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)

use std::collections::HashMap;

fn get_line() -> String {
    let mut line = String::new();
    std::io::stdin().read_line(&mut line).unwrap();
    line.trim().to_string()
}

fn main() {
    let (n, m) =  {
        let nm = get_line().split_whitespace()
            .map(|e| e.parse().unwrap())
            .collect::<Vec<i64>>();
        (nm[0], nm[1])
    };

    let heights = get_line().split_whitespace()
        .map(|e| e.parse().unwrap())
        .collect::<Vec<i64>>();

    let mut map: HashMap<usize, Vec<usize>> = HashMap::new();
    for i in 1..n + 1 {
        map.insert(i as usize, Vec::new());
    }

    for _ in 0..m {
        let (a, b) =  {
            let ab = get_line().split_whitespace()
                .map(|e| e.parse().unwrap())
                .collect::<Vec<usize>>();
            (ab[0], ab[1])
        };
        map.get_mut(&a).unwrap().push(b);
        map.get_mut(&b).unwrap().push(a);
    }

    let mut count = 0;
    for (key, v) in &map {
        let is_good = v.iter()
            .all(|x| heights[key - 1] > heights[x - 1]);
        if is_good { count += 1; }
    }

    println!("{}", count);
}