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;
class Program
{
    public struct Tow
    {
        public int height;
        public bool[] HaveRoad;
    }
    static void Main()
    {
        string[] In1 = Console.ReadLine().Split(' ');
        int n = int.Parse(In1[0]);
        int m = int.Parse(In1[1]);
        string[] In2 = Console.ReadLine().Split(' ');
        var tow = new Tow[n];
        for(int i=0; i < n; i++)
        {
            tow[i].height = int.Parse(In2[i]);
            tow[i].HaveRoad = new bool[n];
        }
        string[] In3;
        int a, b;
        for(int i=0; i < m; i++)
        {
            In3 = Console.ReadLine().Split(' ');
            a = int.Parse(In3[0]);
            b = int.Parse(In3[1]);
            tow[a-1].HaveRoad[b-1] = true;
            tow[b-1].HaveRoad[a-1] = true;
        }
        int cnt = 0;
        bool flag;
        for(int i=0; i<n; i++)
        {
            flag = true;
            for(int j=0; j < n; j++)
            {
                if (tow[i].HaveRoad[j] == true)
                {
                    if (tow[i].height <= tow[j].height) { flag = false; break; }
                }
            }
            if (flag) cnt++;
        }
        Console.WriteLine(cnt);
    }
}