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.Linq;

namespace AtCoder.Abc
{
    class QuestionC
    {
        public static void Main(string[] args)
        {
            var sw = new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);

            var sp = Console.ReadLine().Split(' ');
            var n = int.Parse(sp[0]);
            var m = int.Parse(sp[1]);
            var h = Console.ReadLine().Split(' ').Select(i => int.Parse(i)).ToArray();
            var abAry = new int[m][];
            for (int c = 0; c < m; c++)
            {
                abAry[c] = Console.ReadLine().Split(' ').Select(i => int.Parse(i)).ToArray();
            }

            var fromA = abAry.ToLookup(ab => ab[0]);
            var fromB = abAry.ToLookup(ab => ab[1]);

            int cnt = 0;
            for (int c = 0; c < n; c++)
            {
                int max = 0;
                foreach(var ab in fromA[c+1])
                {
                    max = Math.Max(max, h[ab[1] - 1]);
                }
                foreach(var ab in fromB[c+1])
                {
                    max = Math.Max(max, h[ab[0] - 1]);
                }
                if (max < h[c])
                {
                    cnt++;
                }
            }

            Console.WriteLine(cnt);

            Console.Out.Flush();
        }
    }
}