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: Wrong Answer)

// abc166
// c
#include <bits/stdc++.h>
using namespace std;

#define FOR(i, l, r) for(size_t i = (l); i < (r); i = i + 1)
#define REP(i, n) FOR(i, 0, n)
using ll = long long;

int main() {
    int N, M;
    cin >> N >> M;
    vector<int> H(N);
    REP(i, N) {
        cin >> H[i];
    }
    vector<int> D(N);
    vector<int> A(M);
    vector<int> B(M);
    REP(i, M) {
        cin >> A[i];
        cin >> B[i];
    }

    int start, end;
    REP(i, M) {
        start = A[i] - 1;
        end = B[i] - 1;
        cout << start << ":" << H[start] << "[m]\t" << end << ":" << H[end] << "[m]" << endl;
        if(H[start] > H[end]) {
            D[end] = -1;
            if(D[start] != -1) {
                D[start] = 1;
            }
        }
        else if(H[start] < H[end]) {
            D[start] = -1;
            if(D[end] != -1) {
                D[end] = 1;
            }
        }
        else {
            D[start] = -1;
            D[end] = -1;
        }
    }
    int count = 0;
    REP(i, N) {
        if(D[i] != -1) {
            count++;
        }
    }
    cout << count << endl;

    return 0;
}