Counting Rectangles in a 2D Plane

You are given n points in a 2D plane. Your task is to count the number of distinct rectangles that can be formed such that each rectangle's four corners belong to the given points. In this problem, a rectangle is defined as a quadrilateral whose sides are parallel to the coordinate axes. That is, a rectangle is formed by the points \((x_1, y_1)\), \((x_1, y_2)\), \((x_2, y_1)\) and \((x_2, y_2)\) where \(x_1 \neq x_2\) and \(y_1 \neq y_2\).

Input is given via standard input (stdin) and output should be written to standard output (stdout).

Examples:

• If there are no points, the answer is 0.
• If there are only 3 points such as (0, 0), (1, 0) and (0, 1), no rectangle can be formed.
• If the points are (0, 0), (0, 1), (1, 0) and (1, 1), there is exactly 1 rectangle.

inputFormat

The first line of input contains an integer n representing the number of points.

The following n lines each contain two space-separated integers, representing the x and y coordinates of a point.

\(\textbf{Constraints}:\)

• \(0 \leq n \leq 10^5\)
• The coordinates will be integers and may be negative.

outputFormat

Output a single integer, representing the number of rectangles that can be formed using the given points.

## sample

0

0

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