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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
public class Hello{
    static long CntDigit(long n){
        long count = 0;
        while(n > 0){
            n /= 10;
            count++;
        }
        return count;
    }
    public static void Main(){
        var N = long.Parse(Console.ReadLine());
        long ans = CntDigit(N);
        for(var i = 1;i <= N / 2;i++){
            if(N % i != 0){
                continue;
            }
            var x = N / i;
            
            var max = Math.Max(CntDigit(x),CntDigit(i));
            ans = Math.Min(ans,max);
        }
        Console.WriteLine(ans);
    }
}