// bitset standard header
#ifndef _BITSET_
#define _BITSET_
#include <istream>

#ifdef  _MSC_VER
#pragma pack(push,8)
#endif  /* _MSC_VER */
		// TEMPLATE CLASS bitset
_STD_BEGIN
template<size_t _N> class bitset {
	typedef unsigned long _Ty;
public:
	typedef bool element_type;
	class reference {
	friend class bitset<_N>;
	public:
		reference& operator=(bool _X)
			{_Pbs->set(_Off, _X);
			return (*this); }
		reference& operator=(const reference& _Bs)
			{_Pbs->set(_Off, bool(_Bs));
			return (*this); }
		reference& flip()
			{_Pbs->flip(_Off);
			return (*this); }
		bool operator~() const
			{return (!_Pbs->test(_Off)); }
		operator bool() const
			{return (_Pbs->test(_Off)); }
	private:
		reference(bitset<_N>& _X, size_t _P)
			: _Pbs(&_X), _Off(_P) {}
		bitset<_N> *_Pbs;
		size_t _Off;
		};
	_STCONS(size_t, bitset_size, _N);
	bool at(size_t _P) const
		{if (_N <= _P)
			_Xran();
		return (test(_P)); }
	reference at(size_t _P)
		{if (_N <= _P)
			_Xran();
		return (reference(*this, _P)); }
	bool operator[](size_t _P) const
		{return (test(_P)); }
	reference operator[](size_t _P)
		{return (reference(*this, _P)); }
	bitset()
		{_Tidy(); }
	bitset(unsigned long _X)
		{_Tidy();
		for (size_t _P = 0; _X != 0 && _P < _N; _X >>= 1, ++_P)
			if (_X & 1)
				set(_P); }
	explicit bitset(const string& _S, size_t _P = 0,
		size_t _L = (size_t)(-1))
		{size_t _I;
		if (_S.size() < _P)
			_Xran();
		if (_S.size() - _P < _L)
			_L = _S.size() - _P;
		if (_N < _L)
			_L = _N;
		_Tidy(), _P += _L;
		for (_I = 0; _I < _L; ++_I)
			if (_S[--_P] == '1')
				set(_I);
			else if (_S[_P] != '0')
				_Xinv(); }
	bitset<_N>& operator&=(const bitset<_N>& _R)
		{for (int _I = _Nw; 0 <= _I; --_I)
			_A[_I] &= _R._W(_I);
		return (*this); }
	bitset<_N>& operator|=(const bitset<_N>& _R)
		{for (int _I = _Nw; 0 <= _I; --_I)
			_A[_I] |= _R._W(_I);
		return (*this); }
	bitset<_N>& operator^=(const bitset<_N>& _R)
		{for (int _I = _Nw; 0 <= _I; --_I)
			_A[_I] ^= _R._W(_I);
		return (*this); }
	bitset<_N>& operator<<=(size_t _P)
		{if (_P < 0)
			return (*this >>= -_P);
		const int _D = _P / _Nb;
		if (_D != 0)
			for (int _I = _Nw; 0 <= _I; --_I)
				_A[_I] = _D <= _I ? _A[_I - _D] : 0;
		if ((_P %= _Nb) != 0)
			{for (int _I = _Nw; 0 < _I; --_I)
				_A[_I] = (_A[_I] << _P)
					| (_A[_I - 1] >> (_Nb - _P));
			_A[0] <<= _P, _Trim(); }
		return (*this); }
	bitset<_N>& operator>>=(size_t _P)
		{if (_P < 0)
			return (*this <<= -_P);
		const int _D = _P / _Nb;
		if (_D != 0)
			for (int _I = 0; _I <= _Nw; ++_I)
				_A[_I] = _D <= _Nw - _I ? _A[_I + _D] : 0;
		if ((_P %= _Nb) != 0)
			{for (int _I = 0; _I < _Nw; ++_I)
				_A[_I] = (_A[_I] >> _P)
					| (_A[_I + 1] << (_Nb - _P));
			_A[_Nw] >>= _P; }
		return (*this); }
	bitset<_N>& set()
		{_Tidy(~(_Ty)0);
		return (*this); }
	bitset<_N>& set(size_t _P, bool _X = true)
		{if (_N <= _P)
			_Xran();
		if (_X)
			_A[_P / _Nb] |= (_Ty)1 << _P % _Nb;
		else
			_A[_P / _Nb] &= ~((_Ty)1 << _P % _Nb);
		return (*this); }
	bitset<_N>& reset()
		{_Tidy();
		return (*this); }
	bitset<_N>& reset(size_t _P)
		{return (set(_P, 0)); }
	bitset<_N> operator~() const
		{return (bitset<_N>(*this).flip()); }
	bitset<_N>& flip()
		{for (int _I = _Nw; 0 <= _I; --_I)
			_A[_I] = ~_A[_I];
		_Trim();
		return (*this); }
	bitset<_N>& flip(size_t _P)
		{if (_N <= _P)
			_Xran();
		_A[_P / _Nb] ^= (_Ty)1 << _P % _Nb;
		return (*this); }
	unsigned long to_ulong() const
		{enum {_Assertion = 1 /
			(sizeof (unsigned long) % sizeof (_Ty) == 0)};
		int _I = _Nw;
		for (; sizeof (unsigned long) / sizeof (_Ty) <= _I; --_I)
			if (_A[_I] != 0)
				_Xoflo();
		unsigned long _V = _A[_I];
		for (; 0 <= --_I; )
			_V = _V << _Nb | _A[_I];
		return (_V); }
	string to_string() const
		{string _S;
		_S.reserve(_N);
		for (size_t _P = _N; 0 < _P; )
			_S += test(--_P) ? '1' : '0';
		return (_S); }
	size_t count() const
		{size_t _V = 0;
		for (int _I = _Nw; 0 <= _I; --_I)
			for (_Ty _X = _A[_I]; _X != 0; _X >>= 4)
				_V += "\0\1\1\2\1\2\2\3"
					"\1\2\2\3\2\3\3\4"[_X & 0xF];
		return (_V); }
	size_t size() const
		{return (_N); }
	bool operator==(const bitset<_N>& _R) const
		{for (int _I = _Nw; 0 <= _I; --_I)
			if (_A[_I] != _R._W(_I))
				return (false);
		return (true); }
	bool operator!=(const bitset<_N>& _R) const
		{return (!(*this == _R)); }
	bool test(size_t _P) const
		{if (_N <= _P)
			_Xran();
		return ((_A[_P / _Nb] & ((_Ty)1 << _P % _Nb)) != 0); }
	bool any() const
		{for (int _I = _Nw; 0 <= _I; --_I)
			if (_A[_I] != 0)
				return (true);
		return (false); }
	bool none() const
		{return (!any()); }
	bitset<_N> operator<<(size_t _R) const
		{return (bitset<_N>(*this) <<= _R); }
	bitset<_N> operator>>(size_t _R) const
		{return (bitset<_N>(*this) >>= _R); }
	friend bitset<_N> operator&(const bitset<_N>& _L,
		const bitset<_N>& _R)
		{return (bitset<_N>(_L) &= _R); }
	friend bitset<_N> operator|(const bitset<_N>& _L,
		const bitset<_N>& _R)
		{return (bitset<_N>(_L) |= _R); }
	friend bitset<_N> operator^(const bitset<_N>& _L,
		const bitset<_N>& _R)
		{return (bitset<_N>(_L) ^= _R); }
	friend ostream& operator<<(ostream& _O, const bitset<_N>& _R)
	{for (size_t _P = _N; 0 < _P; )
		_O << (_R.test(--_P) ? '1' : '0');
	return (_O); }
		// TEMPLATE operator>>
	friend istream& operator>>(istream& _I, bitset<_N>& _R)
	{ios_base::iostate _St = ios_base::goodbit;
	bool _Chg = false;
	string _X;
	const istream::sentry _Ok(_I);
	if (_Ok)
		{_TRY_IO_BEGIN
		int _C = _I.rdbuf()->sgetc();
		for (size_t _M = _R.size(); 0 < _M;
			_C = _I.rdbuf()->snextc(), --_M)
			{if (_C == EOF)
				{_St |= ios_base::eofbit;
				break; }
			else if (_C != '0' && _C != '1')
				break;
			else if (_X.max_size() <= _X.size())
				{_St |= ios_base::failbit;
				break; }
			else
				_X.append(1, (char)_C), _Chg = true; }
		_CATCH_IO_(_I); }
	if (!_Chg)
		_St |= ios_base::failbit;
	_I.setstate(_St);
	_R = bitset<_N>(_X);
	return (_I); }
	_Ty _W(size_t _I) const
		{return (_A[_I]); }
private:
	enum {_Nb = CHAR_BIT * sizeof (_Ty),
		_Nw = _N == 0 ? 0 : (_N - 1) / _Nb};
	void _Tidy(_Ty _X = 0)
		{for (int _I = _Nw; 0 <= _I; --_I)
			_A[_I] = _X;
		if (_X != 0)
			_Trim(); }
	void _Trim()
		{if (_N % _Nb != 0)
			_A[_Nw] &= ((_Ty)1 << _N % _Nb) - 1; }
	void _Xinv() const
		{_THROW(invalid_argument, "invalid bitset<N> char"); }
	void _Xoflo() const
		{_THROW(overflow_error,
			"bitset<N> conversion overflow"); }
	void _Xran() const
		{_THROW(out_of_range, "invalid bitset<N> position"); }
	_Ty _A[_Nw + 1];
	};
_STD_END
#ifdef  _MSC_VER
#pragma pack(pop)
#endif  /* _MSC_VER */

#endif /* _BITSET */

/*
 * Copyright (c) 1994 by P.J. Plauger.  ALL RIGHTS RESERVED. 
 * Consult your license regarding permissions and restrictions.
 */