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: Accepted)

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

public class Program {
    public static void Main() {
        var n = Library.ParseLong();

        long b = 10000000001;
        long a = 0;
        long max = (long)Math.Round(Math.Sqrt(n), MidpointRounding.AwayFromZero); 
        for (long i = 1; i <= max; i++) {
            if (n % i != 0)
                continue;

            a = i;
            b = n / i;
        }

        Console.WriteLine(Math.Max(a.ToString().Length, b.ToString().Length));
    }
}

static class Library {
    public static long ParseLong() {
        return long.Parse(Console.ReadLine());
    }
}