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:
# エラーチェックを入れるなど

class LazySegmentTree:

    __slots__ = ["n", "original_size", "log", "data", "lazy", "me", "oe", "fmm", "fmo", "foo"]

    def __init__(self, length_or_list, monoid_identity, operator_identity, func_monoid_monoid, func_monoid_operator, func_operator_operator):
        self.me = monoid_identity
        self.oe = operator_identity
        self.fmm = func_monoid_monoid
        self.fmo = func_monoid_operator
        self.foo = func_operator_operator

        if isinstance(length_or_list, int):
            self.original_size = length_or_list
            self.log = (self.original_size - 1).bit_length()
            self.n = 1 << self.log
            self.data = [self.me] * (self.n * 2)
            self.lazy = [self.oe] * (self.n * 2)
        elif isinstance(length_or_list, list):
            self.original_size = len(length_or_list)
            self.log = (self.original_size - 1).bit_length()
            self.n = 1 << self.log
            self.data = [self.me] * self.n + length_or_list + [self.me] * (self.n - self.original_size)
            for i in range(self.n-1, 0, -1):
                self.data[i] = self.fmm(self.data[2*i], self.data[2*i+1])
            self.lazy = [self.oe] * (self.n * 2)
        else:
            raise TypeError(f"The argument 'length_or_list' must be an integer or a list, not {type(length_or_list).__name__}")
            

    def replace(self, index, value):
        if index < -self.original_size or self.original_size <= index:
            raise IndexError("LazySegmentTree index out of range")
        if index < 0:
            index += self.original_size

        index += self.n

        # propagation
        for shift in range(self.log, 0, -1):
            i = index >> shift
            self.lazy[2*i]   = self.foo(self.lazy[2*i],   self.lazy[i])
            self.lazy[2*i+1] = self.foo(self.lazy[2*i+1], self.lazy[i])
            self.data[i] = self.fmo(self.data[i], self.lazy[i])
            self.lazy[i] = self.oe

        # update
        self.data[index] = value
        self.lazy[index] = self.oe

        # recalculation
        i = index
        while i > 1:
            i //= 2
            self.data[i] = self.fmm( self.fmo(self.data[2*i], self.lazy[2*i]), self.fmo(self.data[2*i+1], self.lazy[2*i+1]) )
            self.lazy[i] = self.oe

    def __getitem__(self, index):
        if index < -self.original_size or self.original_size <= index:
            raise IndexError("LazySegmentTree index out of range")
        if index < 0:
            index += self.original_size

        index += self.n

        # propagation
        for shift in range(self.log, 0, -1):
            i = index >> shift
            self.lazy[2*i]   = self.foo(self.lazy[2*i],   self.lazy[i])
            self.lazy[2*i+1] = self.foo(self.lazy[2*i+1], self.lazy[i])
            self.data[i] = self.fmo(self.data[i], self.lazy[i])
            self.lazy[i] = self.oe

        # self.data[index] = self.fmo(self.data[index], self.lazy[index])
        # self.lazy[index] = self.oe

        return self.data[index]

    def effect(self, l, r, operator):
        if l < 0:
            l += self.original_size
        if r < 0:
            r += self.original_size
        if not 0 <= l < r <= self.original_size:
            raise IndexError("LazySegmentTree index out of range")

        l += self.n
        r += self.n
        
        # preparing indices 
        indices = []
        l0 = l
        r0 = r - 1
        while l0 % 2 == 0:
            l0 //= 2
        while r0 % 2 == 1:
            r0 //= 2
        l0 //= 2
        r0 //= 2
        while r0 > l0:
            indices.append(r0)
            r0 //= 2
        while l0 > r0:
            indices.append(l0)
            l0 //= 2
        while l0 and l0 != r0:
            indices.append(r0)
            r0 //= 2
            indices.append(l0)
            l0 //= 2
        while r0:
            indices.append(r0)
            r0 //= 2

        # propagation
        for i in reversed(indices):
            self.lazy[2*i]   = self.foo(self.lazy[2*i],   self.lazy[i])
            self.lazy[2*i+1] = self.foo(self.lazy[2*i+1], self.lazy[i])
            self.data[i] = self.fmo(self.data[i], self.lazy[i])
            self.lazy[i] = self.oe

        # effect
        while l < r:
            if l % 2:
                self.lazy[l] = self.foo(self.lazy[l], operator)
                l += 1
            if r % 2:
                r -= 1
                self.lazy[r] = self.foo(self.lazy[r], operator)
            l //= 2
            r //= 2

        # recalculation
        for i in indices:
            self.data[i] = self.fmm( self.fmo(self.data[2*i], self.lazy[2*i]), self.fmo(self.data[2*i+1], self.lazy[2*i+1]) )
            self.lazy[i] = self.oe
            
        
    def folded(self, l, r):
        if l < 0:
            l += self.original_size
        if r < 0:
            r += self.original_size
        if not 0 <= l < r <= self.original_size:
            raise IndexError("LazySegmentTree index out of range")

        l += self.n
        r += self.n

        # preparing indices 
        indices = []
        l0 = l
        r0 = r - 1
        while l0 % 2 == 0:
            l0 //= 2
        while r0 % 2 == 1:
            r0 //= 2
        l0 //= 2
        r0 //= 2
        while r0 > l0:
            indices.append(r0)
            r0 //= 2
        while l0 > r0:
            indices.append(l0)
            l0 //= 2
        while l0 and l0 != r0:
            indices.append(r0)
            r0 //= 2
            indices.append(l0)
            l0 //= 2
        while r0:
            indices.append(r0)
            r0 //= 2

        # propagation
        for i in reversed(indices):
            self.lazy[2*i]   = self.foo(self.lazy[2*i],   self.lazy[i])
            self.lazy[2*i+1] = self.foo(self.lazy[2*i+1], self.lazy[i])
            self.data[i] = self.fmo(self.data[i], self.lazy[i])
            self.lazy[i] = self.oe

        # fold
        left_folded = self.me
        right_folded = self.me
        while l < r:
            if l % 2:
                left_folded = self.fmm(left_folded, self.fmo(self.data[l], self.lazy[l]))
                l += 1
            if r % 2:
                r -= 1
                right_folded = self.fmm(self.fmo(self.data[r], self.lazy[r]), right_folded)
            l //= 2
            r //= 2
        return self.fmm(left_folded, right_folded)



def atc2():
    # Monoid:   ((0の数), (1の数), (転倒数))
    # Operator: 反転するか? (1 or 0) 

    import sys
    input = sys.stdin.buffer.readline

    N, Q = map(int, input().split())
    monoid_data = [(0, 1, 0) if A == b'1' else (1, 0, 0) for A in input().split()]

    def fmm(m1, m2):
        return (m1[0] + m2[0], m1[1] + m2[1], m1[2] + m2[2] + m1[1] * m2[0])

    def fmo(m1, o1):
        if o1:
            return (m1[1], m1[0], m1[0] * m1[1] - m1[2])
        else:
            return m1 

    def foo(o1, o2):
        return o1 ^ o2

    lst = LazySegmentTree(monoid_data, (0, 0, 0), 0, fmm, fmo, foo)
    ans = []
    for _ in range(Q):
        T, L, R = map(int, input().split())
        if T == 1:
            lst.effect(L-1, R, 1)
        else:
            ans.append(lst.folded(L-1, R)[2])
    print('\n'.join(map(str, ans)))

if __name__ == "__main__":
    atc2()