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

class Program
{
    public static Queue<long> Factors(long a)
    {
        Queue<long> r = new Queue<long>();
        if (a <= 1)
            return r;
        while ((a & 1) == 0)
        {
            r.Enqueue(2);
            a >>= 1;
        }
        for (long i = 3; a != 1; i += 2)
        {
            while (a % i == 0)
            {
                r.Enqueue(i);
                a /= i;
            }
        }
        return r;
    }
    public static void Main()
    {
        long N = long.Parse(Console.ReadLine());
        long a = 1;
        long b = 1;
        Queue<long> q = Factors(N);
        List<long> p = new List<long>() { Capacity = q.Count};
        while (q.Count > 0)
            p.Add(q.Dequeue());
        p.Sort((x, y) =>
        {
            if (y > x)
                return 1;
            if (y < x)
                return -1;
            else
                return 0;
        }
        );
        for (int i = 0; i < p.Count; i++)
        {
            if (a < b)
                a *= p[i];
            else
                b *= p[i];
        }
        Console.WriteLine(Math.Max(a.ToString().Length, b.ToString().Length));
    }
}