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 (_, _, h, path) = input();
    println!("{}", solve(h, path));
}

struct Hill {
    height: usize,
    path: Vec<usize>,
}

impl Hill {
    fn new(height: usize, path: Vec<usize>) -> Self {
        Hill {
            height: height,
            path: path,
        }
    }
    fn push_path(&mut self, path: usize) {
        self.path.push(path);
    }
}

fn input() -> (usize, usize, Vec<usize>, Vec<(usize, usize)>) {
    let mut buf1 = String::new();
    std::io::stdin().read_line(&mut buf1).unwrap();
    buf1.pop();
    let mut iter1 = buf1.split_whitespace();
    let n: usize = iter1.next().unwrap().parse().unwrap();
    let m: usize = iter1.next().unwrap().parse().unwrap();
    let mut buf2 = String::new();
    std::io::stdin().read_line(&mut buf2).unwrap();
    buf2.pop();
    let iter2 = buf2.split_whitespace();
    let h: Vec<usize> = iter2.map(|i| i.parse().unwrap() ).collect();
    let mut path: Vec<(usize, usize)> = Vec::new();
    for i in 0..m {
        let mut buf = String::new();
        std::io::stdin().read_line(&mut buf).unwrap();
        buf.pop();
        let mut iter = buf.split_whitespace();
        let a: usize = iter.next().unwrap().parse().unwrap();
        let b: usize = iter.next().unwrap().parse().unwrap();
        path.push((a, b));
    }
    (n, m, h, path)
}

fn from_input(h: Vec<usize>, path: Vec<(usize, usize)>) -> Vec<Hill> {
    // make empty path hills
    let mut hills: Vec<Hill> = h.iter().map(|v| Hill{height: *v, path: vec![]}).collect();
    for p in path.iter() {
        hills[p.0 - 1].push_path(p.1-1);
        hills[p.1-1].push_path(p.0-1);
    }
    hills
}

fn solve(h: Vec<usize>, path: Vec<(usize, usize)>) -> usize {
    let hills = from_input(h, path);
    let mut ans = 0;
    for hill in hills.iter() {
        let mut high = true;
        for p in hill.path.iter() {
            if hills[*p].height >= hill.height {
                high = false;
                break;
            }
        }
        if high {
            ans += 1;
        }
    }
    ans
}