Problem:
Score : 400 points

Problem Statement

There are N islands lining up from west to east, connected by N-1 bridges.

The i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.

One day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:

Request i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.

You decided to remove some bridges to meet all these M requests.

Find the minimum number of bridges that must be removed.

Constraints

All values in input are integers.

2 \leq N \leq 10^5

1 \leq M \leq 10^5

1 \leq a_i < b_i \leq N

All pairs (a_i, b_i) are distinct.

Input

Input is given from Standard Input in the following format:

N M
a_1 b_1
a_2 b_2
:
a_M b_M

Output

Print the minimum number of bridges that must be removed.

Sample Input 1

5 2
1 4
2 5

Sample Output 1

1

The requests can be met by removing the bridge connecting the second and third islands from the west.

Sample Input 2

9 5
1 8
2 7
3 5
4 6
7 9

Sample Output 2

2

Sample Input 3

5 10
1 2
1 3
1 4
1 5
2 3
2 4
2 5
3 4
3 5
4 5

Sample Output 3

4

Solution in Rust (1.15.1) (judge verdict: Time Limit Exceeded)

pub fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

pub fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

pub fn read_vec2<T: std::str::FromStr>(n: usize) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}

pub fn read_col<T: std::str::FromStr>(n: usize) -> Vec<T> {
    (0..n).map(|_| read()).collect()
}

fn main() {
    let nm: Vec<usize> = read_vec();
    let m = nm[1];
    let mut abv_prt: Vec<Vec<u32>> = read_vec2(m);
    abv_prt.sort_by(|x, y| x[0].partial_cmp(&y[0]).unwrap());

    let mut abv: Vec<Vec<u32>> = vec![abv_prt[0].clone()];
    for i in 1..m {
        let l = abv.len();
        let a = abv_prt[i][0];
        let b = abv_prt[i][1];

        if b <= abv[l - 1][1] {
            abv[l - 1] = vec![a, b];
        } else if abv[l - 1][0] < a {
            abv.push(vec![a, b]);
        }
    }

    for i in 1..abv_prt.len() {
        if abv_prt[i - 1][1] > abv_prt[i][1] {
            loop {}
        }
    }

    let mut i = 0;
    let mut r;
    let mut ans = 0;
    while i < abv.len() {
        r = abv[i][1];
        while i < abv.len() && abv[i][0] < r {
            i += 1;
        }
        ans += 1;
    }

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