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.Collections.Generic;
using System.Linq;
using static AtCoder.Io;

namespace AtCoder
{
    class Program
    {
        static void Main()
        {
            var n = ReadLong();
            var sqrt = Math.Sqrt(n);
            var list = new List<long>();

            while (n % 2 == 0)
            {
                list.Add(2);
                n /= 2;
            }

            for (var i = 3; i <= sqrt; i += 2)
            {
                while (n % i == 0)
                {
                    list.Add(i);
                    n /= i;
                }
            }
            if (n != 1)
            {
                list.Add(n);
            }

            long a = 1;
            long b = 1;
            list.Reverse();
            foreach (var fact in list)
            {
                if (a < b)
                {
                    a *= fact;
                }
                else
                {
                    b *= fact;
                }
            }
            Console.WriteLine($"{(long)Math.Log10(a < b ? b : a) + 1}");
        }
    }

    public static class Io
    {
        public static string ReadString() => Console.ReadLine();
        public static string[] ReadStringArray() => ReadString().Split(' ');
        public static int ReadInt() => int.Parse(ReadString());
        public static long ReadLong() => long.Parse(ReadString());
        public static int[] ReadIntArray() => ReadStringArray().ParseInt().ToArray();
        public static long[] ReadLongArray() => ReadStringArray().ParseLong().ToArray();
        public static IEnumerable<int> ParseInt(this IEnumerable<string> source) => source.Select(int.Parse);
        public static IEnumerable<long> ParseLong(this IEnumerable<string> source) => source.Select(long.Parse);
    }
}