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)

#[derive(Debug)]
struct ObservatoryPath {
    from: usize,
    to: usize,
}

fn main() {
    let s = read_line();
    let s = read_num_vec(s, 2);
    let n = s.get(0).unwrap().to_owned();
    let m = s.get(1).unwrap().to_owned();
    let s = read_line();
    let height_vec = read_num_vec(s, n as usize);
    let mut path_vec: Vec<ObservatoryPath> = vec![];
    for _ in 0..m {
        let s = read_line();
        let s = read_num_vec(s, 2);
        let a = s.get(0).unwrap().to_owned();
        let b = s.get(1).unwrap().to_owned();
        path_vec.push(ObservatoryPath {
            from: (a - 1) as usize,
            to: (b - 1) as usize,
        });
    }
    let mut is_good_vec = vec![];
    for _ in 0..n {
        is_good_vec.push(true);
    }

    for path in path_vec {
        let from_height = height_vec.get(path.from).unwrap().to_owned();
        let to_height = height_vec.get(path.to).unwrap().to_owned();
        if from_height >= to_height {
            let is_good = is_good_vec.get_mut(path.to).unwrap();
            *is_good = false;
        }
        if to_height >= from_height {
            let is_good = is_good_vec.get_mut(path.from).unwrap();
            *is_good = false;
        }
    }

    let mut num_good = 0;
    for is_good in is_good_vec.clone() {
        if is_good {
            num_good += 1;
        }
    }

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

fn read_line() -> String {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim_end().to_owned()
}

fn read_num_vec(s: String, length: usize) -> Vec<i64> {
    let mut ws = s.split_whitespace();
    let mut result = vec![];
    for _ in 0..length {
        result.push(ws.next().unwrap().parse().unwrap());
    }
    result
}