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 Rust (1.42.0) (judge verdict: Accepted)

fn readline() -> String {
    let mut buf = String::new();
    std::io::stdin().read_line(&mut buf).unwrap();
    buf.trim().to_string()
}
fn readnums() -> Vec<i64> {
    readline().split(" ").map(|x| x.parse().unwrap()).collect()
}

fn main() {
    let (n, m) = match readnums().as_slice() {
        &[n, m] => (n, m),
        _ => panic!(),
    };

    let hs = readnums();
    let mut hs_sorted = (&hs).into_iter().enumerate().collect::<Vec<_>>();
    hs_sorted.sort_unstable_by(|(_, a), (_, b)| b.cmp(a));

    let mut path = vec![std::collections::HashSet::<usize>::new(); n as usize];

    for _ in 0..m {
        let (a, b) = match readnums().as_slice() {
            &[a, b] => (a as usize - 1, b as usize - 1),
            _ => panic!(),
        };
        path[a].insert(b);
        path[b].insert(a);
    }

    let mut great = vec![true; n as usize];
    let mut answer = 0;

    for (i, _) in hs_sorted {
        if !great[i] {
            continue;
        }

        let mut gr = 1;
        for j in &path[i] {
            great[*j] = false;
            if !(&hs[i] > &hs[*j]) {
                gr = 0;
            }
        }

        answer += gr;
    }

    println!("{:?}", answer)
}