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;

class Program
{
    static void Main(string[] args)
    {
        var n = long.Parse(Console.ReadLine());
        var ans = long.MaxValue;
        for (long i = 1; i * i < n; i++)
        {
            if (n % i == 0)
            {
                ans = Math.Min(ans,
                    Math.Max(f(i), f(n / i)));
            }
        }
        Console.WriteLine(ans);
    }

    static long f(long x)
    {
        var ans = 0;
        while (x != 0)
        {
            ans++;
            x /= 10;
        }
        return ans;
    }
}