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 main() {
    let first_line = read_all_and_parse::<usize>();
    let tenbou_cnt = first_line[0];
    let road_cnt = first_line[1];
    let heights = read_all_and_parse::<usize>();
    // roads[a]からたどり着ける道たち
    let mut tenbous = Vec::with_capacity(tenbou_cnt);
    for tenbou_idx in 0..tenbou_cnt {
        tenbous.push(Road {
            highest_idx: tenbou_idx,
            highest_height: heights[tenbou_idx],
        });
    }
    for _ in 0..road_cnt {
        let line = read_all_and_parse::<usize>();
        let from = line[0] - 1;
        let to = line[1] - 1;
        let from_road = tenbous[from];
        if from == from_road.highest_idx {
            let to_height = heights[to];
            if from_road.highest_height <= to_height {
                tenbous[from].highest_idx = to;
                tenbous[from].highest_height = to_height;
            }
        }
        let to_road = tenbous[to];
        if to == to_road.highest_idx {
            let from_height = heights[from];
            if to_road.highest_height <= from_height {
                tenbous[to].highest_idx = from;
                tenbous[to].highest_height = from_height;
            }
        }
    }
    let mut good_cnt = 0;
    for (idx, tenbou) in tenbous.iter().enumerate() {
        if idx == tenbou.highest_idx {
            good_cnt += 1;
        }
    }
    println!("{}", good_cnt);
}
#[derive(Copy, Clone, Debug)]
struct Road {
    highest_idx: usize,
    highest_height: usize,
}
fn read_all_and_parse<T: std::str::FromStr + std::fmt::Debug>() -> Vec<T> {
    let mut line = String::new();
    std::io::stdin().read_line(&mut line).unwrap();
    let line = line.trim();
    line.split(' ').map(|s| s.parse::<T>().ok().unwrap()).collect()
}