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;
using System.Text;
using System.Threading.Tasks;

namespace ABC057_C_2
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = long.Parse(Console.ReadLine());
            var ans = F(N);
            Console.WriteLine(ans);
        }

        static int F(long n)
        {
            int res;
            var sqrt_n = Math.Sqrt(n);
            var dividAble = new List<long>();
            if (sqrt_n == (int)sqrt_n)
            {
                res = (int)Math.Log10(sqrt_n) + 1;
                return res;
            }


            for (long i = 1; i < sqrt_n; i++)
            {
                double A = i;
                double B = n / A;
                if (B == (long)B)
                {
                    dividAble.Add(Math.Max((long)A, (long)B));
                }
            }
            return (int)Math.Log10(dividAble.Min()) + 1;
        }
    }
}