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: Wrong Answer)

fn main() {
    ioset! { inp, buf }
    macro_rules! scan {
        ($($r:tt)*) => {
            input! { inp, $($r)* }
        }
    }
    macro_rules! print {
        ($($t:expr),*) => {
            write!(buf, $($t),*).unwrap();
        } 
    }

    scan! { N: usize, M: usize, H: [usize; N], AB: [(usize, usize); M],}

    let mut G = vec![Vec::new(); N];

    for (a, b) in AB {
        G[a - 1].push(b - 1);
        G[b - 1].push(a - 1);
    }
    let mut ok = vec![2; N];
    let mut vec = H.iter().enumerate().map(|(a, b)| (b, a)).tovec();
    vec.sort();
    vec.reverse();
    for (x, i) in vec.into_iter() {
        if ok[i] == 2 {
            ok[i] = 1;
            for t in G[i].iter() {
                ok[*t] = 0;
            }
        }
    }
    print! { "{}\n", ok.into_iter().filter(|x| *x == 1).count() };
}

pub trait ToVec {
    type Item;
    fn tovec(self) -> Vec<Self::Item>;
}

impl<I: std::iter::Iterator> ToVec for I {
    type Item = <Self as std::iter::Iterator>::Item;
    fn tovec(self) -> Vec<Self::Item> {
        self.collect::<Vec<Self::Item>>()
    }
}

/* I/O */

use std::io::{ stdout, BufWriter, Write };

#[macro_export]
macro_rules! ioset {
    ($inp:ident, $buf:ident) => {
        inset!($inp);
        outset!($buf);
    }
}

#[macro_export]
macro_rules! inset {
    (source = $s:expr, $iter:ident) => {
        let mut $iter = $s.split_whitespace();
    };
    ($iter:ident) => {
        let s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut $iter = s.split_whitespace();
    }
}

#[macro_export]
macro_rules! input {
    ($iter:expr) => {};
    ($iter:expr, ) => {};
    ($iter:expr, $var:ident : $t:tt, $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input! { $iter, $($r)* }
    };
    ($iter:expr, mut $var:ident : $t:tt, $($r:tt)*) => {
        let mut $var = read_value!($iter, $t);
        input! { $iter, $($r)* }
    };
    ($iter:expr, ($var:expr) : $t:tt, $($r:tt)*) => {
        $var = read_value!($iter, $t);
        input! { $iter, $($r)* }
    };
}

#[macro_export]
macro_rules! read_value {

    // tuple
    ($iter:expr, ( $($t:tt), * )) => {
        ( $(read_value!($iter, $t)), * )
    };
    
    // array
    ($iter:expr, [ $t:tt; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };
    
    // string
    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };
    
    // any other
    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}

#[macro_export]
macro_rules! outset {
    ($buf:ident) => {
        let sout = stdout();
        let mut $buf = BufWriter::new(sout.lock());
    }
}

#[macro_export]
macro_rules! output {
    ($buf:expr, $($t:expr),*) => {
        write!($buf, $($t),*).unwrap();
    }
}

struct Chars<'a>(&'a Vec<char>);

impl<'a> std::fmt::Display for Chars<'a> {
    fn fmt(&self, f: &mut std::fmt::Formatter) -> Result<(), std::fmt::Error> {
        write!(f, "{}", self.0.iter().collect::<String>())
    }
}

use std::cmp::Ordering;

pub trait BinarySearch<T> {
    fn lower_bound(&self, x: &T) -> usize;
    fn upper_bound(&self, x: &T) -> usize;
}

impl<T: Ord> BinarySearch<T> for [T] {
    fn lower_bound(&self, x: &T) -> usize {
        let mut ng = -1i64;
        let mut ok = self.len() as i64;
        while ok - ng > 1 {
            let m = (ok + ng) / 2;
            match self[m as usize].cmp(x) {
                Ordering::Greater | Ordering::Equal => {
                    ok = m;
                }
                _ => {
                    ng = m;
                }
            }
        }
        ok as usize
    }
    fn upper_bound(&self, x: &T) -> usize {
        let mut ng = -1i64;
        let mut ok = self.len() as i64;
        while ok - ng > 1 {
            let m = (ok + ng) / 2;
            match self[m as usize].cmp(x) {
                Ordering::Greater => {
                    ok = m;
                }
                _ => {
                    ng = m;
                }
            }
        }
        ok as usize
    }
}