题目描述
Chef loves squares! You are given N points with integers coordinates, Chef asks you to find out how many points he should add to these set of N points, so that one could create at least one square having its vertices from the points of the resulting set. Note that the square created need not to be parallel to the axis.
Input
The first line contains singe integer N.
Each of next N lines contains two integers Xi and Yi denotine the coordinates of i-th point.
Output
In a single line print single integer - the minimal number of points Chef need to paint to receive at least one square.
Constraints
0 ≤ N ≤ 2000
-10^6 ≤ Xi, Yi ≤ 10^6
There are NO coincided points
Example
Input:
3
0 0
2 2
3 3
Output:
2
Input:
5
0 0
100 100
200 200
100 0
0 100
Output:
0
Explanation
For the first example Chef can add points (2, 0), (0, 2) or (2, 3), (3, 2)
For the second example Chef already has square (0, 0), (100, 0), (0, 100), (100, 100).
输入格式
见题面
输出格式
见题面