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:
/**
 * code generated by JHelper
 * More info: https://github.com/AlexeyDmitriev/JHelper
 * @author aajisaka
 */


#include<bits/stdc++.h>

using namespace std;

void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}
#ifdef LOCAL
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif

#define SPEED ios_base::sync_with_stdio(false);cin.tie(nullptr)
#define rep(i,n) for(int i=0; i<(int)(n); i++)
#define all(v) v.begin(), v.end()
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; }

using ll = long long;
using ull = unsigned long long;
using P = pair<ll, ll>;

constexpr long double PI = 3.14159265358979323846264338327950288L;
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());


#include <algorithm>
#include <cassert>
#include <iostream>
#include <vector>


#ifdef _MSC_VER
#include <intrin.h>
#endif

namespace internal {

// @param n `0 <= n`
// @return minimum non-negative `x` s.t. `n <= 2**x`
    int ceil_pow2(int n) {
      int x = 0;
      while ((1U << x) < (unsigned int)(n)) x++;
      return x;
    }

// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
    int bsf(unsigned int n) {
#ifdef _MSC_VER
      unsigned long index;
    _BitScanForward(&index, n);
    return index;
#else
      return __builtin_ctz(n);
#endif
    }

}  // namespace internal


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 {
    ll zero, one, inversion;
};

using F = bool;
S op(S l, S r) {
  return S {
    l.zero + r.zero,l.one + r.one, l.inversion + r.inversion + l.one * r.zero
  };
}

S e() {
  return S {0, 0, 0};
}

S mapping(F f, S s) {
  if (!f) {
    return s;
  } else {
    return S {s.one, s.zero, s.one * s.zero - s.inversion};
  }
}

F composition(F f, F g) {
  return f^g;
}

F id() {
  return false;
}

class LLazySegmentTree {
public:
    void solve(istream& cin, ostream& cout) {
      SPEED;
      int n, q; cin >> n >> q;
      vector<S> a(n);
      rep(i, n) {
        int x; cin >> x;
        if (x == 0) {
          a[i] = {1, 0, 0};
        } else {
          a[i] = {0, 1, 0};
        }
      }

      auto seg = lazy_segtree<S, op, e, F, mapping, composition, id>(a);
      while(q--) {
        int t, l, r; cin >> t >> l >> r;
        if (t==1) {
          seg.apply(l-1, r, true);
        } else {
          cout << seg.prod(l-1, r).inversion << '\n';
        }
      }
    }
};

signed main() {
  LLazySegmentTree solver;
  std::istream& in(std::cin);
  std::ostream& out(std::cout);
  solver.solve(in, out);
  return 0;
}