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: Accepted)

using System;
using System.Collections.Generic;
using System.Security.Cryptography;

namespace C
{
    class Program
    {
        static void Main(string[] args)
        {
            string[] S = Console.ReadLine().Split(' ');
            int N = int.Parse(S[0]);
            int M = int.Parse(S[1]);

            string[] H = Console.ReadLine().Split(' ');

            Dictionary<int, Tower> dict = new Dictionary<int, Tower>();

            for (int i = 1; i < N+1; i++)
            {
                dict.Add(i, new Tower { Hight = int.Parse(H[i-1])} );
            }

            for (int i = 0; i < M; i++)
            {
                string[] pair = Console.ReadLine().Split(' ');
                int A = int.Parse(pair[0]);
                int B = int.Parse(pair[1]);
                dict[A].nodeDest.Add(B);
                dict[B].nodeDest.Add(A);
            }

            int cnt = 0;
            for (int i = 1; i < N+1; i++)
            {
                if (!dict.ContainsKey(i)) continue;

                if (dict[i].nodeDest.Count == 0)
                {
                    cnt++;
                    continue;
                }

                int nowHight = dict[i].Hight;
                bool flag = true;
                foreach (int dest in dict[i].nodeDest)
                {
                    if (dict.ContainsKey(dest))
                    {
                        if (dict[dest].Hight >= nowHight)
                        {
                            flag = false;
                            break;
                        }
                    }
                }
                if(flag) cnt++;

                //dict.Remove(i);
            }

            Console.WriteLine(cnt);

        }

        class Tower
        {
            public int Hight = 0;
            public List<int> nodeDest = new List<int>();
        }
    }
}