One day, you found $L + M + N$ points on a 2D plane, which you named $A_1, ..., A_L, B_1, ...,B_M, C_1,...,C_N$. Note that two or more points of them can be at the same coordinate. These were named after the following properties:

- the points $A_1,...,A_L$ were located on a single straight line,
- the points $B_1,...,B_M$ were located on a single straight line, and
- the points $C_1,...,C_N$ were located on a single straight line.

Now, you are interested in a triplet $(i, j, k)$ such that $C_k$ is the midpoint between $A_i$ and $B_j$. Your task is counting such triplets.

The first line contains three space-separated positive integers $L$, $M$, and $N$ $(1 \leq L, M, N \leq 10^5)$. The next $L$ lines describe $A$. The $i$-th of them contains two space-separated integers representing the $x$-coordinate and the $y$-coordinate of $A_i$. The next $M$ lines describe $B$. The $j$-th of them contains two space-separated integers representing the $x$-coordinate and the $y$-coordinate of $B_j$. The next $N$ lines describe $C$. The $k$-th of them contains two space-separated integers representing the $x$-coordinate and the $y$-coordinate of $C_k$. It is guaranteed that the absolute values of all the coordinates do not exceed $10^5$.

Print the number of the triplets which fulfill the constraint.

2 2 3 0 0 2 0 0 0 0 2 0 0 1 1 1 1

3

4 4 4 3 5 0 4 6 6 9 7 8 2 11 3 2 0 5 1 4 3 7 4 10 5 1 2

8

4 4 4 0 0 3 2 6 4 9 6 7 14 9 10 10 8 13 2 4 2 5 4 6 6 8 10

3

Source: Japan Alumni Group Spring Contest 2015
, Japan, 2015-04-19

http://acm-icpc.aitea.net/

http://jag2015spring.contest.atcoder.jp/

http://acm-icpc.aitea.net/

http://jag2015spring.contest.atcoder.jp/