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)

class Mount():
    def __init__(self, i, H):
        self.i = i
        self.H = H
        self.rel_H = []
        self.max_H = 0

    def add_rel_H(self, H):
        self.rel_H.append(H)
        if self.max_H < H:
            self.max_H = H

N, M = map(int, input().split())

d_mount = {}
for i, H in enumerate(input().split()):
	d_mount[i+1] = Mount(i+1, int(H))
    
inputs = [input() for i in range(M)]
for l in inputs:
    A = int(l.split()[0])  # mount id
    B = int(l.split()[1])  # mount id
    d_mount[A].add_rel_H(d_mount[B].H)
    d_mount[B].add_rel_H(d_mount[A].H)

count = 0
for k, v in d_mount.items():
    if len(v.rel_H) == 0:
        count += 1
    elif v.max_H < v.H:
        count += 1
        
print(count)