Problem: 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.

Examples

Input

4 3
1 2 3 4
1 3
2 3
2 4


Output

2


Input

6 5
8 6 9 1 2 1
1 3
4 2
4 3
4 6
4 6


Output

3

Solution (in CPP):

Solution:
#include <iostream>

int main()
{
	int N, M, A, B,ans=0;
	long *H;
	bool *t;
	std::cin >> N >> M;
	H = new long[N];
	t = new bool[N];
	for (int i = 0; i < N; i++)
	{
		std::cin >> H[i];
	}
	for (int i = 0; i < M; i++)
	{
		std::cin >> A >> B;
		if (H[A-1] <= H[B-1])t[A-1] = true;
		if (H[A-1] >= H[B-1])t[B-1] = true;
	}
	for (int i = 0; i < N; i++)
	{
		if (t[i] != true)ans += 1;
	}
    std::cout << ans;
}