시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
10 초 256 MB 7 3 3 42.857%

## 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 1

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


## 예제 출력 1

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