Problem:
Score : 100 points

Problem Statement

You are given a binary array A=(A_1,A_2,\cdots,A_N) of length N.

Process Q queries of the following types. The i-th query is represented by three integers T_i,L_i,R_i.

T_i=1: Replace the value of A_j with 1-A_j for each L_i \leq j \leq R_i.

T_i=2: Calculate the inversion(*) of the array A_{L_i},A_{L_i+1},\cdots,A_{R_i}．

Note：The inversion of the array x_1,x_2,\cdots,x_k is the number of the pair of integers i,j with 1 \leq i < j \leq k, x_i > x_j.

Constraints

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

0 \leq A_i \leq 1

1 \leq Q \leq 2 \times 10^5

1 \leq T_i \leq 2

1 \leq L_i \leq R_i \leq N

All values in Input are integer.

Input

Input is given from Standard Input in the following format:

N Q
A_1 A_2 \cdots A_N
T_1 L_1 R_1
T_2 L_2 R_2
\vdots
T_Q L_Q R_Q

Output

For each query with T_i=2, print the answer.

Sample Input 1

5 5
0 1 0 0 1
2 1 5
1 3 4
2 2 5
1 1 3
2 1 2

Sample Output 1

2
0
1

First query: Print 2, which is the inversion of (A_1,A_2,A_3,A_4,A_5)=(0,1,0,0,1).

Second query: Replace the value of A_3 and A_4 with 1 and 1, respectively.

Third query: Print 0, which is the inversion of (A_2,A_3,A_4,A_5)=(1,1,1,1).

Fourth query: Replace the value of A_1, A_2 and A_4 with 1, 0 and 0, respectively.

Fifth query: Print 1, which is the inversion of (A_1,A_2)=(1,0).

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

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

macro_rules! trace {
    ($x:expr) => {
        #[cfg(debug_assertions)]
        eprintln!(">>> {} = {:?}", stringify!($x), $x)
    };
    ($($xs:expr),*) => { trace!(($($xs),*)) }
}
macro_rules! put {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        if let Some(x) = it.next() { print!("{}", x); }
        for x in it { print!(" {}", x); }
        println!("");
    }};
    ($x:expr) => { println!("{}", $x) };
    ($x:expr, $($xs:expr),*) => { print!("{} ", $x); put!($($xs),*) }
}

#[derive(Debug, Clone, Copy)]
struct D {
    zero: usize,
    one: usize,
    inversion: usize,
    proportion: usize, // flip したときの転倒数
}

impl D {
    fn from(x: &usize) -> Self {
        let mut d = D {
            zero: 0,
            one: 0,
            inversion: 0,
            proportion: 0,
        };
        if *x == 0 {
            d.zero += 1;
        } else {
            d.one += 1;
        }
        d
    }
}

impl std::ops::Mul for D {
    type Output = D;
    fn mul(self, other: D) -> D {
        D {
            zero: self.zero + other.zero,
            one: self.one + other.one,
            inversion: self.inversion + other.inversion + self.one * other.zero,
            proportion: self.proportion + other.proportion + self.zero * other.one,
        }
    }
}

impl Monoid for D {
    fn unit() -> D {
        D {
            zero: 0,
            one: 0,
            inversion: 0,
            proportion: 0,
        }
    }
}

#[derive(Debug, Clone, Copy)]
struct Flip(bool);

impl std::ops::Mul for Flip {
    type Output = Flip;
    fn mul(self, other: Flip) -> Flip {
        Flip(self.0 ^ other.0)
    }
}

impl Monoid for Flip {
    fn unit() -> Flip {
        Flip(false)
    }
}

impl Act<D> for Flip {
    fn act(&self, d: D) -> D {
        if self.0 {
            D {
                zero: d.one,
                one: d.zero,
                inversion: d.proportion,
                proportion: d.inversion,
            }
        } else {
            d.clone()
        }
    }
}

fn main() {
    let mut sc = Scanner::new();
    let n: usize = sc.cin();
    let q: usize = sc.cin();
    let xs: Vec<usize> = sc.vec(n);

    let mut st = LazySegmentTree::from(xs.iter().map(D::from).collect());

    for _ in 0..q {
        let t: usize = sc.cin();
        let left = sc.cin::<usize>() - 1;
        let right = sc.cin::<usize>();
        if t == 1 {
            st.update(left..right, Flip(true));
        } else {
            let d = st.product(left..right);
            put!(d.inversion);
        }
    }
}

// @seq.lazy_segment_tree.rs
// @algebra.monoid.rs
trait Monoid: std::ops::Mul<Output = Self> + Clone + Copy {
    fn unit() -> Self;
}
impl Monoid for i64 {
    fn unit() -> Self {
        0
    }
}
impl Monoid for f64 {
    fn unit() -> Self {
        0.0
    }
}

// @algebra.act.rs
trait Act<X> {
    fn act(&self, x: X) -> X;
}

#[derive(Clone)]
struct LazySegmentTree<X, M> {
    length: usize,       // of leaves
    length_upper: usize, // power of 2
    size: usize,         // of nodes
    data: Vec<X>,
    act: Vec<M>,
}
impl<X: Monoid, M: Monoid + Act<X>> LazySegmentTree<X, M> {
    fn new(length: usize) -> Self {
        let mut length_upper = 1;
        loop {
            if length_upper >= length {
                break;
            }
            length_upper *= 2;
        }
        let size = length_upper * 2 - 1;
        let data = vec![X::unit(); size];
        let act = vec![M::unit(); size];
        LazySegmentTree {
            length,
            length_upper,
            size,
            data,
            act,
        }
    }
    fn from(xs: Vec<X>) -> Self {
        let mut tree = Self::new(xs.len());
        for i in 0..xs.len() {
            tree.data[tree.size / 2 + i] = xs[i];
        }
        for i in (0..tree.size / 2).rev() {
            tree.data[i] = tree.data[2 * i + 1] * tree.data[2 * i + 2];
        }
        tree
    }
    fn propagation(&mut self, idx: usize) {
        if idx < self.size / 2 {
            self.act[idx * 2 + 1] = self.act[idx * 2 + 1] * self.act[idx];
            self.act[idx * 2 + 2] = self.act[idx * 2 + 2] * self.act[idx];
        }
        self.data[idx] = self.act[idx].act(self.data[idx]);
        self.act[idx] = M::unit();
    }
    fn update_sub(
        &mut self,
        range: std::ops::Range<usize>,
        m: M,
        idx: usize,
        focus: std::ops::Range<usize>,
    ) {
        self.propagation(idx);
        if focus.end <= range.start || range.end <= focus.start {
            return;
        }
        if range.start <= focus.start && focus.end <= range.end {
            self.act[idx] = self.act[idx] * m;
            self.propagation(idx);
        } else if idx < self.data.len() / 2 {
            let mid = (focus.start + focus.end) / 2;
            self.update_sub(range.clone(), m, idx * 2 + 1, focus.start..mid);
            self.update_sub(range.clone(), m, idx * 2 + 2, mid..focus.end);
            self.data[idx] = self.data[idx * 2 + 1] * self.data[idx * 2 + 2];
        }
    }
    fn update(&mut self, range: std::ops::Range<usize>, m: M) {
        self.update_sub(range, m, 0, 0..self.length_upper);
    }
    fn product_sub(
        &mut self,
        range: std::ops::Range<usize>,
        idx: usize,
        focus: std::ops::Range<usize>,
    ) -> X {
        self.propagation(idx);
        if focus.end <= range.start || range.end <= focus.start {
            X::unit()
        } else if range.start <= focus.start && focus.end <= range.end {
            self.data[idx]
        } else {
            let mid = (focus.start + focus.end) / 2;
            let a = self.product_sub(range.clone(), idx * 2 + 1, focus.start..mid);
            let b = self.product_sub(range.clone(), idx * 2 + 2, mid..focus.end);
            a * b
        }
    }
    fn product(&mut self, range: std::ops::Range<usize>) -> X {
        self.product_sub(range, 0, 0..self.length_upper)
    }
    fn index(&mut self, i: usize) -> X {
        self.product(i..i + 1)
    }
    fn to_vec(&mut self) -> Vec<X> {
        (0..self.length).map(|i| self.index(i)).collect()
    }
}
impl<X: std::fmt::Debug, M: std::fmt::Debug> LazySegmentTree<X, M> {
    fn debug(&self) {
        for i in 0..self.size {
            if i > 0 && (i + 1).count_ones() == 1 {
                eprintln!();
            }
            eprint!("{:?} / {:?}; ", &self.data[i], &self.act[i]);
        }
        eprintln!();
    }
}

use std::collections::VecDeque;
use std::io::{self, Write};
use std::str::FromStr;

struct Scanner {
    stdin: io::Stdin,
    buffer: VecDeque<String>,
}
impl Scanner {
    fn new() -> Self {
        Scanner {
            stdin: io::stdin(),
            buffer: VecDeque::new(),
        }
    }
    fn cin<T: FromStr>(&mut self) -> T {
        while self.buffer.is_empty() {
            let mut line = String::new();
            let _ = self.stdin.read_line(&mut line);
            for w in line.split_whitespace() {
                self.buffer.push_back(String::from(w));
            }
        }
        self.buffer.pop_front().unwrap().parse::<T>().ok().unwrap()
    }
    fn chars(&mut self) -> Vec<char> {
        self.cin::<String>().chars().collect()
    }
    fn vec<T: FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.cin()).collect()
    }
}