Geometry

struct point
{
	int x, y, idx;
};

//Finds squared euclidean distance between two points
int dist(point &a, point &b)
{
	return (a.x-b.x)*(a.x-b.x) + (a.y-b.y)*(a.y-b.y);
}

//Checks if angle ABC is a right angle
int isOrthogonal(point &a, point &b, point &c)
{
	return (b.x-a.x) * (b.x-c.x) + (b.y-a.y) * (b.y-c.y) == 0;
}

//Checks if ABCD form a rectangle (in that order)
int isRectangle(point &a, point &b, point &c, point &d)
{
	return isOrthogonal(a, b, c) && isOrthogonal(b, c, d) && isOrthogonal(c, d, a);
}

//Checks if ABCD form a rectangle, in any orientation
int isRectangleAnyOrder(point &a, point &b, point &c, point &d)
{
	return isRectangle(a, b, c, d) || isRectangle(b, c, a, d) | isRectangle(c, a, b, d);
}

//Checks if ABCD form a square (in that order)
int isSquare(point &a, point &b, point &c, point &d)
{
	return isRectangle(a, b, c, d) && dist(a, b) == dist(b, c);
}

//Checks if ABCD form a square, in any orientation
int isSquareAnyOrder(point &a, point &b, point &c, point &d)
{
	return isSquare(a, b, c, d) || isSquare(b, c, a, d) | isSquare(c, a, b, d);
}