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: Wrong Answer)

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

namespace AtCoder
{
	class Program
	{
		static void Main(string[] args)
		{
			Question.Exec();
		}
	}

	public static class Question
	{
		public static void Exec()
		{
			long n = long.Parse(Console.ReadLine());
			long min = long.MaxValue;

			var ans = n.ToString().Length;
			if (ans < min) {
				min = ans;
			}

			if (n % 2 == 0) {
				for (long i = 2; i * i <= n; ++i) {
					if (n % i != 0) {
						continue;
					}

					var a = n / i;
					ans = Math.Max(i.ToString().Length, a.ToString().Length);
					if (ans < min) {
						min = ans;
					}
				}
			}

			Console.WriteLine($"{min}");

			Console.ReadKey();
		}
	}
}