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;

namespace A
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = Io.Read<long>();

            var output = 11;
            for (var A = 1; A <= Math.Sqrt(N); A++)
            {
                if (N % A != 0) continue;

                var B = N / A;
                output = Math.Min(output, Math.Max(NumberOfDigits(A), NumberOfDigits(B)));
            }

            Console.WriteLine(output);
        }

        static int NumberOfDigits(long x)
        {
            if (x < 10) return 1;

            var result = 0;
            while (x > 0)
            {
                result++;
                x /= 10;
            }

            return result;
        }
    }

    class Io
    {
        public static string Read()
        {
            return Console.ReadLine();
        }

        public static IEnumerable<string> ReadRepeat(int count)
        {
            return Enumerable.Range(0, count).Select(_ => Read());
        }

        public static T Read<T>()
        {
            return (T)Convert.ChangeType(Read(), typeof(T));
        }

        public static IEnumerable<T> ReadRepeat<T>(int count)
        {
            return Enumerable.Range(0, count).Select(_ => Read<T>());
        }

        public static string[] ReadSplit(char devide = ' ')
        {
            return Read().Split(devide);
        }

        public static T[] ReadSplit<T>(char devide = ' ')
        {
            return ReadSplit(devide)
                .Select(s => (T)Convert.ChangeType(s, typeof(T)))
                .ToArray();
        }

        public static IEnumerable<T[]> ReadSplitRepeat<T>(int count, char devide = ' ')
        {
            return Enumerable.Range(0, count).Select(_ => ReadSplit<T>(devide));
        }
    }
}