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 C# (Mono 4.6.2.0) (judge verdict: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Math;

class Program{
  public static void Main(){

    //入力
    int n = int.Parse(Console.ReadLine());
    
    //処理
    int a = 0 , b = 0;
    //1/2乗を整数値で求める
	int m = (int)Pow(n,0.5);
    //mから割り切れる数を探して、F(a,b)が最小となる組み合わせを探す
    for(int i=m; i>0; i--){
      if(n % i == 0){
        a = i;
        b = n / a;
        break;
      }
    }
    
    //桁数を求める
    int ans = 0;
    while(b>0){
      b /= 10;
      ans++;
    }
    
    Console.WriteLine(ans);
  }
}