Midpoint

Time Limit : 10 sec, Memory Limit : 262144 KB

Problem I Midpoint

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.

Input

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 $10^5$.

Output

Print the number of the triplets which fulfill the constraint.

Sample Input 1

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

Output for the Sample Input 1

3

Sample Input 2

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

Output for the Sample Input 2

8

Sample Input 3

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

Output for the Sample Input 3

3

Source: Japan Alumni Group Spring Contest 2015 , Japan, 2015-04-19
http://acm-icpc.aitea.net/
http://jag2015spring.contest.atcoder.jp/