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 (GCC 9.2.1) (judge verdict: Accepted)

#include <stdio.h>

const int MAX_TEMBODAI_NUMBER = 200010;

int main() {
  int tembodai_count, temboway_count;
  scanf("%d %d", &tembodai_count, &temboway_count);

  int height_array[tembodai_count];
  int max_height_array[tembodai_count];
  for (int i = 0; i < tembodai_count; i += 1) {
    scanf("%d", height_array + i);
    max_height_array[i] = 0;
  }

  int bad_tembodai[MAX_TEMBODAI_NUMBER];
  for (int i = 0; i < temboway_count; i += 1) {
    int tembodai_number_a, tembodai_number_b;
    scanf("%d %d", &tembodai_number_a, &tembodai_number_b);
    if (height_array[tembodai_number_a - 1] >= height_array[tembodai_number_b - 1]) {
      bad_tembodai[tembodai_number_b] += 1;
    }
    if (height_array[tembodai_number_a - 1] <= height_array[tembodai_number_b - 1]) {
      bad_tembodai[tembodai_number_a] += 1;
    }
  }

  int output = 0;
  for (int i = 1; i <= tembodai_count; i += 1) {
    if (bad_tembodai[i] == 0) {
      output += 1;
    }
  }
  printf("%d", output);

  return 0;
}