13233번 - Celtic Symmetry 다국어

문제

After taking an Ancient Irish History class, Diarmuid has become interested in finding geometric patterns in neolithic tomb locations around Ireland. He carefully plots the locations of N tombs (2 ≤ N ≤ 1000), each one occupying a distinct point in the 2D plane, and he wonders how many different lines of symmetry exist for this set of points. A line of symmetry, of course, is a line across which the points on both sides are mirror images of each other.

Help Diarmuid answer this most pressing geometric question.

입력

First line: The number of tombs N.

The following N lines: Two integers x, y separated by a space indicating the position x and y of each tomb (-­10,000 ≤ x,y ≤ 10,000).

출력

The number of different lines of symmetry of the point set.

제한

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