Given a convex polygon with $n$ vertices on a grid. Let $S$ be the set of grid points inside and on the boundary of this convex polygon. Find the number of ways to choose four distinct, unordered points $(x, y, z, w)$ from $S$ such that $x, y, z, w$ form a square.

Input

The first line contains an integer $n$.

The next $n$ lines each contain two non-negative integers $(x_i, y_i)$, representing the vertices of the convex polygon on the grid in clockwise order.

Output

Output a single integer representing the number of ways to choose four distinct, unordered points $(x, y, z, w)$ such that they form a square.

Examples

Input 1

5
0 0
0 2
1 2
2 1
2 0

Output 1

4

Input 2

3
0 0
0 100
100 0

Output 2

1473186

Input 3

4
0 100
100 200
200 100
100 0

Output 3

34001650

Subtasks

Subtask 1 ($10\%$): The input is a rectangle, and the first point is the bottom-left corner (the point with the minimum $x$ and $y$ coordinates).

Subtask 2 ($25\%$): The input is a right-angled triangle, the right angle is at the bottom-left, and the first point is the bottom-left corner (the point with the minimum $x$ and $y$ coordinates).

Subtask 3 ($15\%$): $n \le 8, 0 \le x_i, y_i \le 10$

Subtask 4 ($20\%$): $n \le 8, 0 \le x_i, y_i \le 300$

Subtask 5 ($15\%$): $n \le 8, 0 \le x_i, y_i \le 800$

Subtask 6 ($15\%$): $n \le 8, 0 \le x_i, y_i \le 2000$