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>
#define rep(i,n) for(int i=0;i<(int)(n);i++)
using namespace std;
using ll = long long ;
using P = pair<int,int> ;
using pll = pair<long long,long long>;
constexpr int INF = 1e9;
constexpr long long LINF = 1e17;
constexpr int MOD = 1000000007;
constexpr double PI = 3.14159265358979323846;

template<typename Mono,typename Ope>
struct LazySegmentTree{
    using F = function<Mono(Mono,Mono)>;
    using G = function<Mono(Mono,Ope)>;
    using H = function<Ope(Ope,Ope)>;
    int n,height;
    F f; G g; H h; Mono tu; Ope eu;
    vector<Mono> node;
    vector<Ope> lazy;

    LazySegmentTree(F f,G g,H h,Mono tu,Ope eu):f(f),g(g),h(h),tu(tu),eu(eu){}

    void init(vector<Mono> v){
        int n_ = (int)(v.size());
        n = 1;height = 0;
        while(n < n_) n <<= 1,++ height;
        node.assign(2*n,tu);
        lazy.assign(2*n,eu);
        for(int i=0;i<n_;i++) node[i+n] = v[i];
        for(int i=n-1;i>0;i--) node[i] = f(node[i<<1],node[i<<1|1]);
    }

    Mono eval(int k){
        return (lazy[k]==eu)?node[k]:g(node[k],lazy[k]);
    }

    void prop(int k){
        if(lazy[k]==eu) return;
        lazy[k<<1] = h(lazy[k<<1],lazy[k]);
        lazy[k<<1|1] = h(lazy[k<<1|1],lazy[k]);
        node[k] = eval(k);
        lazy[k] = eu;
    }

    void prop_above(int k){
        for(int i=height;i>0;i--) prop(k>>i);
    }

    void recalc_above(int k){
        while(k>0){
            k >>= 1;
            node[k] = f(eval(k<<1),eval(k<<1|1));
        }
    }

    void set_val(int k,Mono x){
        k += n;
        prop_above(k);
        node[k] = x;
        lazy[k] = eu;
        recalc_above(k);
    }

    void update(int l,int r,Ope x){
        if(l >= r) return;
        l += n;r += n-1;
        prop_above(l);
        prop_above(r);
        int a = l,b = r;
        ++ r;
        while(l < r){
            if(l&1) lazy[l] = h(lazy[l],x), ++l;
            if(r&1) --r, lazy[r] = h(lazy[r],x);
            l >>= 1;r >>= 1;
        }
        recalc_above(a);
        recalc_above(b);
    }

    Mono query(int l,int r){
        if(l >= r) return tu;
        l += n;r += n-1;
        prop_above(l);
        prop_above(r);++r;
        Mono vl = tu,vr = tu;
        while(l < r){
            if(l&1) vl = f(vl,eval(l)), ++l;
            if(r&1) --r, vr = f(eval(r),vr);
            l >>= 1;r >>= 1;
        }
        return f(vl,vr);
    }
};

struct m{
    ll one,zero,inv;
};

int main(){
    auto f = [](m l,m r){
        return m{l.one+r.one,l.zero+r.zero,l.inv+r.inv+l.one*r.zero};
    };
    auto g = [](m l,bool b){
        if(b%2==1) return m{l.zero,l.one,l.one*l.zero-l.inv};
        else return l;
    };
    auto h = [](bool l,bool r){
        return (l^r);
    };
    LazySegmentTree<m,bool> seg(f,g,h,{0,0,0},false);

 

    int n,q;
    cin >> n >> q;
    vector<m> a(n);
    rep(i,n){
        int t;
        cin >> t;
        a[i].one = (t==1?1:0);
        a[i].zero = (t==0?1:0);
        a[i].inv = 0;
    }
    seg.init(a);

    while(q--){
        int t,l,r;
        cin >> t >> l >> r;
        if(t==1){
            --l;
            seg.update(l,r,true);
        }else{
            --l;
            cout << seg.query(l,r).inv << endl;
        }
    }

    return 0;
}