Problem:
Score : 300 points

Problem Statement

There are N observatories in AtCoder Hill, called Obs. 1, Obs. 2, ..., Obs. N. The elevation of Obs. i is H_i.
There are also M roads, each connecting two different observatories. Road j connects Obs. A_j and Obs. B_j.

Obs. i is said to be good when its elevation is higher than those of all observatories that can be reached from Obs. i using just one road.
Note that Obs. i is also good when no observatory can be reached from Obs. i using just one road.

How many good observatories are there?

Constraints

2 \leq N \leq 10^5

1 \leq M \leq 10^5

1 \leq H_i \leq 10^9

1 \leq A_i,B_i \leq N

A_i \neq B_i

Multiple roads may connect the same pair of observatories.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M
H_1 H_2 ... H_N
A_1 B_1
A_2 B_2
:
A_M B_M

Output

Print the number of good observatories.

Sample Input 1

4 3
1 2 3 4
1 3
2 3
2 4

Sample Output 1

2

From Obs. 1, you can reach Obs. 3 using just one road. The elevation of Obs. 1 is not higher than that of Obs. 3, so Obs. 1 is not good.

From Obs. 2, you can reach Obs. 3 and 4 using just one road. The elevation of Obs. 2 is not higher than that of Obs. 3, so Obs. 2 is not good.

From Obs. 3, you can reach Obs. 1 and 2 using just one road. The elevation of Obs. 3 is higher than those of Obs. 1 and 2, so Obs. 3 is good.

From Obs. 4, you can reach Obs. 2 using just one road. The elevation of Obs. 4 is higher than that of Obs. 2, so Obs. 4 is good.

Thus, the good observatories are Obs. 3 and 4, so there are two good observatories.

Sample Input 2

6 5
8 6 9 1 2 1
1 3
4 2
4 3
4 6
4 6

Sample Output 2

3

Solution in C# (Mono-mcs 6.8.0.105) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace c
{
    class Program
    {
        static void Main(string[] args)
        {
            (var points, var roadCount) = IOUtils.Read2Ints();

            var heights = IOUtils.ReadLongs().ToList();

            var roads = IOUtils.ReadIntLines(roadCount).ToList();

            var roadList1 = roads.GroupBy(l => l[0])
                                   .ToDictionary(g => g.Key, g => new HashSet<int>(g.Select(l => l[1])));
            var roadList2 = roads.GroupBy(l => l[1])
                                   .ToDictionary(g => g.Key, g => new HashSet<int>(g.Select(l => l[0])));

            var res = 0;

            for (int p = 1; p <= points; p++)
            {
                if (!roadList1.TryGetValue(p, out HashSet<int> nb1))
                {
                    nb1 = new HashSet<int>();
                }
                if (!roadList2.TryGetValue(p, out HashSet<int> nb2))
                {
                    nb2 = new HashSet<int>();
                }

                foreach (var nb in nb2)
                {
                    nb1.Add(nb);
                }

                if (nb1.Count == 0)
                {
                    res++;
                    continue;
                }
                var max = nb1.Max(n => heights[n - 1]);
                if (max < heights[p - 1])
                {
                    res++;
                }
            }

            Console.WriteLine(res);




            Console.ReadLine(); //TODO kes

        }
    }

    static class IOUtils
    {
        public static (int a, int b) Read2Ints()
        {
            var vals = ReadInts();
            return (vals[0], vals[1]);
        }
        public static (int a, int b, int c) Read3Ints()
        {
            var vals = ReadInts();
            return (vals[0], vals[1], vals[2]);
        }
        public static IEnumerable<int[]> ReadIntLines(int count)
        {
            for (int i = 0; i < count; i++)
            {
                yield return ReadInts();
            }
        }
        public static IEnumerable<long[]> ReadLongLines(int count)
        {
            for (int i = 0; i < count; i++)
            {
                yield return ReadLongs();
            }
        }
        public static int ReadInt()
        {
            return int.Parse(Console.ReadLine());
        }
        public static long ReadLong()
        {
            return long.Parse(Console.ReadLine());
        }
        public static ulong ReadUlong()
        {
            return ulong.Parse(Console.ReadLine());
        }
        public static int[] ReadInts()
        {
            return Console.ReadLine().Split(' ').Select(v => int.Parse(v)).ToArray();
        }
        public static long[] ReadLongs()
        {
            return Console.ReadLine().Split(' ').Select(v => long.Parse(v)).ToArray();
        }

        public static void WriteNums(params int[] nums)
        {
            Console.WriteLine(string.Join(" ", nums));
        }
    }
}