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: Wrong Answer)

using System;

class Program
{
    static void Main(string[] args)
    {
        var observatory = Console.ReadLine().Split(' ');
        var elevation = Console.ReadLine().Split(' ');
        bool[] goodObservatory = new bool[int.Parse(observatory[0])];
        bool[] selectObservatory = new bool[int.Parse(observatory[0])];

        for (int idx = 0; idx < int.Parse(observatory[1]); idx++)
        {
            var road = Console.ReadLine().Split(' ');
            selectObservatory[int.Parse(road[0]) - 1] = true;
            selectObservatory[int.Parse(road[1]) - 1] = true;

            if (int.Parse(elevation[int.Parse(road[0]) - 1]) == int.Parse(elevation[int.Parse(road[1]) - 1]))
            {
                goodObservatory[int.Parse(road[0]) - 1] = false;
                goodObservatory[int.Parse(road[1]) - 1] = false;
                continue;
            }

            if (int.Parse(elevation[int.Parse(road[0]) - 1]) > int.Parse(elevation[int.Parse(road[1]) - 1]))
            {
                goodObservatory[int.Parse(road[0]) - 1] = true;
                goodObservatory[int.Parse(road[1]) - 1] = false;
            }
            else
            {
                goodObservatory[int.Parse(road[0]) - 1] = false;
                goodObservatory[int.Parse(road[1]) - 1] = true;
            }
        }

        int count = 0;
        for(int idx = 0; idx < goodObservatory.Length; idx++)
        {
            if (!selectObservatory[idx])
            {
                count++;
                continue;
            }
            if (goodObservatory[idx]) count++;
        }

        Console.WriteLine(count.ToString());
    }
}