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 PYTHON3):

Solution:
class LazySegmentTree():
    def __init__(self,n,init,merge,merge_unit,operate,merge_operate,operate_unit):
        self.merge=merge
        self.merge_unit=merge_unit
        self.operate=operate
        self.merge_operate=merge_operate
        self.operate_unit=operate_unit

        self.n=(n-1).bit_length()
        self.num = 1<<self.n
        self.data=[merge_unit for i in range(1<<(self.n+1))]
        self.lazy=[operate_unit for i in range(1<<(self.n+1))]
        if init:
            for i in range(n):
                self.data[2**self.n+i]=init[i]
            for i in range(2**self.n-1,0,-1):
                self.data[i]=self.merge(self.data[2*i],self.data[2*i+1])

    def propagate(self,v):
        ope = self.lazy[v]
        if ope == self.operate_unit:
            return
        self.lazy[v]=self.operate_unit
        self.data[2*v]=self.operate(self.data[2*v],ope)
        self.data[2*v+1]=self.operate(self.data[2*v+1],ope)
        self.lazy[2*v]=self.merge_operate(self.lazy[2*v],ope)
        self.lazy[2*v+1]=self.merge_operate(self.lazy[2*v+1],ope)

    def propagate_above(self,i):
        m=i.bit_length()-1
        for bit in range(m,0,-1):
            v=i>>bit
            self.propagate(v)

    def remerge_above(self,i):
        while i:
            i>>=1
            self.data[i]=self.operate(self.merge(self.data[2*i],self.data[2*i+1]),self.lazy[i])

    def update(self,l,r,x):
        l+=1<<self.n
        r+=1<<self.n
        l0=l//(l&-l)
        r0=r//(r&-r)-1
        while l<r:
            if l&1:
                self.data[l]=self.operate(self.data[l],x)
                self.lazy[l]=self.merge_operate(self.lazy[l],x)
                l+=1
            if r&1:
                self.data[r-1]=self.operate(self.data[r-1],x)
                self.lazy[r-1]=self.merge_operate(self.lazy[r-1],x)
            l>>=1
            r>>=1
        self.remerge_above(l0)
        self.remerge_above(r0)

    def query(self,l,r):
        l+=1<<self.n
        r+=1<<self.n
        l0=l//(l&-l)
        r0=r//(r&-r)-1
        self.propagate_above(l0)
        self.propagate_above(r0)
        res=self.merge_unit
        L = []
        R = []
        while l<r:
            if l&1:
                L.append(l)
                l+=1
            if r&1:
                R.append(r-1)
            l>>=1
            r>>=1

        if L and R and R[-1]==L[-1]:
            R.pop()
        R=R[::-1]
        m = L+R
        for idx in m:
            res = self.merge(res,self.data[idx])
        return res

    def bisect_l(self,l,r,x):
        l += 1<<self.n
        r += 1<<self.n
        l0=l//(l&-l)
        r0=r//(r&-r)-1
        self.propagate_above(l0)
        self.propagate_above(r0)
        Lmin = -1
        Rmin = -1
        while l<r:
            if l & 1:
                if self.data[l][0] <= x and Lmin==-1:
                    Lmin = l
                l += 1
            if r & 1:
                if self.data[r-1][0] <=x:
                    Rmin = r-1
            l >>= 1
            r >>= 1

        res = -1
        if Lmin != -1:
            pos = Lmin
            while pos<self.num:
                self.propagate(pos)
                if self.data[2 * pos][0] <=x:
                    pos = 2 * pos
                else:
                    pos = 2 * pos +1
            res =  pos-self.num
        if Rmin != -1:
            pos = Rmin
            while pos<self.num:
                self.propagate(pos)
                if self.data[2 * pos][0] <=x:
                    pos = 2 * pos
                else:
                    pos = 2 * pos +1
            if res==-1:
                res = pos-self.num
            else:
                res = min(res,pos-self.num)

        return res

import sys

input = sys.stdin.readline

merge = lambda x,y:(x[0]+y[0]+x[2]*y[1],x[1]+y[1],x[2]+y[2])
merge_unit = (0,0,0)

def operate(x,y):
    if y:
        return (x[1]*x[2]-x[0],x[2],x[1])
    else:
        return x

merge_operate = lambda x,y: (x+y)%2

operate_unit = 0

N,Q = map(int,input().split())
A = list(map(int,input().split()))

for i in range(N):
    if A[i]==0:
        A[i]=(0,1,0)
    else:
        A[i]=(0,0,1)

LST = LazySegmentTree(N,A,merge,merge_unit,operate,merge_operate,operate_unit)

for i in range(Q):
    t,l,r = map(int,input().split())
    l = l-1
    if t==1:
        LST.update(l,r,1)
    else:
        print(LST.query(l,r)[0])