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 (1.42.0) (judge verdict: Wrong Answer)

#![allow(unused_imports)]
use proconio::{
   fastout, input,
   marker::{Bytes, Isize1, Usize1},
};

#[fastout]
fn main() {
   input! {
      n: usize,
      m: usize,
      mut ab: [(Usize1, Usize1); m]
   }
   ab.sort_by_key(|&(a, b)| (b - a, a));
   let mut br = vec![0; n];
   for &(a, b) in ab.iter() {
      if br.range(a, b) == 0 {
         br.add(b - 1, 1);
      }
   }
   println!("{}", br.sum(n - 2));
}

use std::ops::{AddAssign, Sub};
trait BIT<T: Copy + Clone + Sub + AddAssign> {
   fn add(&mut self, idx: usize, w: T);
   fn sum(&self, idx: usize) -> T;
   fn range(&self, l: usize, r: usize) -> T;
}
impl<T: Copy + Clone + Sub<Output = T> + AddAssign> BIT<T> for [T] {
   /// let mut bit = vec![0; n+1];
   /// for (i, w) in 0..q {
   ///    bit.add(i, w);
   /// }
   fn add(&mut self, idx: usize, w: T) {
      let mut j = (idx + 1) as i64;
      while j < self.len() as i64 {
         self[j as usize] += w;
         j += j & -j;
      }
   }
   fn sum(&self, idx: usize) -> T {
      let mut i = (idx + 1) as i64;
      let mut sum = self[0];
      while i != 0 {
         sum += self[i as usize];
         i -= i & -i;
      }
      sum
   }
   /// [l, r)
   fn range(&self, l: usize, r: usize) -> T {
      match (l, r) {
         (0, _) => self.sum(r - 1),
         _ => self.sum(r - 1) - self.sum(l - 1),
      }
   }
}