Problem:
Score : 600 points

Problem Statement

There is a grid with N rows and N columns of squares. Let (i, j) be the square at the i-th row from the top and the j-th column from the left.

Each of the central (N-2) \times (N-2) squares in the grid has a black stone on it.
Each of the 2N - 1 squares on the bottom side and the right side has a white stone on it.

Q queries are given. We ask you to process them in order.
There are two kinds of queries. Their input format and description are as follows:

1 x: Place a white stone on (1, x). After that, for each black stone between (1, x) and the first white stone you hit if you go down from (1, x), replace it with a white stone.

2 x: Place a white stone on (x, 1). After that, for each black stone between (x, 1) and the first white stone you hit if you go right from (x, 1), replace it with a white stone.

How many black stones are there on the grid after processing all Q queries?

Constraints

3 \leq N \leq 2\times 10^5

0 \leq Q \leq \min(2N-4,2\times 10^5)

2 \leq x \leq N-1

Queries are pairwise distinct.

Input

Input is given from Standard Input in the following format:

N Q
Query_1
\vdots
Query_Q

Output

Print how many black stones there are on the grid after processing all Q queries.

Sample Input 1

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

Sample Output 1

1

After each query, the grid changes in the following way:

Sample Input 2

200000 0

Sample Output 2

39999200004

Sample Input 3

176527 15
1 81279
2 22308
2 133061
1 80744
2 44603
1 170938
2 139754
2 15220
1 172794
1 159290
2 156968
1 56426
2 77429
1 97459
2 71282

Sample Output 3

31159505795

Solution in Rust (1.42.0) (judge verdict: Accepted)

#![allow(unused_macros)]
#![allow(dead_code)]
#![allow(unused_imports)]

use itertools::Itertools;
use proconio::*;
use std::collections::VecDeque;
use std::io::stdin;
use std::str::FromStr;
use text_io::*;

const U_INF: usize = 1 << 60;
const I_INF: isize = 1 << 60;

fn main() {
    let mut sc = Scanner::new();
    let n = sc.next_usize();
    let q = sc.next_usize();

    let mut a = Vec::new();
    let mut b = Vec::new();
    a.push((n, n - 2));
    b.push((n, n - 2));
    let mut left = n;
    let mut up = n;
    let mut ans = 0;

    for _ in 0..q {
        // eprintln!("{:?}", a);
        // eprintln!("{:?}\n", b);
        let q = sc.next_usize();
        let x = sc.next_usize();
        let x = x - 1;

        if q == 1 {
            let i = a.lower_bound(|(j, _)| *j < x) - 1;
            ans += a[i].1;

            if x < left {
                left = x;
                b.push((up, x.saturating_sub(1)));
            }
        } else {
            let i = b.lower_bound(|(j, _)| *j < x) - 1;
            ans += b[i].1;

            if x < up {
                up = x;
                a.push((left, x.saturating_sub(1)));
            }
        }
    }

    println!("{}", ((n - 2) * (n - 2)).saturating_sub(ans));
}

/// ランダムアクセス可能なデータ構造に、順序付け可能な要素が入っているとき
/// ある関数の適用結果に一様性があるようにソートされているならば
/// ある関数の適用結果がTrueになるような最小のIndexを返すような関数を定義するトレイト
pub trait BinarySearch<T: Ord> {
    /// ある関数の適用結果が真になる最小のIndex（存在しない場合はデータ構造の長さを返す）
    fn lower_bound(&self, f: impl Fn(&T) -> bool) -> usize;
    /// ある関数の適用結果が真になる最小のIndex（存在しない場合はNone）
    fn lower_bound_safe(&self, f: impl Fn(&T) -> bool) -> Option<usize>;
}

impl<T: Ord> BinarySearch<T> for [T] {
    fn lower_bound(&self, f: impl Fn(&T) -> bool) -> usize {
        let mut left: isize = -1;
        let mut right = self.len() as isize;

        while right - left > 1 {
            let mid = (left + right) / 2;
            if f(&self[mid as usize]) {
                right = mid;
            } else {
                left = mid;
            }
        }

        right as usize
    }

    fn lower_bound_safe(&self, f: impl Fn(&T) -> bool) -> Option<usize> {
        let mut left: isize = -1;
        let mut right = self.len() as isize;

        while right - left > 1 {
            let mid = (left + right) / 2;
            if f(&self[mid as usize]) {
                right = mid;
            } else {
                left = mid;
            }
        }

        if right as usize == self.len() {
            None
        } else {
            Some(right as usize)
        }
    }
}

pub struct Scanner {
    buf: VecDeque<String>,
}

impl Scanner {
    pub fn new() -> Self {
        Self {
            buf: VecDeque::new(),
        }
    }

    fn scan_line(&mut self) {
        let mut flag = 0;
        while self.buf.is_empty() {
            let mut s = String::new();
            stdin().read_line(&mut s).unwrap();
            let mut iter = s.split_whitespace().peekable();
            if iter.peek().is_none() {
                if flag >= 5 {
                    panic!("There is no input!");
                }
                flag += 1;
                continue;
            }

            for si in iter {
                self.buf.push_back(si.to_string());
            }
        }
    }

    pub fn next<T: FromStr>(&mut self) -> T {
        self.scan_line();
        self.buf
            .pop_front()
            .unwrap()
            .parse()
            .unwrap_or_else(|_| panic!("Couldn't parse!"))
    }

    pub fn next_usize(&mut self) -> usize {
        self.next()
    }

    pub fn next_isize(&mut self) -> isize {
        self.next()
    }

    pub fn next_chars(&mut self) -> Vec<char> {
        self.next::<String>().chars().collect_vec()
    }

    pub fn next_string(&mut self) -> String {
        self.next()
    }

    pub fn fill_vec_line<T: FromStr>(&mut self, v: &mut Vec<T>) {
        for vi in v {
            *vi = self.next();
        }
    }

    pub fn fill_vec<T: FromStr>(&mut self, v: &mut Vec<Vec<T>>) {
        for vi in v {
            for vii in vi {
                *vii = self.next();
            }
        }
    }

    pub fn make_vec_line<T: FromStr + Default + Clone>(&mut self, i: usize) -> Vec<T> {
        let mut v = vec![Default::default(); i];
        self.fill_vec_line(&mut v);
        v
    }

    pub fn make_vec<T: FromStr + Default + Clone>(&mut self, i: usize, j: usize) -> Vec<Vec<T>> {
        let mut v = vec![vec![Default::default(); j]; i];
        self.fill_vec(&mut v);
        v
    }
}