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 C# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Threading;
using System.Text;
using System.Text.RegularExpressions;
using System.Diagnostics;
using static util;
using P = pair<int, int>;

class Program {
    static void Main(string[] args) {
        var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        var solver = new Solver(sw);
        // var t = new Thread(solver.solve, 1 << 28); // 256 MB
        // t.Start();
        // t.Join();
        solver.solve();
        sw.Flush();
    }
}

class Solver {
    StreamWriter sw;
    Scan sc;
    void Prt(string a) => sw.WriteLine(a);
    void Prt<T>(IEnumerable<T> a) => Prt(string.Join(" ", a));
    void Prt(params object[] a) => Prt(string.Join(" ", a));
    public Solver(StreamWriter sw) {
        this.sw = sw;
        this.sc = new Scan();
    }

    struct node {
        int c0, c1;
        public long inv;
        public node(int x) {
            c0 = c1 = 0;
            if (x == 0) ++c0;
            if (x == 1) ++c1;
            inv = 0;
        }
        public node(int c0, int c1, long inv) {
            this.c0 = c0;
            this.c1 = c1;
            this.inv = inv;
        }
        public static node calc(node l, node r) => new node(l.c0 + r.c0, l.c1 + r.c1, l.inv + r.inv + l.c1 * (long)r.c0);
        public node flip() => new node(c1, c0, c0 * (long)c1 - inv);
    }

    public void solve() {
        int n, q;
        sc.Multi(out n, out q);
        var a = sc.IntArr.Select(x => new node(x)).ToArray();
        var sg = new LazySegtree<node, bool>(n, node.calc, (x, y) => y ? x.flip() : x, (x, y) => x ^ y, new node(-1), a);
        for (int i = 0; i < q; i++)
        {
            int t, l, r;
            sc.Multi(out t, out l, out r);
            --l;
            if (t == 1) {
                sg.update(l, r, true);
            }
            else {
                Prt(sg.run(l, r).inv);
            }
        }
    }
}

class pair<T, U> : IComparable<pair<T, U>> {
    public T v1;
    public U v2;
    public pair() : this(default(T), default(U)) {}
    public pair(T v1, U v2) { this.v1 = v1; this.v2 = v2; }
    public int CompareTo(pair<T, U> a) {
        int c = Comparer<T>.Default.Compare(v1, a.v1);
        return c != 0 ? c : Comparer<U>.Default.Compare(v2, a.v2);
    }
    public override string ToString() => v1 + " " + v2;
    public void Deconstruct(out T a, out U b) { a = v1; b = v2; }
}
static class util {
    public static readonly int M = 1000000007;
    // public static readonly int M = 998244353;
    public static readonly long LM = 1L << 60;
    public static readonly double eps = 1e-11;
    public static void DBG(string a) => Console.Error.WriteLine(a);
    public static void DBG<T>(IEnumerable<T> a) => DBG(string.Join(" ", a));
    public static void DBG(params object[] a) => DBG(string.Join(" ", a));
    public static void Assert(params bool[] conds) {
        if (conds.Any(x => !x)) throw new Exception();
    }
    public static pair<T, U> make_pair<T, U>(T v1, U v2) => new pair<T, U>(v1, v2);
    public static int CompareList<T>(IList<T> a, IList<T> b) where T : IComparable<T> {
        for (int i = 0; i < a.Count && i < b.Count; i++)
            if (a[i].CompareTo(b[i]) != 0) return a[i].CompareTo(b[i]);
        return a.Count.CompareTo(b.Count);
    }
    public static bool inside(int i, int j, int h, int w) => i >= 0 && i < h && j >= 0 && j < w;
    public static readonly int[] dd = { 0, 1, 0, -1 };
    // static readonly string dstring = "RDLU";
    public static IEnumerable<P> adjacents(int i, int j)
        => Enumerable.Range(0, dd.Length).Select(k => new P(i + dd[k], j + dd[k ^ 1]));
    public static IEnumerable<P> adjacents(int i, int j, int h, int w)
        => adjacents(i, j).Where(p => inside(p.v1, p.v2, h, w));
    public static IEnumerable<P> adjacents(this P p) => adjacents(p.v1, p.v2);
    public static IEnumerable<P> adjacents(this P p, int h, int w) => adjacents(p.v1, p.v2, h, w);
    public static IEnumerable<int> all_subset(this int p) {
        for (int i = 0; ; i = i - p & p) {
            yield return i;
            if (i == p) break;
        }
    }
    public static Dictionary<T, int> compress<T>(this IEnumerable<T> a)
        => a.Distinct().OrderBy(v => v).Select((v, i) => new { v, i }).ToDictionary(p => p.v, p => p.i);
    public static Dictionary<T, int> compress<T>(params IEnumerable<T>[] a) => compress(a.SelectMany(x => x));
    public static T[] inv<T>(this Dictionary<T, int> dic) {
        var res = new T[dic.Count];
        foreach (var item in dic) res[item.Value] = item.Key;
        return res;
    }
    public static void swap<T>(ref T a, ref T b) where T : struct { var t = a; a = b; b = t; }
    public static void swap<T>(this IList<T> a, int i, int j) where T : struct { var t = a[i]; a[i] = a[j]; a[j] = t; }
    public static T[] copy<T>(this IList<T> a) {
        var ret = new T[a.Count];
        for (int i = 0; i < a.Count; i++) ret[i] = a[i];
        return ret;
    }
}

class Scan {
    StreamReader sr;
    public Scan() { sr = new StreamReader(Console.OpenStandardInput()); }
    public Scan(string path) { sr = new StreamReader(path); }
    public int Int => int.Parse(Str);
    public long Long => long.Parse(Str);
    public double Double => double.Parse(Str);
    public string Str => ReadLine.Trim();
    public string ReadLine => sr.ReadLine();
    public pair<T, U> Pair<T, U>() {
        T a; U b;
        Multi(out a, out b);
        return new pair<T, U>(a, b);
    }
    public P P => Pair<int, int>();
    public int[] IntArr => StrArr.Select(int.Parse).ToArray();
    public long[] LongArr => StrArr.Select(long.Parse).ToArray();
    public double[] DoubleArr => StrArr.Select(double.Parse).ToArray();
    public string[] StrArr => Str.Split(new[]{' '}, StringSplitOptions.RemoveEmptyEntries);
    bool eq<T, U>() => typeof(T).Equals(typeof(U));
    T ct<T, U>(U a) => (T)Convert.ChangeType(a, typeof(T));
    T cv<T>(string s) => eq<T, int>()    ? ct<T, int>(int.Parse(s))
                       : eq<T, long>()   ? ct<T, long>(long.Parse(s))
                       : eq<T, double>() ? ct<T, double>(double.Parse(s))
                       : eq<T, char>()   ? ct<T, char>(s[0])
                                         : ct<T, string>(s);
    public void Multi<T>(out T a) => a = cv<T>(Str);
    public void Multi<T, U>(out T a, out U b) {
        var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]);
    }
    public void Multi<T, U, V>(out T a, out U b, out V c) {
        var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]);
    }
    public void Multi<T, U, V, W>(out T a, out U b, out V c, out W d) {
        var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]);
    }
    public void Multi<T, U, V, W, X>(out T a, out U b, out V c, out W d, out X e) {
        var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]);
    }
}

class LazySegtree<T, U> {
    int n;
    T[] data;
    U[] lazy;
    bool[] is_lazy;
    Func<T, T, T> calc;
    Func<T, U, T> apply;
    Func<U, U, U> merge;
    T identity;

    public LazySegtree(int m, Func<T, T, T> calc, Func<T, U, T> apply, Func<U, U, U> merge, T identity) {
        this.calc = calc;
        this.apply = apply;
        this.merge = merge;
        this.identity = identity;
        n = 1;
        while (n < m) n <<= 1;
        data = new T[n * 2 - 1];
        lazy = new U[n * 2 - 1];
        is_lazy = new bool[n * 2 - 1];
        for (int i = 0; i < data.Length; i++) data[i] = identity;
    }
    public LazySegtree(int m, Func<T, T, T> calc, Func<T, U, T> apply, Func<U, U, U> merge, T identity, T ini) : this(m, calc, apply, merge, identity) {
        for (int i = 0; i < m; i++) data[i + n - 1] = ini;
        for (int i = n - 2; i >= 0; i--) data[i] = calc(data[i * 2 + 1], data[i * 2 + 2]);
    }
    public LazySegtree(int m, Func<T, T, T> calc, Func<T, U, T> apply, Func<U, U, U> merge, T identity, IList<T> ini) : this(m, calc, apply, merge, identity) {
        for (int i = 0; i < m; i++) data[i + n - 1] = ini[i];
        for (int i = n - 2; i >= 0; i--) data[i] = calc(data[i * 2 + 1], data[i * 2 + 2]);
    }
    void assign_lazy(int k, U x) {
        if (k >= lazy.Length) return;
        lazy[k] = is_lazy[k] ? merge(lazy[k], x) : x;
        is_lazy[k] = true;
    }
    void eval(int k){
        if (!is_lazy[k]) return;
        assign_lazy(k * 2 + 1, lazy[k]);
        assign_lazy(k * 2 + 2, lazy[k]);
        data[k] = apply(data[k], lazy[k]);
        is_lazy[k] = false;
    }
    T update(int s, int t, U x, int k, int l, int r) {
        eval(k);
        if (r <= s || t <= l) return data[k];
        if (s <= l && r <= t) {
            assign_lazy(k, x);
            return apply(data[k], lazy[k]);
        }
        return data[k] = calc(update(s, t, x, k * 2 + 1, l, (l + r) / 2),
                              update(s, t, x, k * 2 + 2, (l + r) / 2, r));
    }
    T run(int s, int t, int k, int l, int r) {
        eval(k);
        if (r <= s || t <= l) return identity;
        if (s <= l && r <= t) return data[k];
        return calc(run(s, t, k * 2 + 1, l, (l + r) / 2),
                    run(s, t, k * 2 + 2, (l + r) / 2, r));
    }

    // [s, t)
    public void update(int s, int t, U x) => update(s, t, x, 0, 0, n);
    // [s, t)
    public T run(int s, int t) => run(s, t, 0, 0, n);
}