Burak and Gizem are working on their physics project. They are given \(n\) 2-dimensional vectors that represent forces and they are required to find the maximum equivalent force possible using a subset of these forces.

Can you help them to find a subset of these vectors so that their sum is the greatest possible?

Input

The first line contains a single integer \(n\). The next \(n\) lines contain 2 integers each \(x_i\) and \(y_i\), the coordinates of the \(i^{th}\) vector.

• \(1 \le n \le 2 \cdot 10^5\),
• \(-10^9 \le x_i, y_i \le 10^9\).

Output

Print one integer, the squared length of the longest possible vector Burak and Gizem can create.

Example

Input:

4
1 0
0 1
1 1
-1 -1

Output:

8

Input:

7
1000000000 1000000000
1000000000 1000000000
1000000000 1000000000
1000000000 1000000000
1000000000 1000000000
1000000000 1000000000
1000000000 1000000000

Output:

98000000000000000000

Explanation

In the first sample, summing up the first three vectors gives vector \(\texttt{2 2}\) which squared length is 8.