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문제

Mirror, mirror, on the wall, which mirror symmetric subset of these points is the largest of them all?

The set $P$ consists of $N$ points. We say that a subset $S \subseteq P$ is \emph{mirror symmetric} if there exists a line $\ell$ such that for each point $p \in S$, the reflection of $p$ across $\ell$ is also in $S$.

Given the set $P$, what is the largest size of any mirror symmetric subset?

입력

The first line of the input contains $N$, the number of points. The next $N$ lines each consist of two integers $x_i, y_i$ ($-30\,000 \le x_i, y_i \le 30\,000$), the coordinates of each point.

There will be no duplicate points in the input.

출력

Output a single integer -- the largest size of a mirror symmetric subset.

제한

  • $1 \leq N \leq 1500$

예제 입력 1

7
2 4
5 5
5 4
4 2
3 0
0 3
0 1

예제 출력 1

5