Time Limit: 1s
Memory Limit: 128MB
xiaoY is crazy about determinant, One day he ask Mr HH a question “Mr HH, I have a hard computing problem on determinant, there is N point on 3-D plane (all point is grid, which means coordinates are integer), and we define
Now the question is how many Det(pi,pj,pk) is Multiple of 3.” (i != j, j != k, k != i)
The first line is an integer T, means T cases followed:
Each case is described in the following way:
An integer N (N<=10000)
N lines followed, each line is an point xi yi zi(|xi|<2*10^9,|yi|<2*10^9,|zi|<2*10^9 )
For each case output the number of Det which is Multiple of 3.
2 3 1 1 1 1 1 2 1 1 3 3 1 1 2 3 3 2 5 6 8
Case #1: 6 Case #2: 0
Because answer may be too large, long long is recommended