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:
#pragma GCC target ("avx")
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#define _USE_MATH_DEFINES
#include<iostream>
#include<string>
#include<queue>
#include<cmath>
#include<map>
#include<set>
#include<list>
#include<iomanip>
#include<vector>
#include<random>
#include<functional>
#include<algorithm>
#include<stack>
#include<cstdio>
#include<cstring>
#include<bitset>
#include<unordered_map>
#include<climits>
#include<fstream>
#include<complex>
#include<time.h>
#include<cassert>
#include<functional>
#include<numeric>
#include<tuple>
using namespace std;
using ll = long long;
using ld = long double;
using H = pair<ll, ll>;
using P = pair<ll, H>;
using vi = vector<ll>;
#define all(a) (a).begin(),(a).end()
#define fs first
#define sc second
#define xx first
#define yy second.first
#define zz second.second
#define Q(i,j,k) mkp(i,mkp(j,k))
#define rng(i,s,n) for(ll i = (s) ; i < (n) ; i++)
#define rep(i,n) rng(i, 0, (n))
#define mkp make_pair
#define vec vector
#define pb emplace_back
#define siz(a) (int)(a).size()
#define crdcomp(b) sort(all((b)));(b).erase(unique(all((b))),(b).end())
#define getidx(b,i) (lower_bound(all(b),(i))-(b).begin())
#define ssp(i,n) (i==(ll)(n)-1?"\n":" ")
#define ctoi(c) (int)(c-'0')
#define itoc(c) (char)(c+'0')
#define cyes printf("Yes\n")
#define cno printf("No\n")
#define cdf(n) for(int quetimes_=(n);quetimes_>0;quetimes_--)
#define gcj printf("Case #%lld: ",qq123_+1)
#define readv(a,n) a.resize(n,0);rep(i,(n)) a[i]=read()
#define found(a,x) (a.find(x)!=a.end())
constexpr ll mod = (ll)1e9 + 7;
constexpr ll Mod = 998244353;
constexpr ld EPS = 1e-10;
constexpr ll inf = (ll)3 * 1e18;
constexpr int Inf = (ll)15 * 1e8;
constexpr int dx[] = { -1,1,0,0 }, dy[] = { 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; }
ll read() { ll u, k = scanf("%lld", &u); return u; }
string reads() { string s; cin >> s; return s; }
H readh(short g = 0) { H u; int k = scanf("%lld %lld", &u.fs, &u.sc); if (g == 1) u.fs--, u.sc--; if (g == 2) u.fs--; return u; }
bool ina(H t, int h, int w) { return 0 <= t.fs && t.fs < h && 0 <= t.sc && t.sc < w; }
bool ina(int t, int l, int r) { return l <= t && t < r; }
ll gcd(ll i, ll j) { return j ? gcd(j, i % j) : i; }
ll popcount(ll x) {
    int sum = 0; for (int i = 0; i < 60; i++)if ((1ll << i) & x) sum++;
    return sum;
}
template<typename T>
class csum {
    vec<T> v;
public:
    csum(vec<T>& a) :v(a) { build(); }
    csum() {}
    void init(vec<T>& a) { v = a; build(); }
    void build() {
        for (int i = 1; i < v.size(); i++) v[i] += v[i - 1];
    }
    //[l,r]
    T a(int l, int r) {
        if (r < l) return 0;
        return v[r] - (l == 0 ? 0 : v[l - 1]);
    }
    //[l,r)
    T b(int l, int r) {
        return a(l, r - 1);
    }
    T a(pair<int, int>t) {
        return a(t.first, t.second);
    }
    T b(pair<int, int>t) {
        return b(t.first, t.second);
    }
};
class mint {
public:ll v;
      mint(ll v = 0) { s(v % mod + mod); }
      constexpr static int mod = Mod;// (ll)1e9 + 7;
      constexpr static int fn_ = (ll)2e6 + 5;
      static mint fact[fn_], comp[fn_];
      mint pow(int x) const {
          mint b(v), c(1);
          while (x) {
              if (x & 1) c *= b;
              b *= b;
              x >>= 1;
          }
          return c;
      }
      inline mint& s(int vv) {
          v = vv < mod ? vv : vv - mod;
          return *this;
      }
      inline mint inv()const { return pow(mod - 2); }
      inline mint operator-()const { return mint() - *this; }
      inline mint& operator+=(const mint b) { return s(v + b.v); }
      inline mint& operator-=(const mint b) { return s(v + mod - b.v); }
      inline mint& operator*=(const mint b) { v = v * b.v % mod; return *this; }
      inline mint& operator/=(const mint b) { v = v * b.inv().v % mod; return *this; }
      inline mint operator+(const mint b) const { return mint(v) += b; }
      inline mint operator-(const mint b) const { return mint(v) -= b; }
      inline mint operator*(const mint b) const { return mint(v) *= b; }
      inline mint operator/(const mint b) const { return mint(v) /= b; }
      friend ostream& operator<<(ostream& os, const mint& m) {
          return os << m.v;
      }
      friend istream& operator>>(istream& is, mint& m) {
          int x; is >> x; m = mint(x);
          return is;
      }
      bool operator<(const mint& r)const { return v < r.v; }
      bool operator>(const mint& r)const { return v > r.v; }
      bool operator<=(const mint& r)const { return v <= r.v; }
      bool operator>=(const mint& r)const { return v >= r.v; }
      bool operator==(const mint& r)const { return v == r.v; }
      bool operator!=(const mint& r)const { return v != r.v; }
      explicit operator bool()const { return v; }
      explicit operator int()const { return v; }
      mint comb(mint k) {
          if (k > * this) return mint();
          if (!fact[0]) combinit();
          if (v >= fn_) {
              if (k > * this - k) k = *this - k;
              mint tmp(1);
              for (int i = v; i >= v - k.v + 1; i--) tmp *= mint(i);
              return tmp * comp[k.v];
          }
          return fact[v] * comp[k.v] * comp[v - k.v];
      }//nCk
      mint perm(mint k) {
          if (k > * this) return mint();
          if (!fact[0]) combinit();
          if (v >= fn_) {
              mint tmp(1);
              for (int i = v; i >= v - k.v + 1; i--) tmp *= mint(i);
              return tmp;
          }
          return fact[v] * comp[v - k.v];
      }//nPk
      static void combinit() {
          fact[0] = 1;
          for (int i = 1; i < fn_; i++) fact[i] = fact[i - 1] * mint(i);
          comp[fn_ - 1] = fact[fn_ - 1].inv();
          for (int i = fn_ - 2; i >= 0; i--) comp[i] = comp[i + 1] * mint(i + 1);
      }
}; mint mint::fact[fn_], mint::comp[fn_];

//--------------------------------------------------------------
//--------------------------------------------------------------

template<class T>
class LazySegmentTree {
protected:
    using UPF = function<void(T&)>;
    using QRF = function<void(T&, const T)>;
    using F = function<bool(T a)>;
    int n, rr;
    vector<T>dat;
    T e;

    LazySegmentTree() {}
    LazySegmentTree(int size) { init(size); }
    LazySegmentTree(vector<T>& v) {
        init(v);
    }
    virtual ~LazySegmentTree() {}

    virtual void eval(T& par, T& a, T& b) = 0;
    virtual T proc(const T& a, const T& b) = 0;

public:
    void init(int size) {
        n = size, rr = 1;
        while (rr < n) rr <<= 1;
        dat.assign(2 * rr - 1, T());
        for (int i = rr - 2; i >= 0; i--)
            dat[i] = proc(dat[i * 2 + 1], dat[i * 2 + 2]);
    }
    void init(vector<T>& v) {
        n = v.size(), rr = 1;
        while (rr < n) rr <<= 1;
        dat.assign(2 * rr - 1, T());
        for (int i = 0; i < n; i++)
            dat[i + rr - 1] = v[i];
        for (int i = rr - 2; i >= 0; i--) {
            T k = proc(dat[i * 2 + 1], dat[i * 2 + 2]);
            dat[i] = k;
        }
    }
    //one point update
    void set(int at, T x) {
        update(0, at, at + 1, 0, rr, [x](T& a) {a = x; });
    }
    void upd(int a, int b, UPF func) {
        upd(0, a, b, 0, rr, func);
    }
    T qry(int a, int b) {
        return qry(0, a, b, 0, rr);
    }
    T get0() {
        return dat[0];
    }
    //func([a,i))==true, func([a,i+1))==false
    int lb(int a, int b, F func) {
        e = T();
        return lb(0, a, b, 0, rr, func, e);
    }
    //func([i,b))==true, func([i-1,b))==false
    int ub(int a, int b, F func) {
        e = T();
        return ub(0, a, b, 0, rr, func, e);
    }
private:
    void upd(int i, const int& a, const int& b, int l, int r, UPF& func) {
        if (b <= l || r <= a) return;
        if (a <= l && r <= b) {
            func(dat[i]);
            return;
        }

        eval(dat[i], dat[i * 2 + 1], dat[i * 2 + 2]);

        upd(i * 2 + 1, a, b, l, (l + r) / 2, func);
        upd(i * 2 + 2, a, b, (l + r) / 2, r, func);

        dat[i] = proc(dat[i * 2 + 1], dat[i * 2 + 2]);
    }
    T qry(int i, const int& a, const int& b, int l, int r) {
        if (b <= l || r <= a) return T();
        if (a <= l && r <= b) return dat[i];

        eval(dat[i], dat[i * 2 + 1], dat[i * 2 + 2]);

        return proc(qry(i * 2 + 1, a, b, l, (l + r) / 2),
            qry(i * 2 + 2, a, b, (l + r) / 2, r));
    }
    int lb(int i, int a, int b, int l, int r, F& func, T& wa) {
        if (b <= l || r <= a) return b;
        if (a <= l && r <= b) {
            if (func(proc(wa, dat[i]))) {
                wa = proc(wa, dat[i]);
                return b;
            }
            if (r - l == 1) return l;
        }
        eval(dat[i], dat[i * 2 + 1], dat[i * 2 + 2]);

        int tmp = lb(i * 2 + 1, a, b, l, (l + r) / 2, func, wa);
        if (tmp < b) return tmp;
        return lb(i * 2 + 2, a, b, (l + r) / 2, r, func, wa);
    }
    int ub(int i, int a, int b, int l, int r, F& func, T& wa) {
        if (b <= l || r <= a) return a;
        if (a <= l && r <= b) {
            if (func(proc(dat[i], wa))) {
                wa = proc(dat[i], wa);
                return a;
            }
            if (r - l == 1) return r;
        }
        eval(dat[i], dat[i * 2 + 1], dat[i * 2 + 2]);

        int tmp = ub(i * 2 + 2, a, b, (l + r) / 2, r, func, wa);
        if (tmp > a) return tmp;
        return ub(i * 2 + 1, a, b, l, (l + r) / 2, func, wa);
    }
};
template<class T>
class Segtree :public LazySegmentTree<T> {
    using Base = LazySegmentTree<T>;
public:
    Segtree() {}
    Segtree(int size) :Base(size) {}
    Segtree(vector<ll>& v) {
        init(v);
    }
    Segtree(vector<T>& v) { init(v); }
    void init(int size) {
        Base::init(size);
    }
    void init(vector<T>& v) {
        Base::init(v);
    }
    void update(int a, int b) {
        Base::upd(a, b, [](T& a) {
            a.inv = a.one * a.zero - a.inv;
            swap(a.zero, a.one);
            a.upd = !a.upd;
            });
    }
    ll query(int a, int b) {
        return Base::qry(a, b).inv;
    }
private:
    void eval(T& par, T& a, T& b)override {
        if (par.upd) {
            a.inv = a.one * a.zero - a.inv;
            swap(a.one, a.zero);
            b.inv = b.one * b.zero - b.inv;
            swap(b.one, b.zero);
            a.upd = !a.upd, b.upd = !b.upd;
        }
        par.upd = 0;
    }
    T proc(const T& a, const T& b)override {

        T k = T{ a.zero + b.zero ,a.one + b.one,a.inv + b.inv + a.one * b.zero,0 };
        return k;
    }
};
struct Monoid {
    ll zero, one, inv;bool upd;
    Monoid() :zero(0), one(0), inv(0), upd(0) {}
    Monoid(ll zero, ll one, ll inv,bool upd) :zero(zero), one(one), inv(inv), upd(upd) {}
};


signed main() {
    int n, q; n = read(); q = read();
    vec<Monoid> a;
    rep(i, n) {
        bool t; cin >> t;
        if (t) a.pb(Monoid{ 0,1,0,0 });
        else a.pb(Monoid{ 1,0,0,0 });
    }
    Segtree<Monoid> seg(a);
    rep(i, q) {
        int t, a, b; t = read(); a = read(); b = read();
        if (t == 1) {
            seg.update(a - 1, b);
        }
        else if (t == 2) {
            printf("%lld\n", seg.query(a - 1, b));
        }
    }
}