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 System.Text;

namespace Practice
{
    class Program
    {
        static void Main(string[] args)
        {
            Solve();
        }
        private const long MOD = 1000000007;

        private class Data
        {
            public long prime;
            public long cnt;
            public Data(long prime, long cnt)
            {
                this.prime = prime;
                this.cnt = cnt;
            }
        }
        static void Solve()
        {
            var n = ReadAndParseLong();
            var list = new List<long>();

            long m = n;
            for (long i = 2; i * i <= n; ++i)
            {

                while (m % i == 0)
                {
                    list.Add(i);
                    m /= i;
                }
            }
            list.Add(m);

            list.Sort();
            list.Reverse();

            long A = 1;
            long B = 1;
            if (list.Count >= 1)
            {
                foreach (var prime in list)
                {

                    if (A <= B)
                    {
                        A *= prime;
                    }
                    else
                    {
                        B *= prime;
                    }

                }
            }
            else
            {
                A = 1;
                B = n;
            }
            int ans = Math.Max(CalcDigit(A), CalcDigit(B));
            Console.WriteLine(ans);
        }
        private static int CalcDigit(long n)
        {
            int digit = 1;
            while (n >= 10)
            {
                n /= 10;
                digit++;
            }
            return digit;
        }
        #region よく使う便利関数
        private static bool isPrime(long x)
        {
            if (x == 2) { return true; }
            if (x < 2 || x % 2 == 0) { return false; }
            long i = 3;
            while (i * i <= x)
            {
                if (x % i == 0) { return false; }
                i = i + 2;
            }
            return true;
        }
        private static long lcm(long x, long y)
        {
            return x / gcd(x, y) * y;
        }
        private static long gcd(long x, long y)
        {
            return y > 0 ? gcd(y, x % y) : x;
        }
        private static long pow(long x, long n)
        {
            if (n == 0) { return 1; }
            long res = pow(x * x % MOD, n / 2);
            if (n % 2 == 1)
            {
                res = res * x % MOD;
            }
            return res;
        }
        private static int ReadAndParseInt()
        {
            return int.Parse(Console.ReadLine());
        }
        private static int[] ReadAndParseIntArr()
        {
            return Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
        }
        private static long ReadAndParseLong()
        {
            return long.Parse(Console.ReadLine());
        }
        private static long[] ReadAndParseLongArr()
        {
            return Array.ConvertAll(Console.ReadLine().Split(' '), long.Parse);
        }
        #endregion
    }
}