**Time limit:**1.00 s**Memory limit:**512 MB

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`