11714번 - Midpoint 다국어

One day, you found L + M + N points on a 2D plane, which you named A₁, . . . , A_L, B₁, . . . , B_M, C₁, . . . ,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 A₁, . . . , A_L were located on a single straight line,
• the points B₁, . . . , B_M were located on a single straight line, and
• the points C₁, . . . ,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 ≤ L, M, N ≤ 10⁵). 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 10⁵.

Print the number of the triplets which fulfill the constraint.