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 Python (3.8.2) (judge verdict: Accepted)

#!/usr/bin/env python
import sys
from collections import Counter
from itertools import permutations, combinations
#from fractions import gcd
from math import gcd
from math import ceil, floor
import bisect
sys.setrecursionlimit(10 ** 6)
inf = float("inf")

def input():
    return sys.stdin.readline()[:-1]

def main():
    n, m = map(int, input().split())
    H = tuple(map(int, input().split()))
    AB = [tuple(map(int, input().split())) for _ in range(m)]

    ans = [True] * n
    for i in range(m):
        if H[AB[i][0]-1] > H[AB[i][1]-1]:
            ans[AB[i][1]-1] = False
        elif H[AB[i][0]-1] < H[AB[i][1]-1]:
            ans[AB[i][0]-1] = False
        elif H[AB[i][0]-1] == H[AB[i][1]-1]:
            ans[AB[i][0]-1] = False
            ans[AB[i][1]-1] = False

    print(sum(ans))


if __name__ == '__main__':
    main()