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: Runtime Error)

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

class Program
{
    void Calc()
    {
        var sc = new Scanner();
        int N = sc.NextInt();
        double root = Math.Sqrt(N);
        double roottt = Math.Floor(root);
        int ret3 = (int)roottt;
        for (int i = ret3; i > 0; i--)
        {
            if (N % i == 0)
            {
                int l = N / i;
                string a = l.ToString();
                Console.WriteLine(a.Length);
                break;
            }
        }
    }

    static void Main()
    {
        new Program().Calc();
    }

    class Scanner
    {
        string[] s = new string[0];
        int i = 0;
        char[] cs = new char[] { ' ' };

        public string Next()
        {
            if (i < s.Length) return s[i++];
            s = Console.ReadLine().Split(cs, StringSplitOptions.RemoveEmptyEntries);
            i = 0;
            return s[i++];
        }
        public int NextInt() { return int.Parse(Next()); }
        public long NextLong() { return long.Parse(Next()); }
        public double NextDouble() { return double.Parse(Next()); }
    }
}