Midpoint

You found $L + M + N$ points on the coordinate plane and named them $A_1, \dots, A_L$, $B_1, \dots, B_M$, $C_1, \dots, C_N$. Two or more of the points can sit at the same coordinate. The names follow these properties:

• $A_1, \dots, A_L$ lie on a single straight line.
• $B_1, \dots, B_M$ lie on a single straight line.
• $C_1, \dots, C_N$ lie on a single straight line.

Count the triples $(i, j, k)$ such that $C_k$ is the midpoint of $A_i$ and $B_j$.

The first line contains three space separated positive integers $L$, $M$, and $N$ ($1 \le L, M, N \le 10^5$). The next $L$ lines describe $A$. The $i$-th of them contains two space separated integers, the $x$ coordinate and the $y$ coordinate of $A_i$. The next $M$ lines describe $B_1, \dots, B_M$ in the same format, and the $N$ lines after that describe $C_1, \dots, C_N$. The absolute value of every coordinate is at most $10^5$.

Print the number of triples $(i, j, k)$ that satisfy the condition.