Boundary
时间限制：C/C++/Rust/Pascal 1秒，其他语言2秒
空间限制：C/C++/Rust/Pascal 256 M，其他语言512 M
64bit IO Format: %lld

题目描述

Given points in 2D plane. Considering all circles that the origin point is on their boundries, find the one with the maximum given points on its boundry. Print the maximum number of points.

输入描述:

The first line contains one integer , denoting the number of given points.
Following  lines each contains two integers , denoting a given point .
It's guaranteed that the points are pairwise different and no given point is the origin point.

输出描述:

Only one line containing one integer, denoting the answer.
示例1

输入

复制 
4
1 1
0 2
2 0
2 2

输出

复制 
3

说明

Considering circle (x-1)^2+(y-1)^2=2, we can see that the origin point is on its boundry and that there are 3 given points {(0,2),(2,0),(2,2)} on its boundry.