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 1

Input:

4
2 1
4 4
1 2
6 3

Output:

2

Example 2

Input:

2
-999999999 -999999999
999999999 999999999

Output:

7999999984000000008