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;

namespace ABC057_C_Digits_in_Multiplication
{
	internal class Program
	{
		public static void Main(string[] args)
		{
			long n = long.Parse(Console.ReadLine());
			long a;
			long b;

			int resultLength = n.ToString().Length;
			for (long i = 1; i < Math.Sqrt(n); i++)
			{
				if (n % i == 0)
				{
					a = i;
					b = n / i;
					int length;
					if (a.ToString().Length <= b.ToString().Length)
						length = b.ToString().Length;
					else
						length = a.ToString().Length;

					if (resultLength > length)
						resultLength = length;
				}
			}
			
			Console.WriteLine(resultLength);
		}
	}
}