Hard challenge

Time Limit: 4000/2000 MS (Java/Others)

Memory Limit: 524288/524288 K (Java/Others)

Description

There are $n$ points on the plane, and the $i$th points has a value $val_i$, and its coordinate is $(x_i,y_i)$. It is guaranteed that no two points have the same coordinate, and no two points makes the line which passes them also passes the origin point. For every two points, there is a segment connecting them, and the segment has a value which equals the product of the values of the two points. Now HazelFan want to draw a line throgh the origin point but not through any given points, and he define the score is the sum of the values of all segments that the line crosses. Please tell him the maximum score.

Input

The first line contains a positive integer $T(1\leq T\leq5)$, denoting the number of test cases.
For each test case:
The first line contains a positive integer $n(1\leq n\leq5\times10^4)$.
The next $n$ lines, the $i$th line contains three integers $x_i,y_i,val_i(|x_i|,|y_i|\leq10^9,1\leq val_i\leq10^4)$.

Output

For each test case:
A single line contains a nonnegative integer, denoting the answer.

Sample Input

2 2 1 1 1 1 -1 1 3 1 1 1 1 -1 10 -1 0 100

Sample Output

1 1100

Hint

liuyiding

Source

2017 Multi-University Training Contest - Te

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