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.Generic;
using static System.Math;

namespace C
{
    class Program
    {
        static void Main(string[] args)
        {
            Func<long, long, int> f = (x, y) => Max(x.ToString().Count(), y.ToString().Count());

            var n = long.Parse(Console.ReadLine());
            var sqrtN = Sqrt(n);

            var minF = int.MaxValue;

            //nが素数の場合、処理を中断
            if (isPrime(n))
            {
                var a = n.ToString().Count();
                Console.WriteLine(f(1, n));
            }
            else
            {
                for (int i = 1; i <= sqrtN; i++)
                {
                    var a = i;
                    if (n % a == 0)
                    {
                        var b = n / a;
                        minF = Min(minF, f(a, b));
                    }
                }
                Console.WriteLine(minF);
            }

        }

        static bool isPrime(long x)
        {
            if (x < 2) return false;
            else if (x == 2) return true;
            else if (x % 2 == 0) return false;

            double sqrtX = Math.Sqrt(x);

            for (int i = 3; i < sqrtX; i += 2)
            {
                if (x % i == 0)
                {
                    return false;
                }
            }
            return true;
        }

    }
}