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.Linq;
using System.Collections.Generic;
using System;

public class P
{
    public int x { get; set; }
    public int y { get; set; }
}

public class Hello
{
    public static void Main()
    {
        var alist = new List<long>();
        var n = long.Parse(Console.ReadLine().Trim());
        var n2 = (long)Math.Sqrt(n+1);
        for (long i = 2; i <=  n2; i++)
            if (n % i == 0)  alist.Add(getF(i, n / i));
        Console.WriteLine(alist.Min());
    }
    public static long getF (long a , long b)
    {
        var wa = a.ToString().Length;
        var wb = b.ToString().Length;
        if (wa >= wb) return wa;
        else return wb;
    }
}