++){
      check += tmp[j];
    }
    output = Math.min(output, check);
  }
  myout(output);
}

Main(require("fs").readFileSync("/dev/stdin", "utf8").trim());