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;

public class Program {
	public static void Main() {
		new Calc().calc();
	}
	public class Calc {
		public Calc() { }
		public void calc() {
			long N = long.Parse(Console.ReadLine());
			int ans = N.ToString().Length;
			for (long i = 1; i < N/i; ++i) {
				if (N % i != 0) continue;
				long b = N / i;
				int f = F(i, b);
				if(f<ans) { ans = f; }
			}
			Console.WriteLine(ans);
		}
		private int F(long A,long B) =>A > B ? A.ToString().Length : B.ToString().Length;
	}
}