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# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

using System;

namespace ProgramingStydying
{
    class Program
    {
        static void Main(string[] args)
        {
            var n = long.Parse(Console.ReadLine());
            var ans = 20;

            for(long a = 1; a < Math.Sqrt(n); a++)
            {
                if (n % a != 0)
                {
                    continue;
                }
                else
                {
                    var b = n / a;
                    if(F(a,b) < ans)
                    {
                        ans = F(a, b);
                    }
                }
            }
            Console.WriteLine(ans);
        }

        public static int F(long a, long b)
        {
            return Math.Max(DigitFinder(a), DigitFinder(b));
        } 

        public static int DigitFinder(long x)
        {
            var digit = 0;
            while(x > 0)
            {
                x /= 10;
                digit++;
            }

            return digit;
        }
    }
}