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: Time Limit Exceeded)

use proconio::fastout;
use whiteread::parse_line;
use std::collections::{HashMap, HashSet};

#[fastout]
fn main() {
    let (N, M): (usize, usize) = parse_line().unwrap();
    let heights: Vec<usize> = parse_line().unwrap();
    let mut map: HashMap<usize, HashSet<usize>> = HashMap::new();
    for i in 0..M {
        let (A, B): (usize, usize) = parse_line().unwrap();

        map.entry(A).or_insert(HashSet::new());
        map.entry(B).or_insert(HashSet::new());
        map.get_mut(&A).unwrap().insert(heights[B-1]);
        map.get_mut(&B).unwrap().insert(heights[A-1]);
    }
    let mut cnt = 0;
    for (k, v) in map.iter() {
        let v_max: usize = *v.iter().max().unwrap();
        if heights[k-1] > v_max {
            cnt += 1;
        } else {
            continue;
        }
        // println!("{:?} {:?}", k, v);
    }
    let all_keys: Vec<usize> = (1..N+1).collect();
    for k in &all_keys {
        if !map.keys().collect::<Vec<&usize>>().contains(&k) {
            cnt+=1;
        }
    }
    println!("{}", cnt)
}