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 <bits/stdc++.h>
using namespace std;

namespace internal {
int ceil_pow2(int n) {
    int x = 0;
    while ((1U << x) < (unsigned int)(n)) x++;
    return x;
}
int bsf(unsigned int n) {
#ifdef _MSC_VER
    unsigned long index;
    _BitScanForward(&index, n);
    return index;
#else
    return __builtin_ctz(n);
#endif
}
}

template <class S, S(*op)(S, S), S(*e)(), class F, S(*mapping)(F, S), F(*composition)(F, F), F(*id)()>
struct lazy_segtree {
    public:
        lazy_segtree() : lazy_segtree(0) {}
        lazy_segtree(int n) : lazy_segtree(std::vector<S>(n, e())) {}
        lazy_segtree(const std::vector<S>& v) : _n(int(v.size())) {
            log = internal::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 prod(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_prod() { return d[1]; }
 
        void apply(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 apply(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();
        }
};

struct S { long long zero, one, inv; };
S op (S a, S b) { return S{a.zero + b.zero, a.one + b.one, a.inv + b.inv + a.one * b.zero}; }
S e () { return S{0ll, 0ll, 0ll}; }
using F = bool;
S mapping (F f, S a) {
    if (!f) return a;
    return S{a.one, a.zero, a.zero * a.one - a.inv};
}
F composition (F f, F g) { return (!f && g) || (f && !g); }
F id () { return false; }
 
int main(){
    int n, q;  cin >> n >> q;
    vector<S> a(n);
    for (int i = 0; i < n; i++) {
        int aa; cin >> aa;
        if (aa == 0) a[i] = S{1ll, 0ll, 0ll};
        else a[i] = {0ll, 1ll, 0ll};
    }
 
    lazy_segtree<S, op, e, F, mapping, composition, id> data(a);
 
    while (q--) {
        int t, l,  r; cin >> t >> l >> r; l--;
        if (t == 1) data.apply(l, r, true);
        else cout << data.prod(l, r).inv << "\n";
    }
    return 0;
}