Funni-chan loves watching stars. There are (n) stars in the sky, which can be regarded as points on a plane with Cartesian coordinates. The coordinates of the (i)-th star are ((x_i, y_i)). It is guaranteed that all (x_1, x_2, \ldots, x_n) are pairwise distinct, and all (y_1, y_2, \ldots, y_n) are pairwise distinct. The stars are numbered from (1) to (n) in the order they are given in the input. Funni-chan wants to connect some pairs of these stars to form a constellation. She defines the basic unit of a constellation as a triangle formed by three stars connected pairwise. A triangle is called harmonious if there exists an axis-aligned rectangle such that all three vertices of the triangle lie on the boundary of the rectangle. Funni-chan imposes the following constraints on the constellation: Every triangle in the constellation must be harmonious . The interiors of any two triangles in the constellation must be disjoint. Note that the boundary of a triangle is not considered part of its interior. Under these constraints, Funni-chan wants her constellation to contain the maximum possible number of triangles. Your task is to find this maximum number and construct a valid constellation that achieves it. Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 2\cdot 10^4)). The description of the test cases follows. The first line of each test case contains a single integer (n) ((3 \le n \le 2 \cdot 10^5)) — the number of stars. Each of the next (n) lines contains two integers (x_i) and (y_i) ((-10^9\le x_i, y_i \le 10^9)) — the coordinates of the (i)-th star. It is guaranteed that all (x_i)-s are pairwise distinct, and all (y_i)-s are pairwise distinct. It is guaranteed that the sum of (n) over all test cases does not exceed (2\cdot 10^5). In the first line of each test case, you should print a single integer (m) ($$$0\le m\le