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# (.NET Core 3.1.201) (judge verdict: Time Limit Exceeded)

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

namespace contest_Csharp
{
    class Program
    {
        static long power(long a, long b, long modulo)
        {
            long result = 1;
            long buff = a;
            for (long i = 1; i <= b; i *= 2)
            {
                result = result * ((b / i % (2) == 1) ? buff : 1) % modulo;
                buff = (buff * buff) % modulo;
            }
            return result % modulo;
        }
        static void Main(string[] args)
        {
            var vals = Console.ReadLine().Split(' ')
               .Select(x => int.Parse(x)).ToList();
            var N = vals[0];
            var M = vals[1];
            var H = Console.ReadLine().Split(' ')
                            .Select(x => int.Parse(x)).ToList();
            var Hpair = Enumerable.Range(1, N).Select(x => (h: H[x - 1], index: x)).ToList();
            Hpair.Sort();
            var pathes = new List<List<int>>(new List<int>[N + 1]);
            for (int i = 0; i < N + 1; i++)
            {
                pathes[i] = new List<int>();
            }
            for (int i = 0; i < M; i++)
            {
                var get = Console.ReadLine().Split(' ')
                            .Select(x => int.Parse(x)).ToList();

                pathes[get[0]].Add(get[1]);
                pathes[get[1]].Add(get[0]);
            }
            PriorityQueue<(int h, int index)> pq = new PriorityQueue<(int h, int index)>();
            int count = 0;
            bool[] checker = new bool[N + 1];
            for (int i = 0; i < N + 1; i++)
            {
                checker[i] = true;
            }
            Action<int> dfs = null;
            dfs = x =>
            {
                var child = pathes[x].Where(y => H[y - 1] < H[x - 1]);
                foreach (var item in child)
                {
                    checker[item] = false;
                    dfs(item);
                }
            };
            for (int i = N - 1; i >= 0; i--)
            {
                if (checker[Hpair[i].index])
                {
                    dfs(Hpair[i].index);
                    if (!pathes[Hpair[i].index].Any(x => (H[x - 1] == Hpair[i].h)))
                    {
                        count++;
                    }
                }
            }
            Console.WriteLine(count);


        }



    }
    class PriorityQueue<T> where T : IComparable<T>
    {
        private List<T> heap = new List<T>();
        private int lastindex = -1;
        private void swap(int n, int m)
        {
            T wait = heap[n];
            heap[n] = heap[m];
            heap[m] = wait;
        }
        public int Count()
        {
            return lastindex + 1;
        }
        public void Enqueue(T data)
        {
            int p;
            if (lastindex + 1 < heap.Count())
            {
                heap[lastindex + 1] = data;
            }
            else
            {
                heap.Add(data);
            }
            lastindex++;
            p = lastindex;

            while (true)
            {
                if (p > 0 && heap[p].CompareTo(heap[(p - 1) / 2]) <= -1)
                {
                    swap(p, (p - 1) / 2);
                    p = (p - 1) / 2;
                }
                else
                {
                    break;
                }
            }
        }
        public T Peek()
        {
            return heap[0];
        }
        public T Dequeue()
        {
            T result = Peek();
            heap[0] = default(T);
            swap(0, lastindex);
            lastindex--;
            int p = 0;
            while (true)
            {
                int np;
                if (2 * p + 1 > lastindex)
                {
                    break;
                }
                else
                {
                    np = ((2 * p + 1 == lastindex) || heap[2 * p + 1].CompareTo(heap[2 * p + 2]) <= -1)
                        ? (2 * p + 1) : (2 * p + 2);
                }
                if (heap[p].CompareTo(heap[np]) >= 1)
                {
                    swap(p, np);
                    p = np;
                }
                else
                {
                    break;
                }
            }

            return result;
        }





    }
}