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.Runtime.CompilerServices;
using System.Text;
using System.Diagnostics;
using System.Numerics;
using static System.Console;
using static System.Convert;
using static System.Math;
using static Template;
using SC = FastScanner;

public partial class Solver
{
    public void Solve()
    {
        int N=sc.Int, Q=sc.Int;
        P mr(P a, P b) => new P(a.zero + b.zero, a.one + b.one, a.inv + b.inv + (long)a.one * b.zero);
        P up(P a, bool b, int c) => !b ? a : new P(a.one, a.zero, (long)a.one * a.zero - a.inv);
        bool lz(bool a, bool b) => a ^ b;
        var seg = new LazySegmentTree<P, bool>(N, new P(0, 0, 0), false, mr, up, lz);
        for(int i = 0; i < N; i++)
        {
            int a = sc.Int;
            seg[i] = new P(1 - a, a, 0);
        }
        seg.Build();
        while (Q-- > 0)
        {
            int t = sc.Int, L = sc.Int, R = sc.Int;
            L--;
            if (t == 1)
            {
                seg.Update(L, R, true);
            }
            else
            {
                Console.WriteLine(seg.Query(L,R).inv);
            }
        }
    }
    struct P { public int zero, one;public long inv;public P(int z,int o,long i) { zero = z;one = o;inv = i; } }
}

public class LazySegmentTree<T, E>
{
    protected readonly int size;
    protected readonly T idT;
    protected readonly T[] data;
    protected readonly E idE;
    protected readonly E[] lazy;
    protected readonly Func<T, T, T> mergeT;
    protected readonly Func<T, E, int, T> update;
    protected readonly Func<E, E, E> mergeE;
    protected readonly Comparison<E> cmpE;

    public T this[int i]
    {
        get { return data[i + size - 1]; }
        set { data[i + size - 1] = value; }
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    protected int Parent(int index)
        => (index - 1) >> 1;
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    protected int Left(int index)
        => (index << 1) + 1;
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    protected int Right(int index)
        => (index + 1) << 1;
    public LazySegmentTree(int N, T idT, E idE, Func<T, T, T> mergeT, Func<T, E, int, T> update = null, Func<E, E, E> mergeE = null, Comparison<E> cmp = null)
    {
        this.mergeT = mergeT;
        this.size = 1;
        this.idT = idT;
        this.idE = idE;
        this.update = update ?? ((a, b, c) => a);
        this.mergeE = mergeE ?? ((a, b) => b);
        cmpE = cmp ?? Comparer<E>.Default.Compare;
        while (this.size < N)
            this.size <<= 1;
        data = new T[2 * this.size - 1];
        for (var i = 0; i < 2 * this.size - 1; i++)
            data[i] = idT;
        lazy = Enumerable.Repeat(0, 2 * this.size + 1).Select(_ => idE).ToArray();
    }
    protected void eval(int len, int k)
    {
        if (cmpE(lazy[k], idE) == 0) return;
        if (Right(k) < size * 2)
        {
            lazy[Left(k)] = mergeE(lazy[Left(k)], lazy[k]);
            lazy[Right(k)] = mergeE(lazy[Right(k)], lazy[k]);
        }
        data[k] = update(data[k], lazy[k], len);
        lazy[k] = idE;
    }
    public void Build()
    {
        for (int i = size - 2; i >= 0; i--)
            data[i] = mergeT(data[Left(i)], data[Right(i)]);
    }
    public void Update(int left, int right, E value, int k = 0, int l = 0, int r = -1)
    {
        if (r == -1) r = size;
        eval(r - l, k);
        if (r <= left || right <= l) return;
        if (left <= l && r <= right)
        {
            lazy[k] = mergeE(lazy[k], value);
            eval(r - l, k);
        }
        else
        {
            Update(left, right, value, Left(k), l, (l + r) >> 1);
            Update(left, right, value, Right(k), (l + r) >> 1, r);
            data[k] = mergeT(data[Left(k)], data[Right(k)]);
        }
    }
    public T Query(int left, int right, int k = 0, int l = 0, int r = -1)
    {
        if (r == -1) r = size;
        if (r <= left || right <= l) return idT;
        eval(r - l, k);
        if (left <= l && r <= right) return data[k];
        else
            return mergeT(Query(left, right, Left(k), l, (l + r) >> 1), Query(left, right, Right(k), (l + r) >> 1, r));
    }

    public int Find(int st, Func<T, bool> check)
    {
        var x = idT;
        return Find(st, check, ref x, 0, 0, size);
    }
    private int Find(int st, Func<T, bool> check, ref T x, int k, int l, int r)
    {
        if (l + 1 == r)
        { x = mergeT(x, data[k]); return check(x) ? k - size + 1 : -1; }
        eval(r - l, k);
        var m = (l + r) >> 1;
        if (m <= st) return Find(st, check, ref x, Right(k), m, r);
        if (st <= l && !check(mergeT(x, data[k])))
        { x = mergeT(x, data[k]); return -1; }
        var xl = Find(st, check, ref x, Left(k), l, m);
        if (xl >= 0) return xl;
        return Find(st, check, ref x, Right(k), m, r);
    }
}

public struct ModInt
{
    //public const long MOD = (int)1e9 + 7;
    public const long MOD = 998244353;
    public long Value { get; set; }
    public ModInt(long n = 0) { Value = n; }
    private static ModInt[] fac, inv, facinv;
    public override string ToString() => Value.ToString();
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator +(ModInt l, ModInt r)
    {
        l.Value += r.Value;
        if (l.Value >= MOD) l.Value -= MOD;
        return l;
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator -(ModInt l, ModInt r)
    {
        l.Value -= r.Value;
        if (l.Value < 0) l.Value += MOD;
        return l;
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator *(ModInt l, ModInt r) => new ModInt(l.Value * r.Value % MOD);
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator /(ModInt l, ModInt r) => l * Pow(r, MOD - 2);
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static implicit operator long(ModInt l) => l.Value;
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static implicit operator ModInt(long n)
    {
        n %= MOD; if (n < 0) n += MOD;
        return new ModInt(n);
    }

    public static ModInt Pow(ModInt m, long n)
    {
        if (n == 0) return 1;
        if (n % 2 == 0) return Pow(m * m, n >> 1);
        else return Pow(m * m, n >> 1) * m;
    }

    public static void Build(int n)
    {
        fac = new ModInt[n + 1];
        facinv = new ModInt[n + 1];
        inv = new ModInt[n + 1];
        inv[1] = fac[0] = fac[1] = facinv[0] = facinv[1] = 1;
        for (var i = 2; i <= n; i++)
        {
            fac[i] = fac[i - 1] * i;
            inv[i] = MOD - inv[MOD % i] * (MOD / i);
            facinv[i] = facinv[i - 1] * inv[i];
        }
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt Fac(int n) => fac[n];
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt Inv(int n) => inv[n];
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt FacInv(int n) => facinv[n];
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt Comb(int n, int r)
    {
        if (n < r) return 0;
        if (n == r) return 1;
        return fac[n] * facinv[r] * facinv[n - r];
    }
    public static ModInt Perm(int n, int r)
    {
        if (n < r) return 0;
        return fac[n] * facinv[n - r];
    }

}

public class FastScanner
{
    //0x0a:LF 0x20:SPC 0x2d:- 0x30 ~ 0x39: 0 ~ 9
    static System.IO.Stream str = System.Console.OpenStandardInput();
    const int size = 1 << 10;
    static byte[] buffer = new byte[size];
    static int ptr;
    static int len;
    public int Int
    {
        get
        {
            var c = Read();
            while (c < 0x21)
            {
                c = Read();
            }
            var n = false;
            if (c == '-')
            {
                n = true;
                c = Read();
            }
            var ret = 0;
            while (c >= 0x30)
            {
                ret = ret * 10 + (c & 15);
                c = Read();
            }
            return n ? -ret : ret;
        }
    }
    public long Long
    {
        get
        {
            var c = Read();
            while (c < 0x21)
            {
                c = Read();
            }
            var n = false;
            if (c == '-')
            {
                n = true;
                c = Read();
            }
            var ret = 0L;
            while (c >= 0x30)
            {
                ret = ret * 10 + (c & 15);
                c = Read();
            }
            return n ? -ret : ret;
        }
    }
    byte Read()
    {
        if (ptr == len)
        {
            len = str.Read(buffer, 0, size);
            if (len == 0) return 0;
            ptr = 0;
        }
        return buffer[ptr++];
    }
}
#region Template
public partial class Solver
{
    public SC sc = new SC();
    static void Main(string[] args)
    {
        Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
        var sol = new Solver();
        int testcase = 1;
        //testcase = sol.sc.Int;
        //var th = new Thread(sol.Solve, 1 << 26);th.Start();th.Join();
        while (testcase-- > 0)
            sol.Solve();
        Console.Out.Flush();
    }
}
public static class Template
{
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static bool chmin<T>(ref T a, T b) where T : IComparable<T> { if (a.CompareTo(b) > 0) { a = b; return true; } return false; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static bool chmax<T>(ref T a, T b) where T : IComparable<T> { if (a.CompareTo(b) < 0) { a = b; return true; } return false; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static void swap<T>(ref T a, ref T b) { var t = b; b = a; a = t; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static void swap<T>(this IList<T> A, int i, int j) { var t = A[i]; A[i] = A[j]; A[j] = t; }
    public static T[] Create<T>(int n, Func<T> f) { var rt = new T[n]; for (var i = 0; i < rt.Length; ++i) rt[i] = f(); return rt; }
    public static T[] Create<T>(int n, Func<int, T> f) { var rt = new T[n]; for (var i = 0; i < rt.Length; ++i) rt[i] = f(i); return rt; }
    public static void Out<T>(this IList<T> A, out T a) => a = A[0];
    public static void Out<T>(this IList<T> A, out T a, out T b) { a = A[0]; b = A[1]; }
    public static void Out<T>(this IList<T> A, out T a, out T b, out T c) { A.Out(out a, out b); c = A[2]; }
    public static void Out<T>(this IList<T> A, out T a, out T b, out T c, out T d) { A.Out(out a, out b, out c); d = A[3]; }
    public static string Concat<T>(this IEnumerable<T> A, string sp) => string.Join(sp, A);
    public static char ToChar(this int s, char begin = '0') => (char)(s + begin);
    public static IEnumerable<T> Shuffle<T>(this IEnumerable<T> A) => A.OrderBy(v => Guid.NewGuid());
    public static int CompareTo<T>(this T[] A, T[] B, Comparison<T> cmp = null) { cmp = cmp ?? Comparer<T>.Default.Compare; for (var i = 0; i < Min(A.Length, B.Length); i++) { int c = cmp(A[i], B[i]); if (c > 0) return 1; else if (c < 0) return -1; } if (A.Length == B.Length) return 0; if (A.Length > B.Length) return 1; else return -1; }
    public static string ToStr<T>(this T[][] A) => A.Select(a => a.Concat(" ")).Concat("\n");
    public static int ArgMax<T>(this IList<T> A, Comparison<T> cmp = null) { cmp = cmp ?? Comparer<T>.Default.Compare; T max = A[0]; int rt = 0; for (int i = 1; i < A.Count; i++) if (cmp(max, A[i]) < 0) { max = A[i]; rt = i; } return rt; }
    public static T PopBack<T>(this List<T> A) { var v = A[A.Count - 1]; A.RemoveAt(A.Count - 1); return v; }
    public static void Fail<T>(T s) { Console.WriteLine(s); Console.Out.Close(); Environment.Exit(0); }
}
public class Scanner
{
    public string Str => Console.ReadLine().Trim();
    public int Int => int.Parse(Str);
    public long Long => long.Parse(Str);
    public double Double => double.Parse(Str);
    public int[] ArrInt => Str.Split(' ').Select(int.Parse).ToArray();
    public long[] ArrLong => Str.Split(' ').Select(long.Parse).ToArray();
    public char[][] Grid(int n) => Create(n, () => Str.ToCharArray());
    public int[] ArrInt1D(int n) => Create(n, () => Int);
    public long[] ArrLong1D(int n) => Create(n, () => Long);
    public int[][] ArrInt2D(int n) => Create(n, () => ArrInt);
    public long[][] ArrLong2D(int n) => Create(n, () => ArrLong);
    private Queue<string> q = new Queue<string>();
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public T Next<T>() { if (q.Count == 0) foreach (var item in Str.Split(' ')) q.Enqueue(item); return (T)Convert.ChangeType(q.Dequeue(), typeof(T)); }
    public void Make<T1>(out T1 v1) => v1 = Next<T1>();
    public void Make<T1, T2>(out T1 v1, out T2 v2) { v1 = Next<T1>(); v2 = Next<T2>(); }
    public void Make<T1, T2, T3>(out T1 v1, out T2 v2, out T3 v3) { Make(out v1, out v2); v3 = Next<T3>(); }
    public void Make<T1, T2, T3, T4>(out T1 v1, out T2 v2, out T3 v3, out T4 v4) { Make(out v1, out v2, out v3); v4 = Next<T4>(); }
    public void Make<T1, T2, T3, T4, T5>(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5) { Make(out v1, out v2, out v3, out v4); v5 = Next<T5>(); }
    public void Make<T1, T2, T3, T4, T5, T6>(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5, out T6 v6) { Make(out v1, out v2, out v3, out v4, out v5); v6 = Next<T6>(); }
    public void Make<T1, T2, T3, T4, T5, T6, T7>(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5, out T6 v6, out T7 v7) { Make(out v1, out v2, out v3, out v4, out v5, out v6); v7 = Next<T7>(); }
    public (T1, T2) Make<T1, T2>() { Make(out T1 v1, out T2 v2); return (v1, v2); }
    public (T1, T2, T3) Make<T1, T2, T3>() { Make(out T1 v1, out T2 v2, out T3 v3); return (v1, v2, v3); }
    public (T1, T2, T3, T4) Make<T1, T2, T3, T4>() { Make(out T1 v1, out T2 v2, out T3 v3, out T4 v4); return (v1, v2, v3, v4); }
}

#endregion