Problem:
Score: 200 points

Problem Statement

You are an immigration officer in the Kingdom of AtCoder. The document carried by an immigrant has some number of integers written on it, and you need to check whether they meet certain criteria.

According to the regulation, the immigrant should be allowed entry to the kingdom if and only if the following condition is satisfied:

All even numbers written on the document are divisible by 3 or 5.

If the immigrant should be allowed entry according to the regulation, output APPROVED; otherwise, print DENIED.

Notes

The condition in the statement can be rephrased as "If x is an even number written on the document, x is divisible by 3 or 5".
Here "if" and "or" are logical terms.

Constraints

All values in input are integers.

1 \leq N \leq 100

1 \leq A_i \leq 1000

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 \dots A_N

Output

If the immigrant should be allowed entry according to the regulation, print APPROVED; otherwise, print DENIED.

Sample Input 1

5
6 7 9 10 31

Sample Output 1

APPROVED

The even numbers written on the document are 6 and 10.

All of them are divisible by 3 or 5, so the immigrant should be allowed entry.

Sample Input 2

3
28 27 24

Sample Output 2

DENIED

28 violates the condition, so the immigrant should not be allowed entry.

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

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

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = Io.Read();
            var AList = Io.ReadList<int>();
            var output = AList.All(A => A % 2 != 0 || (A % 3 == 0 || A % 5 == 0))
                ? "APPROVED"
                : "DENIED";

            Io.Write(output);
        }

        static class Permutation
        {
            private static void Search<T>(List<T[]> perms, Stack<T> stack, T[] a)
            {
                int N = a.Length;
                if (N == 0)
                {
                    perms.Add(stack.Reverse().ToArray());
                }
                else
                {
                    var b = new T[N - 1];
                    Array.Copy(a, 1, b, 0, N - 1);
                    for (int i = 0; i < a.Length; ++i)
                    {
                        stack.Push(a[i]);
                        Search(perms, stack, b);
                        if (i < b.Length) { b[i] = a[i]; }
                        stack.Pop();
                    }
                }
            }
            public static IEnumerable<T[]> All<T>(IEnumerable<T> src)
            {
                var perms = new List<T[]>();
                Search(perms, new Stack<T>(), src.ToArray());
                return perms;
            }
        }

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

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

            return result;
        }

        static int SumOfDigits(int x)
        {
            var sum = 0;
            while (x > 0)
            {
                sum += x % 10;
                x /= 10;
            }

            return sum;
        }

        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[] ReadList(char devide = ' ')
            {
                return Read().Split(devide);
            }

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

            public static IEnumerable<string[]> ReadListRepeat(int count, char devide = ' ')
            {
                return Enumerable.Range(0, count).Select(_ => ReadList(devide));
            }

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

            public static void Write(string value)
            {
                Console.WriteLine(value);
            }
        }
    }
}