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)

#![allow(unused_imports)]
#![allow(unused_macros)]
#![allow(non_snake_case)]
#![allow(dead_code)]
#![allow(unused_variables)]
#![allow(unused_mut)]
#![allow(unused_assignments)]
use proconio::input;
use proconio::marker::Usize1;
use std::collections::*;
use std::cmp::*;
use std::f64::consts::*;

const MOD: u64 = 1000000007;
const INF: usize = std::usize::MAX / 4;

fn main() {
    input! {
        N: usize,
        M: usize,
        H: [u64; N],
    }

    let mut edges: Vec<Vec<usize>> = vec![vec![]; N];

    for _ in 0..M {
        input! {
            fr: Usize1,
            to: Usize1,
        }
        edges[fr].push(to);
        edges[to].push(fr);
    }

    let mut ans = 0;
    for i in 0..N {
        if edges[i].iter().all(|&to| H[to] < H[i]) {
            ans += 1;
        }
    }

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