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: Accepted)

using static AddFunction;
using System;
using System.Collections.Generic;
using System.Linq;
using static System.Console;
using static System.Convert;
using static System.Math;

class Program
{
    static void Main(string[] args)
    {
        var num = ToInt64(ReadLine());
        long min = long.MaxValue;
        for(var i = (long)Sqrt(num)+1; i>0; i--)
        {
            if (num % i == 0 && min > BigDigit(i, num / i)) min = BigDigit(i, num / i);
        }
        WriteLine(min);
    }

    private static long BigDigit(long num1,long num2)
    {
        return Max(GetDigit(num1), GetDigit(num2));
    }
}

public static class AddFunction
{
  public static long GetDigit(long num)
    {
        return num == 0 ? 1 : (long)Math.Log10(num) + 1;
    }
}