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.Text;
using System.Linq;

class Program
{
    public void Proc()
    {
        Reader.IsDebug = false;

        long num = long.Parse(Reader.ReadLine());


        int ans = 0;
        long tmp = GetNum(1, num, num);
        for (long i = tmp; i >= 1; i--)
        {
            if (num % i == 0)
            {
                ans = Math.Max(i.ToString().Length, (num / i).ToString().Length);
                break;
            }
        }
        Console.WriteLine(ans);

    }


    private long GetNum(long min, long max, long target)
    {
        if (max - min <= 1)
        {
            if (max * max <= target)
            {
                return max;
            }
            return min;
        }
        long mid = (max + min) / 2;
        if (mid * mid <= target)
        {
            return GetNum(mid, max, target);
        }
        else
        {
            return GetNum(min, mid, target);
        }
    }





    public class Reader
    {
        public static bool IsDebug = true;
        private static String PlainInput = @"

1


";
        private static System.IO.StringReader Sr = null;
        public static string ReadLine()
        {
            if (IsDebug)
            {
                if (Sr == null)
                {
                    Sr = new System.IO.StringReader(PlainInput.Trim());
                }
                return Sr.ReadLine();
            }
            else
            {
                return Console.ReadLine();
            }
        }
    }
    static void Main()
    {
        Program prg = new Program();
        prg.Proc();
    }
}