Problem:
Score : 300 points

Problem Statement

You are given an integer N.

For two positive integers A and B, we will define F(A,B) as the larger of the following: the number of digits in the decimal notation of A, and the number of digits in the decimal notation of B.

For example, F(3,11) = 2 since 3 has one digit and 11 has two digits.

Find the minimum value of F(A,B) as (A,B) ranges over all pairs of positive integers such that N = A \times B.

Constraints

1 \leq N \leq 10^{10}

N is an integer.

Input

The input is given from Standard Input in the following format:

N

Output

Print the minimum value of F(A,B) as (A,B) ranges over all pairs of positive integers such that N = A \times B.

Sample Input 1

10000

Sample Output 1

3

F(A,B) has a minimum value of 3 at (A,B)=(100,100).

Sample Input 2

1000003

Sample Output 2

7

There are two pairs (A,B) that satisfy the condition: (1,1000003) and (1000003,1). For these pairs, F(1,1000003)=F(1000003,1)=7.

Sample Input 3

9876543210

Sample Output 3

6

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

function myout(text){console.log(text);}//standard output
function Main(input) {
	input = parseInt(input);
	//input = input.split(" ");
	//input = input.split("\n");
	//input = input.split(" ").map((a)=>Number(a));
	//input = input.split("\n").map((a)=>Number(a));
  if(input == 1){
     myout("1");
    return;
     }
  
  var list = getDivisorList(input);
  //myout(list);
  var output = 20;
  for(var i = 0; i < list.length / 2; i++){
    var mae = list[i];
    var ato = list[list.length - (i+1)];
    //myout(mae + ":" + ato);
    output = Math.min(output,getKeta(mae,ato));
  }
  myout(output);
}

function getKeta(val1,val2){
  return Math.max(val1.toString().length,val2.toString().length);
}

//約数全列挙(高速)
function getDivisorList(val){
	var list = [];
	for(var i = 1; i * i <= val; i++){
		if(val % i == 0){
			list.push(i);
			if(i * i != val){
				list.push(val / i);
			}
		}
	}
	list.sort(function(a,b){
		return a - b;
	});
	return list;
}
Main(require("fs").readFileSync("/dev/stdin", "utf8").trim());