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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.IO;
using System.Linq;

namespace Tasks
{
    public class C
    {
        static void Main(string[] args)
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            Solve();
            Console.Out.Flush();
        }

        public static void Solve()
        {
            var N = long.Parse(Console.ReadLine());
            Func<long, long, long> F = (x, y) => Math.Max(x.ToString().Length, y.ToString().Length);
            var answer = F(N, 1);
            var prime = new Prime(N);
            if (!prime.IsPrime(N))
            {
                var factors = prime.Factors.SelectMany(x => Enumerable.Repeat(x.Key, x.Value)).ToArray();
                var length = factors.Length;
                for (var bit = 0; bit < (1 << length); bit++)
                {
                    var a = 1L;
                    var b = 1L;
                    for (var i = 0; i < length; i++)
                    {
                        if ((bit >> i & 1) == 1) a *= factors[i];
                        else b *= factors[i];
                    }
                    answer = Math.Min(answer, F(a, b));
                }

            }
            Console.WriteLine(answer);
        }

        public class Prime
        {
            public Dictionary<long, int> Factors => new Dictionary<long, int>(_factors);
            private Dictionary<long, int> _factors;
            private static HashSet<long> _primes;
            public Prime(long n)
            {
                if (_primes == null) _primes = new HashSet<long>();
                _factors = new Dictionary<long, int>();
                var tmp = n;
                var max = (long)Math.Sqrt(n);
                var p = 2;
                while (p <= max)
                {
                    if (tmp % p == 0)
                    {
                        _factors[p] = 0;
                        _primes.Add(p);
                        while (tmp % p == 0)
                        {
                            tmp /= p;
                            _factors[p]++;
                        }
                    }
                    p++;
                }
                if (tmp > 1)
                {
                    _factors[tmp] = 1;
                    _primes.Add(tmp);
                }
            }
            public bool IsPrime(long n)
            {
                if (_primes.Contains(n)) return true;
                var p = new Prime(n);
                return _primes.Contains(n);
            }
        }
    }
}