On a Cartesian plane, there are (n) distinct points painted black, while all other points are painted white. Each black point has integer coordinates. There is also a robot that can move one unit in any of the directions ' U ' (up), ' D ' (down), ' L ' (left), or ' R ' (right) with a single command. A path of the robot from point (p_{1}) to point (p_{2}) is a sequence of commands such that if the robot, starting at point (p_{1}), executes this sequence, it will arrive at point (p_{2}). The shortest path of the robot from point (p_{1}) to point (p_{2}) is a path whose sequence consists of the minimum possible number of commands. You need to count the number of pairs of points (p_i), (p_j) ((i \neq j)) such that for this pair of points the following condition holds: All points with integer coordinates on any shortest path of the robot from point (p_{i}) to point (p_{j}) are painted black. Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 10^4)). The description of the test cases follows. The first line of each test case contains a single integer (n) ((1 \le n \le 5 \cdot 10^{5})) — the number of points painted black. The next (n) lines of each test case contain two integers (x_{i}, y_{i}) ((-10^{9} \le x_{i}, y_{i} \le 10^{9})) — the coordinates of point (p_{i}). All points are pairwise distinct. It is guaranteed that the sum of (n) across all test cases does not exceed (5 \cdot 10^{5}). For each test case, output a single integer — the answer to the problem. In the first test case, there are (16) suitable pairs of points: (p_{1}, p_{2}) (p_{1}, p_{3}) (p_{1}, p_{4}) (p_{1}, p_{5}) (p_{2}, p_{1}) (p_{2}, p_{3}) (p_{2}, p_{4}) (p_{2}, p_{5}) (p_{3}, p_{1}) (p_{3}, p_{2}) (p_{3}, p_{4}) (p_{4}, p_{1}) (p_{4}, p_{2}) (p_{4}, p_{3}) (p_{5}, p_{1}) $$$p_{5},