## MVECTOR - Sum of Vectors

We can represent a 2D vector as a pair (X, Y). The sum of two or more vectors is a vector whose coordinates are the sums of the corresponding coordinates of all the vectors in the sum. e.g. (1, 2) + (3, 4) + (5, 6) = (1 + 3 + 5, 2 + 4 + 6) = (9, 12) Weight of a vector (x, y) is defined as x * x + y * y. You are given N vectors on a plain.

Your task is to write a program that will determine a subset of those vectors so the weight of the sum of all vectors in that subset is maximal.

Note: Use 64-bit integers (int64 in pascal or long long in c)

### Input

In the first line of the input file is an integer N, 1 ≤ N ≤ 30,000, the number of vectors.

The following N lines contain descriptions for each of the vectors. A description is made of two integers X and Y, separated by a single blank, -30,000 ≤ X, Y ≤ 30,000.

None of the given vectors will be (0, 0)

### Output

In the first and only line of the output file you have to write the weight of the maximum sum.

### Sample

```Input:
5
5 -8
-4 2
4 -2
2 1
-6 4

Output:
202```
```Input:
4
1 4
-1 -1
1 -1
-1 4

Output:
64```
```Input:
9
0 1
6 8
0 -1
0 6
-1 1
-1 2
5 -4
1 0
6 -5

Output:
360```

 Được gửi lên bởi: psetter Ngày: 2009-03-22 Thời gian chạy: 1s Giới hạn mã nguồn: 50000B Memory limit: 1536MB Cluster: Cube (Intel G860) Ngôn ngữ cho phép: Tất cả ngoại trừ: ERL GOSU JS-RHINO NODEJS PERL6 PYPY RUST SED VB.NET Nguồn bài: COI 03