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 <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int, int> P;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define repr(i, l, r) for (int i = l; i <= (int)(r); i++)
#define chmin(x, y) x = min(x, y)
#define chmax(x, y) x = max(x, y)
#define all(v) v.begin(), v.end()
#define MOD (int) (1e9+7)
#define INF (int) 1e9
#define LLINF (ll) 1e18

vector<int> edges[100005];

int main(){
    int n, m;
    cin >> n >> m;
    int h[n];
    rep(i, n) cin >> h[i];
    rep(i, m){
        int a, b;
        cin >> a >> b;
        a--;
        b--;
        edges[a].emplace_back(b);
        edges[b].emplace_back(a);
    }

    int ans = 0;
    rep(i, n){
        bool ok = true;
        for (auto ei : edges[i]){
            if(h[ei] >= h[i]) ok = false;
        }
        if(ok) ans++;
    }

    cout << ans << endl;
    // printf("%d\n", N);
    return 0;
}