Problem: 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.

Example

Input

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


Output

2
0
1

Solution (in CPP):

Solution:
#include<iostream>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<complex>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<utility>
#include<tuple>
#include<cassert>
using namespace std;
typedef long long ll;
typedef unsigned int ui;
const ll mod = 1000000007;
const ll INF = (ll)1000000007 * 1000000007;
typedef pair<int, int> P;
#define stop char nyaa;cin>>nyaa;
#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define Per(i,sta,n) for(int i=n-1;i>=sta;i--)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
typedef long double ld;
const ld eps = 1e-8;
const ld pi = acos(-1.0);
typedef pair<ll, ll> LP;
int dx[4] = { 1,-1,0,0 };
int dy[4] = { 0,0,1,-1 };
template<class T>bool chmax(T& a, const T& b) { if (a < b) { a = b; return 1; }return 0; }
template<class T>bool chmin(T& a, const T& b) { if (b < a) { a = b; return 1; }return 0; }

template <class S,
    S(*op)(S, S),
    S(*e)(),
    class F,
    S(*mapping)(F, S),
    F(*composition)(F, F),
    F(*id)()>
    struct SegmentTree {
    public:
        SegmentTree() : SegmentTree(0) {}
        SegmentTree(int n) : SegmentTree(std::vector<S>(n, e())) {}
        SegmentTree(const std::vector<S>& v) : _n(int(v.size())) {
            log = ceil_pow2(_n);
            size = 1 << log;
            d = std::vector<S>(2 * size, e());
            lz = std::vector<F>(size, id());
            for (int i = 0; i < _n; i++) d[size + i] = v[i];
            for (int i = size - 1; i >= 1; i--) {
                update_(i);
            }
        }

        void set(int p, S x) {
            assert(0 <= p && p < _n);
            p += size;
            for (int i = log; i >= 1; i--) push(p >> i);
            d[p] = x;
            for (int i = 1; i <= log; i++) update_(p >> i);
        }

        S get(int p) {
            assert(0 <= p && p < _n);
            p += size;
            for (int i = log; i >= 1; i--) push(p >> i);
            return d[p];
        }

        S query(int l, int r) {
            assert(0 <= l && l <= r && r <= _n);
            if (l == r) return e();

            l += size;
            r += size;

            for (int i = log; i >= 1; i--) {
                if (((l >> i) << i) != l) push(l >> i);
                if (((r >> i) << i) != r) push(r >> i);
            }

            S sml = e(), smr = e();
            while (l < r) {
                if (l & 1) sml = op(sml, d[l++]);
                if (r & 1) smr = op(d[--r], smr);
                l >>= 1;
                r >>= 1;
            }

            return op(sml, smr);
        }

        S all_query() { return d[1]; }

        void update(int p, F f) {
            assert(0 <= p && p < _n);
            p += size;
            for (int i = log; i >= 1; i--) push(p >> i);
            d[p] = mapping(f, d[p]);
            for (int i = 1; i <= log; i++) update_(p >> i);
        }
        void update(int l, int r, F f) {
            assert(0 <= l && l <= r && r <= _n);
            if (l == r) return;

            l += size;
            r += size;

            for (int i = log; i >= 1; i--) {
                if (((l >> i) << i) != l) push(l >> i);
                if (((r >> i) << i) != r) push((r - 1) >> i);
            }

            {
                int l2 = l, r2 = r;
                while (l < r) {
                    if (l & 1) all_apply(l++, f);
                    if (r & 1) all_apply(--r, f);
                    l >>= 1;
                    r >>= 1;
                }
                l = l2;
                r = r2;
            }

            for (int i = 1; i <= log; i++) {
                if (((l >> i) << i) != l) update_(l >> i);
                if (((r >> i) << i) != r) update_((r - 1) >> i);
            }
        }

        template <bool (*g)(S)> int max_right(int l) {
            return max_right(l, [](S x) { return g(x); });
        }
        template <class G> int max_right(int l, G g) {
            assert(0 <= l && l <= _n);
            assert(g(e()));
            if (l == _n) return _n;
            l += size;
            for (int i = log; i >= 1; i--) push(l >> i);
            S sm = e();
            do {
                while (l % 2 == 0) l >>= 1;
                if (!g(op(sm, d[l]))) {
                    while (l < size) {
                        push(l);
                        l = (2 * l);
                        if (g(op(sm, d[l]))) {
                            sm = op(sm, d[l]);
                            l++;
                        }
                    }
                    return l - size;
                }
                sm = op(sm, d[l]);
                l++;
            } while ((l & -l) != l);
            return _n;
        }

        template <bool (*g)(S)> int min_left(int r) {
            return min_left(r, [](S x) { return g(x); });
        }
        template <class G> int min_left(int r, G g) {
            assert(0 <= r && r <= _n);
            assert(g(e()));
            if (r == 0) return 0;
            r += size;
            for (int i = log; i >= 1; i--) push((r - 1) >> i);
            S sm = e();
            do {
                r--;
                while (r > 1 && (r % 2)) r >>= 1;
                if (!g(op(d[r], sm))) {
                    while (r < size) {
                        push(r);
                        r = (2 * r + 1);
                        if (g(op(d[r], sm))) {
                            sm = op(d[r], sm);
                            r--;
                        }
                    }
                    return r + 1 - size;
                }
                sm = op(d[r], sm);
            } while ((r & -r) != r);
            return 0;
        }

    private:
        int _n, size, log;
        std::vector<S> d;
        std::vector<F> lz;

        void update_(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
        void all_apply(int k, F f) {
            d[k] = mapping(f, d[k]);
            if (k < size) lz[k] = composition(f, lz[k]);
        }
        void push(int k) {
            all_apply(2 * k, lz[k]);
            all_apply(2 * k + 1, lz[k]);
            lz[k] = id();
        }
        int ceil_pow2(int n) {
            int x = 0;
            while ((1U << x) < (unsigned int)(n)) x++;
            return x;
        }
};

struct T {
    int num0 = 0, num1 = 0; ll inv = 0;
    T() {}
    T(int n0, int n1, ll in) :num0(n0), num1(n1), inv(in) {}
};

T f(T a, T b) {
    return T(a.num0 + b.num0, a.num1 + b.num1, a.inv + b.inv + (ll)a.num1 * (ll)b.num0);
}
T e() { return T(0, 0, 0); };
T g(int p, T a) {
    if (p == 0) return a;
    return T(a.num1, a.num0, a.num0 * a.num1 - a.inv);
}
int h(int a, int b) {
    return (a + b) % 2;
}
int id() { return 0; };

int n, q;
vector<T> a;

void solve() {
    cin >> n >> q;
    a.resize(n);
    rep(i, n) {
        int p; cin >> p;
        if (p == 0)a[i].num0 = 1;
        else a[i].num1 = 1;
    }
    SegmentTree<T, f, e, int, g, h, id> seg(a);
    rep(i, q) {
        int t; cin >> t;
        if (t == 1) {
            int l, r; cin >> l >> r; l--;
            seg.update(l, r, 1);
        }
        else {
            int l, r; cin >> l >> r; l--;
            cout << seg.query(l, r).inv << endl;
        }
        // rep(i,n){
        //     T a=seg.get(i);
        //     if(a.num0==1) cout << 0 << " ";
        //     else cout << 1 << " ";
        // }
        // cout << "" << endl;
    }

}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout << fixed << setprecision(50);
    solve();
}