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template <class T>struct vector3{	T x, y, z;	vector3(): x(), y(), z() {}	vector3(T _x, T _y, T _z): x(_x), y(_y), z(_z) {}	vector3<T> operator+(vector3<T> rhs)		{ return vector3<T>(x + rhs.x, y + rhs.y, z + rhs.z); }	vector3<T> operator-(vector3<T> rhs)		{ return vector3<T>(x - rhs.x, y - rhs.y, z - rhs.z); }};template <class T>bool intersect(vector3<T> pa1, vector3<T> pa2, vector3<T> pb1, vector3<T> pb2){	vector3<T> va = pa2 - pa1, vb = pb2 - pb1, vc = pb1 - pa1;	T _aybx = va.y * vb.x, _aycx = va.y * vc.x, _bycx = vb.y * vc.x,	  _axcy = va.x * vc.y, _bxcy = vb.x * vc.y;	T det = va.z * (_bycx - _bxcy - vb.y * vb.y) + vb.z * (_axcy - _aycx) + vc.z * _aybx;	if (det > T(1e-8) || det < T(-1e-8)) throw std::domain_error("pa1-pa2 and pb1-pb2 is not in same plane");	T _denom = T(1) / (_aybx - _axby);	T ta = (_bxcy - _bycx) * _denom, tb = (_aycx - _axcy) * _denom;	return (T(0) <= ta && ta <= T(1) && T(0) <= tb && tb = T(1));}