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:
//
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//
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//                                 ....gH@@@@HHB""""7"YYYYHMMMMMMM@@@@@@@Hma,.   
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//                        ..JH@@HY"~                                          _TW@@@Mme.    
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//                  .Jg@@MY!                                                          ?T@@@h,.   
//                .-@@@B!                                                                (TM@@@L     
//              .(H@MY                                                                      ?W@@@+    
//             .W@@@                                                                          .T@@@[       
//           .d@@M!                                                                             .T@@N,   
//          .d@M@'                                                                                -W@@o. 
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//        -d@M%                    ..,                                      ..,                      j@@b  
//       d@@M=                     TM9                                      ?MD                       W@@[ 
//      .H@M:                                                                                         .W@H,
//      H@Ht                                                                                           ,@@#   
//     (@@M~                                                                                           .@@h.
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//    ,@@@L.                                 ?H@Ng&+gd@@#H@@NHaJ+gH@[                                  J@@@] 
//     X@@@[            ......                 ?"YYYYY""   ?"YHHHB"^                 .....            (@@@#   
//      WH@N+.      .W@@@@MHB=                                                      .TWH@M@Hmc       .H@@M~    
//     .H@@@@N,      _!~                                                                            .d@@@N,   
//   .J@@#T@@@N,                                                                                  .d@@@@@@@b. 
//  (@@@@! .T@@@n,                                                                              .(H@@@H>.W@@@x  
// (@@@F      4@@@@MaJ.                                                                       .d@@@@Y77   4@@@r 
//.H@@P         ?TM@@@@N...                                                               .-JH@HMY=        d@@N,
//(@@@F             ?"WM@@@MQa-,.                                                  .(J(JN@@M#"             Z@@@L
// d@@H,                 (M@@@@@@@Ng&maJ....                           .. ...J.J+W@@@@@@HY!               .dH@b 
// ?M@@@N&.        ..(JW@@@MM"?7""TYHMH@@HH@@@@@HHHgkHagHa(mggdmmagH@H@@Q@@HMMMHY"7!TMM@@@HaJ,.        ..H@@@M^ 
//   ?"W@@@@MN@@@@@H@@MMY"                  _???!"= ?WMMBYYTMH=7""Y@""?"~^             _"YM@@@@@@@@MH@@@@@#"^ 
//       ?77WMMMYB""!                                                                        _7"WWMMMY"7=     

// need
#include <iostream>
#include <algorithm>
// data structure
#include <bitset>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <utility>
#include <vector>
#include <complex>
//#include <deque>
#include <valarray>
#include <unordered_map>
#include <unordered_set>
#include <array>
// etc
#include <cassert>
#include <cmath>
#include <functional>
#include <iomanip>
#include <chrono>
#include <random>
#include <numeric>
#include <fstream>

//std::ifstream ifs("b.in");
//auto& scan_in = ifs;
auto& scan_in = std::cin;

// input
#define INIT std::ios::sync_with_stdio(false);std::cin.tie(0);
#define VAR(type, ...)type __VA_ARGS__;MACRO_VAR_Scan(__VA_ARGS__);
template<typename T> void MACRO_VAR_Scan(T& t) { scan_in >> t; }
template<typename First, typename...Rest>void MACRO_VAR_Scan(First& first, Rest& ...rest) { scan_in >> first; MACRO_VAR_Scan(rest...); }
#define VEC_ROW(type, n, ...)std::vector<type> __VA_ARGS__;MACRO_VEC_ROW_Init(n, __VA_ARGS__); for(int w_=0; w_<n; ++w_){MACRO_VEC_ROW_Scan(w_, __VA_ARGS__);}
template<typename T> void MACRO_VEC_ROW_Init(int n, T& t) { t.resize(n); }
template<typename First, typename...Rest>void MACRO_VEC_ROW_Init(int n, First& first, Rest& ...rest) { first.resize(n); MACRO_VEC_ROW_Init(n, rest...); }
template<typename T> void MACRO_VEC_ROW_Scan(int p, T& t) { scan_in >> t[p]; }
template<typename First, typename...Rest>void MACRO_VEC_ROW_Scan(int p, First& first, Rest& ...rest) { scan_in >> first[p]; MACRO_VEC_ROW_Scan(p, rest...); }
#define VEC(type, c, n) std::vector<type> c(n);for(auto& i:c)scan_in>>i;
#define MAT(type, c, m, n) std::vector<std::vector<type>> c(m, std::vector<type>(n));for(auto& R:c)for(auto& w:R)scan_in>>w;
// output
template<typename T>void MACRO_OUT(const T t) { std::cout << t; }
template<typename First, typename...Rest>void MACRO_OUT(const First first, const Rest...rest) { std::cout << first << " "; MACRO_OUT(rest...); }
#define OUT(...) MACRO_OUT(__VA_ARGS__);
#define FOUT(n, dist) std::cout<<std::fixed<<std::setprecision(n)<<(dist);
#define SOUT(n, c, dist) std::cout<<std::setw(n)<<std::setfill(c)<<(dist);
#define VOUT(v) for(size_t i = 0; i < v.size(); ++i) {OUT(v[i]);if(i+1<v.size()){SP}}
#define EOUT(...) do{ OUT(__VA_ARGS__)BR; exit(0); }while(0);
#define SP std::cout<<" ";
#define TAB std::cout<<"\t";
#define BR std::cout<<"\n";
#define SPBR(w, n) std::cout<<(w + 1 == n ? '\n' : ' ');
#define ENDL std::cout<<std::endl;
#define FLUSH std::cout<<std::flush;
#define SHOW(dist) {std::cerr << #dist << "\t: " << (dist) << "\n";}
// utility
#define ALL(a) (a).begin(),(a).end()
#define FOR(w, a, n) for(int w=(a);w<(n);++w)
#define REP(w, n) FOR(w, 0, n)
#define RFOR(w, a, n) for(int w=(n)-1;w>=(a);--w)
#define RREP(w, n) RFOR(w, 0, n)
template<class S, class T, class U> bool IN(S a, T x, U b) { return a <= x && x < b; }
template<class T> inline T CHMAX(T& a, const T b) { return a = (a < b) ? b : a; }
template<class T> inline T CHMIN(T& a, const T b) { return a = (a > b) ? b : a; }
// test
template<class T> using V = std::vector<T>;
template<class T> using VV = V<V<T>>;

template<typename S, typename T>
std::ostream& operator<<(std::ostream& os, const std::pair<S, T>& p) {
	os << "(" << p.first << ", " << p.second << ")"; return os;
}
template<typename T>
std::ostream& operator<<(std::ostream& os, const std::vector<T>& v) {
	os << "{";
	for (size_t i = 0; i < v.size(); ++i) os << v[i] << ((i + 1 < v.size()) ? ", " : ""); os << "}";
	return os;
}
template<typename T>
std::ostream & operator<<(std::ostream & os, const std::set<T> & v) {
	os << "{";
	for (auto it = v.cbegin();;) {
		os << *it; ++it;
		if (it == v.cend()) { os << "}"; break; }
		else { os << ", "; }
	}
	return os;
}
template<typename S, typename T>
std::ostream& operator<<(std::ostream & os, const std::map<S, T> & m) {
	os << "{";
	for (auto it = m.cbegin(); it != m.cend();) { os << it->first << ":" << it->second; ++it; os << (it == m.cend() ? "" : ", "); } os << "}";
	return os;
}
template<typename T>
std::ostream& operator<<(std::ostream & os, std::queue<T> q) {
	os << "<";
	while (!q.empty()) { os << q.front(); q.pop(); os << (q.empty() ? "<" : ", "); }
	return os;
}
template<typename T>
std::ostream& operator<<(std::ostream & os, std::stack<T> q) {
	os << ">";
	while (!q.empty()) { os << q.top(); q.pop(); os << (q.empty() ? "]" : ", "); }
	return os;
}
namespace std {
	template<typename S, typename T> class numeric_limits<pair<S, T>> {
	public:
		static constexpr pair<S, T> max() noexcept { return { numeric_limits<S>::max(), numeric_limits<T>::max() }; }
		static constexpr pair<S, T> lowest() noexcept { return { numeric_limits<S>::lowest(), numeric_limits<T>::lowest() }; }
	};
}

// type/const
using i64 = std::int_fast64_t;
using u64 = std::uint_fast64_t;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using PAIR = std::pair<i64, i64>;
using PAIRLL = std::pair<ll, ll>;
constexpr int INFINT = (1 << 30) - 1;                    // 1.07x10^ 9
constexpr int INFINT_LIM = (1LL << 31) - 1;              // 2.15x10^ 9
constexpr ll INFLL = 1LL << 60;                          // 1.15x10^18
constexpr ll INFLL_LIM = (1LL << 62) - 1 + (1LL << 62);  // 9.22x10^18
constexpr double EPS = 1e-6;
constexpr i64 MOD = 998244353;
constexpr double PI = 3.141592653589793238462643383279;
template<class T, size_t N> void FILL(T(&a)[N], const T & val) { for (auto& x : a) x = val; }
template<class ARY, size_t N, size_t M, class T> void FILL(ARY(&a)[N][M], const T & val) { for (auto& b : a) FILL(b, val); }
template<class T> void FILL(std::vector<T> & a, const T & val) { for (auto& x : a) x = val; }
template<class ARY, class T> void FILL(std::vector<std::vector<ARY>> & a, const T & val) { for (auto& b : a) FILL(b, val); }
// ------------>8---------

// ------------>8---------- LazySegmentTree ---------->8------------
namespace MonoidOfValue {
	template <class T> class sum {
	public:
		using value_type = T;
		inline static T op(const T& a, const T& b) { return a + b; }
		inline static value_type id() { return T(0); }
	};
	template <class T> class max {
	public:
		using value_type = T;
		inline static T op(const T& a, const T& b) { return (a < b) ? b : a; }
		inline static T id() { return std::numeric_limits<T>::lowest(); }
	};
	template <class T> class min {
	public:
		using value_type = T;
		inline static T op(const T& a, const T& b) { return (a < b) ? a : b; }
		inline static T id() { return std::numeric_limits<T>::max(); }
	};

	class X {
	public:
		struct T { i64 v; int n0, n1; };
		using value_type = T;
		inline static T op(const T& l, const T& r) { return T{ l.v + r.v + (i64)l.n1 * r.n0, l.n0 + r.n0, l.n1 + r.n1 }; }
		inline static T id() { return T{ 0, 0, 0 }; }
	};
}
namespace MonoidOfOperator {
	template <class T> class add {
	public:
		using value_type = T;
		inline static T op(const T& a, const T& b) { return a + b; }
		inline static T id() { return T(0); }
	};
	template <class T> class upd {
	public:
		using value_type = T;
		inline static T op(const T& a, const T& b) { return b; }
		inline static T id() { return T(0); }
	};

	class X {
	public:
		using T = bool;
		using value_type = T;
		inline static T op(const T& a, const T& b) { return a ^ b; }
		inline static T id() { return T{ false }; }
	};
}
namespace ApplyOperator {
	template <class T1, class T2> class RSQRAQ {
	public:
		inline static T1 op(const T1& a, const T2& b, int w) { return a + b * w; }
	};
	template <class T1, class T2> class RSQRUQ {
	public:
		inline static T1 op(const T1& a, const T2& b, int w) { return b * w; }
	};
	template <class T1, class T2> class RMQRAQ {
	public:
		inline static T1 op(const T1& a, const T2& b, int w) { return a + b; }
	};
	template <class T1, class T2> class RMQRUQ {
	public:
		inline static T1 op(const T1& a, const T2& b, int w) { return b; }
	};

	template <class T1, class T2> class X {
	public:
		inline static T1 op(const T1& a, const T2& b, int w) {
			if (!b) return a;
			return T1{ (i64)a.n0 * a.n1 - a.v , a.n1, a.n0 };
		}
	};
}
template<class MonoidOfValue, class MonoidOfOperator, template<class, class> class ApplyOperator>
class LazySegmentTree {
private:
	using ValueType = typename MonoidOfValue::value_type;
	using OperatorType = typename MonoidOfOperator::value_type;
	using Applier = ApplyOperator<ValueType, OperatorType>;
	std::vector<ValueType> seg;
	std::vector<OperatorType> laz;
	std::vector<bool> isUpdated;
	int HEIGHT;
	int ARY_SIZE;

	void push(int k, int w) {
		if (!isUpdated[k]) {
			seg[k] = Applier::op(seg[k], laz[k], w);
			if (w > 1) {
				laz[(k << 1) + 0] = MonoidOfOperator::op(laz[(k << 1) + 0], laz[k]);
				laz[(k << 1) + 1] = MonoidOfOperator::op(laz[(k << 1) + 1], laz[k]);
				isUpdated[(k << 1) + 0] = false;
				isUpdated[(k << 1) + 1] = false;
			}
			isUpdated[k] = true;
			laz[k] = MonoidOfOperator::id();
		}
	}
	void update(int k, int w) {
		push(k, w);
		if (k < ARY_SIZE) {
			push((k << 1) + 0, w >> 1);
			push((k << 1) + 1, w >> 1);
			seg[k] = MonoidOfValue::op(seg[(k << 1) + 0], seg[(k << 1) + 1]);
		}
	}
public:
	LazySegmentTree(int n) {
		init(n);
	}
	LazySegmentTree(const std::vector<ValueType> & a) {
		init(a.size());
		std::copy(std::begin(a), std::end(a), std::begin(seg) + ARY_SIZE);
		for (int k = ARY_SIZE - 1; k > 0; --k) seg[k] = MonoidOfValue::op(seg[(k << 1) + 0], seg[(k << 1) + 1]);
	}
	void init(int n) {
		HEIGHT = 0;
		while ((1 << HEIGHT) < n) ++HEIGHT;
		ARY_SIZE = 1 << HEIGHT;
		seg.resize(ARY_SIZE << 1, MonoidOfValue::id());
		laz.resize(ARY_SIZE << 1, MonoidOfOperator::id());
		isUpdated.resize(ARY_SIZE << 1, true);
	}
	// ## update [l, r) with v
	void update(int l, int r, OperatorType v) {
		l += ARY_SIZE; r += ARY_SIZE;
		int L = l, R = r - 1;
		for (int i = HEIGHT; i >= 0; --i) push(L >> i, 1 << i), push(R >> i, 1 << i);
		while (l < r) {
			if (l & 1) laz[l] = MonoidOfOperator::op(laz[l], v), isUpdated[l] = false, ++l;
			if (r & 1) --r, laz[r] = MonoidOfOperator::op(laz[r], v), isUpdated[r] = false;
			l >>= 1; r >>= 1;
		}
		for (int i = 1; i <= HEIGHT; ++i) {
			push(L >> i, 1 << i), push(R >> i, 1 << i);
			update(L >> i, 1 << i), update(R >> i, 1 << i);
		}
	}
	// ## return SUM/MAX/MIN in [l, r)
	ValueType query(int l, int r) {
		l += ARY_SIZE; r += ARY_SIZE - 1;
		for (int i = HEIGHT; i >= 0; --i) push(l >> i, 1 << i), push(r >> i, 1 << i);
		++r;
		ValueType vl = MonoidOfValue::id(), vr = MonoidOfValue::id();
		int w = 1;
		while (l < r) {
			if (l & 1) update(l, w), vl = MonoidOfValue::op(vl, seg[l]), ++l;
			if (r & 1) --r, update(r, w), vr = MonoidOfValue::op(seg[r], vr);
			l >>= 1; r >>= 1; w <<= 1;
		}
		return MonoidOfValue::op(vl, vr);
	}
};
// ------------>8---------- LazySegmentTree ---------->8------------

signed main() {
	INIT;

	VAR(int, n, Q);
	VEC(int, a, n);

	V<MonoidOfValue::X::value_type> tmp(n);
	REP(i, n) {
		if (a[i] == 0) tmp[i].n0 = 1;
		if (a[i] == 1) tmp[i].n1 = 1;
	}
	LazySegmentTree<MonoidOfValue::X, MonoidOfOperator::X, ApplyOperator::X> lst(tmp);
	REP(_, Q) {
		VAR(int, t, l, r); --l;
		if (t == 1) lst.update(l, r, true);
		else { OUT(lst.query(l, r).v)BR; }
	}

	return 0;
}