Problem:
Score : 200 points

Problem Statement

You are given a positive integer X.
Find the largest perfect power that is at most X.
Here, a perfect power is an integer that can be represented as b^p, where b is an integer not less than 1 and p is an integer not less than 2.

Constraints

1 ≤ X ≤ 1000

X is an integer.

Input

Input is given from Standard Input in the following format:

X

Output

Print the largest perfect power that is at most X.

Sample Input 1

10

Sample Output 1

9

There are four perfect powers that are at most 10: 1, 4, 8 and 9.
We should print the largest among them, 9.

Sample Input 2

1

Sample Output 2

1

Sample Input 3

999

Sample Output 3

961

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

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

namespace AtCoder.ABC097.A
{
    class Program
    {
        static void Main ()
        {
            int x = int.Parse (Console.ReadLine ());
            int max = 1;
            for (int p = x - 1; p >= 2; p--)
            {
                int b = (int) Math.Pow (x, 1D / p);
                Console.Error.WriteLine ($"p = {p}, b = {b}");
                if (b <= 1) continue;
                max = Math.Max ((int) Math.Pow (b, p), max);
                Console.Error.WriteLine ($"b = {b}, p = {p}, max = {max}");
            }
            Console.WriteLine (max);
        }
    }

    class Scanner
    {
        string[] s;
        int i;

        char[] cs = new char[] { ' ' };

        public Scanner ()
        {
            s = new string[0];
            i = 0;
        }

        public string Next ()
        {
            if (i < s.Length) return s[i++];
            string st = Console.ReadLine ();
            while (st == "") st = Console.ReadLine ();
            s = st.Split (cs, StringSplitOptions.RemoveEmptyEntries);
            if (s.Length == 0) return Next ();
            i = 0;
            return s[i++];
        }

        public int NextInt ()
        {
            return int.Parse (Next ());
        }
        public int[] ArrayInt (int N, int add = 0)
        {
            int[] Array = new int[N];
            for (int i = 0; i < N; i++)
            {
                Array[i] = NextInt () + add;
            }
            return Array;
        }

        public long NextLong ()
        {
            return long.Parse (Next ());
        }

        public long[] ArrayLong (int N, long add = 0)
        {
            long[] Array = new long[N];
            for (int i = 0; i < N; i++)
            {
                Array[i] = NextLong () + add;
            }
            return Array;
        }

        public double NextDouble ()
        {
            return double.Parse (Next ());
        }

        public double[] ArrayDouble (int N, double add = 0)
        {
            double[] Array = new double[N];
            for (int i = 0; i < N; i++)
            {
                Array[i] = NextDouble () + add;
            }
            return Array;
        }

        public decimal NextDecimal ()
        {
            return decimal.Parse (Next ());
        }

        public decimal[] ArrayDecimal (int N, decimal add = 0)
        {
            decimal[] Array = new decimal[N];
            for (int i = 0; i < N; i++)
            {
                Array[i] = NextDecimal ();
            }
            return Array;
        }
    }

    static class MathExtensions
    {
        public static long Factorial (int n)
        {
            long fact = n;
            for (int i = n - 1; i >= 1; i--)
            {
                fact *= i;
            }
            return fact;
        }

        static long Combination (int n, int r)
        {
            long molecule = 1;
            for (int i = 0; i < r; i++) molecule *= n - i;
            long denominator = 1;
            for (int i = 1; i <= r; i++) denominator *= i;
            return molecule / denominator;
        }
    }

    static class IEnumerableExtensions
    {
        public static long Nearest (this IEnumerable<long> self, long target)
        {
            var min = self.Min (val => Math.Abs (val - target));
            return self.First (val => Math.Abs (val - target) == min);
        }
    }
}