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;

namespace abc_057_C
{
    class Program
    {
        static void Main(string[] args)
        {
            long a = long.Parse(Console.ReadLine());
            if (IsPrime(a)) { string d = "" + a + ""; Console.WriteLine(d.Length); Console.ReadLine(); }
            else
            {
                for (long i = (long)(Math.Sqrt(a)) / 1; i >= 0; i--)
                {
                    if (a % i == 0)
                    {
                        string x = "" + a / i + "";
                        string y = "" + i + "";
                        Console.WriteLine(Math.Max(x.Length, y.Length)); Console.ReadLine();
                        break;
                    }
                }
            }
        }
        static bool IsPrime(long n)
        {
            if (n < 2) return false;
            if (n == 2) return true;

            for (long i = 2; i < n; i++)     // ※1
            {
                if (n % i == 0) return false;
            }
            return true;
        }
    }
}