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)

use input_mcr::*;
use std::cmp::*;

struct SegmentTree {
    n: usize,
    xs: Vec<i64>,
}

impl SegmentTree {
    pub fn new(n: usize) -> SegmentTree {
        let n = n.next_power_of_two();
        let xs = vec![0; 2 * n];
        SegmentTree { n, xs }
    }
    pub fn add(&mut self, l: usize, r: usize, x: i64) {
        let mut l = l + self.n;
        let mut r = r + self.n;
        while l < r {
            if l & 1 != 0 {
                self.xs[l] += x;
                l += 1;
            }
            if r & 1 != 0 {
                r -= 1;
                self.xs[r] += x;
            }
            l >>= 1;
            r >>= 1;
        }
    }
    pub fn get(&self, i: usize) -> i64 {
        let mut i = self.n + i;
        let mut res = 0;
        while i != 0 {
            res += self.xs[i];
            i /= 2;
        }
        res
    }
}

fn main() {
    input! {
        n: usize,
        q: usize,
        qs: [(usize,usize); q],
    }
    let mut x_top = 0;
    let mut y_top = 0;
    let mut seg_x = SegmentTree::new(n + 1);
    let mut seg_y = SegmentTree::new(n + 1);
    let mut res = 0;
    for &(t, c) in &qs {
        let c = n - c;
        // eprintln!("t = {}, c = {}, x_top = {}, y_top = {}", t, c, x_top, y_top);
        // eprint!("seg_x = ");
        for i in 0..=n - 2 {
            //// eprint!("{} ", seg_x.get(i));
        }
        // eprintln!();
        // eprint!("seg_y = ");
        for i in 0..=n - 2 {
            //// eprint!("{} ", seg_y.get(i));
        }
        // eprintln!();
        if t == 1 {
            if c < x_top {
                let u = n - 2 - seg_x.get(c) as usize;
                res += u;
            // eprintln!("u = {}", u);
            } else {
                seg_y.add(y_top + 1, n - 2 + 1, (c - x_top) as i64);
                let u = n - 2 - seg_x.get(c) as usize;
                res += u;
                // eprintln!("u = {}", u);
                x_top = c;
            }
        } else {
            if c < y_top {
                let u = n - 2 - seg_y.get(c) as usize;
                res += u;
            // eprintln!("u = {}", u);
            } else {
                seg_x.add(x_top + 1, n - 2 + 1, (c - y_top) as i64);
                let u = n - 2 - seg_y.get(c) as usize;
                res += u;
                // eprintln!("u = {}", u);
                y_top = c;
            }
        }
    }
    // eprintln!("{}", res);
    let res = (n - 2) * (n - 2) - res;
    println!("{}", res);
}
pub mod input_mcr {
    // ref: tanakh <https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8>
    #[macro_export(local_inner_macros)]
    macro_rules! input {
        (source = $s:expr, $($r:tt)*) => {
            let mut parser = Parser::from_str($s);
            input_inner!{parser, $($r)*}
        };
        (parser = $parser:ident, $($r:tt)*) => {
            input_inner!{$parser, $($r)*}
        };
        (new_stdin_parser = $parser:ident, $($r:tt)*) => {
            let stdin = std::io::stdin();
            let reader = std::io::BufReader::new(stdin.lock());
            let mut $parser = Parser::new(reader);
            input_inner!{$parser, $($r)*}
        };
        ($($r:tt)*) => {
            input!{new_stdin_parser = parser, $($r)*}
        };
    }

    #[macro_export(local_inner_macros)]
    macro_rules! input_inner {
        ($parser:ident) => {};
        ($parser:ident, ) => {};
        ($parser:ident, $var:ident : $t:tt $($r:tt)*) => {
            let $var = read_value!($parser, $t);
            input_inner!{$parser $($r)*}
        };
    }

    #[macro_export(local_inner_macros)]
    macro_rules! read_value {
        ($parser:ident, ( $($t:tt),* )) => {
            ( $(read_value!($parser, $t)),* )
        };
        ($parser:ident, [ $t:tt ; $len:expr ]) => {
            (0..$len).map(|_| read_value!($parser, $t)).collect::<Vec<_>>()
        };
        ($parser:ident, chars) => {
            read_value!($parser, String).chars().collect::<Vec<char>>()
        };
        ($parser:ident, char_) => {
            read_value!($parser, String).chars().collect::<Vec<char>>()[0]
        };
        ($parser:ident, usize1) => {
            read_value!($parser, usize) - 1
        };
        ($parser:ident, line) => {
            $parser.next_line()
        };
        ($parser:ident, line_) => {
            $parser.next_line().chars().collect::<Vec<char>>()
        };
        ($parser:ident, $t:ty) => {
            $parser.next::<$t>().expect("Parse error")
        };
    }

    use std::collections::VecDeque;
    use std::io;
    use std::io::BufRead;
    use std::str;

    pub struct Parser<R> {
        pub reader: R,
        buf: VecDeque<u8>,
        parse_buf: Vec<u8>,
    }

    impl Parser<io::Empty> {
        pub fn from_str(s: &str) -> Parser<io::Empty> {
            Parser {
                reader: io::empty(),
                buf: VecDeque::from(s.as_bytes().to_vec()),
                parse_buf: vec![],
            }
        }
    }

    impl<R: BufRead> Parser<R> {
        pub fn new(reader: R) -> Parser<R> {
            Parser {
                reader: reader,
                buf: VecDeque::new(),
                parse_buf: vec![],
            }
        }
        pub fn update_buf(&mut self) {
            loop {
                let (len, complete) = {
                    let buf2 = self.reader.fill_buf().unwrap();
                    self.buf.extend(buf2.iter());
                    let len = buf2.len();
                    (len, buf2.last() < Some(&0x20))
                };
                self.reader.consume(len);
                if complete {
                    break;
                }
            }
        }
        pub fn next<T: str::FromStr>(&mut self) -> Result<T, T::Err> {
            loop {
                while let Some(c) = self.buf.pop_front() {
                    if c > 0x20 {
                        self.buf.push_front(c);
                        break;
                    }
                }
                self.parse_buf.clear();
                while let Some(c) = self.buf.pop_front() {
                    if c <= 0x20 {
                        self.buf.push_front(c);
                        break;
                    } else {
                        self.parse_buf.push(c);
                    }
                }
                if self.parse_buf.is_empty() {
                    self.update_buf();
                } else {
                    return unsafe { str::from_utf8_unchecked(&self.parse_buf) }.parse::<T>();
                }
            }
        }
        pub fn next_line(&mut self) -> String {
            loop {
                while let Some(c) = self.buf.pop_front() {
                    if c >= 0x20 {
                        self.buf.push_front(c);
                        break;
                    }
                }
                self.parse_buf.clear();
                while let Some(c) = self.buf.pop_front() {
                    if c < 0x20 {
                        self.buf.push_front(c);
                        break;
                    } else {
                        self.parse_buf.push(c);
                    }
                }
                if self.parse_buf.is_empty() {
                    self.update_buf();
                } else {
                    return unsafe { str::from_utf8_unchecked(&self.parse_buf) }.to_string();
                }
            }
        }
    }
}