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문제

One day, you found L + M + N points on a 2D plane, which you named A1, . . . , AL, B1, . . . , BM, C1, . . . ,CN. Note that two or more points of them can be at the same coordinate. These were named after the following properties:

  • the points A1, . . . , AL were located on a single straight line,
  • the points B1, . . . , BM were located on a single straight line, and
  • the points C1, . . . ,CN were located on a single straight line.

Now, you are interested in a triplet (i, j, k) such that Ck is the midpoint between Ai and Bj. Your task is counting such triplets.

입력

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 Ai. 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 Bj. 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 Ck. It is guaranteed that the absolute values of all the coordinates do not exceed 105.

출력

Print the number of the triplets which fulfill the constraint.

예제 입력

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

예제 출력

3

예제 입력 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

예제 출력 2

8

예제 입력 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

예제 출력 3

3

힌트