Minimum Euclidean Distance

Given a set of points in the two-dimensional plane, your task is to find the minimum Euclidean distance between two distinct points. The Euclidean distance of points (x_1,y_1) and (x_2,y_2) is \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}.

Input

The first input line has an integer n: the number of points. After this, there are n lines that describe the points. Each line has two integers x and y. You may assume that each point is distinct.

Output

Print one integer: d^2 where d is the minimum Euclidean distance (this ensures that the result is an integer).

Constraints

$2 \le n \le 2$ \cdot 10^5$

$-10^9 \le x,y \le 10^9$

Example

Input

4
2 1
4 4
1 2
6 3

Output

2