human
Can you provide a Python program to determine the number of ways to select three problems for the problemset given the following:
PYTHON3 solution for "Monocarp is the coach of the Berland State University programming teams. He decided to compose a problemset for a training session for his teams.

Monocarp has n problems that none of his students have seen yet. The i-th problem has a topic a_i (an integer from 1 to n) and a difficulty b_i (an integer from 1 to n). All problems are different, that is, there are no two tasks that have the same topic and difficulty at the same time.

Monocarp decided to select exactly 3 problems from n problems for the problemset. The problems should satisfy at least one of two conditions (possibly, both):

  * the topics of all three selected problems are different.

  * the difficulties of all three selected problems are different. 


Your task is to determine the number of ways to select three problems for the problemset.

Input

The first line contains a single integer t (1 ≤ t ≤ 50000) — the number of testcases.

The first line of each testcase contains an integer n (3 ≤ n ≤ 2 ⋅ 10^5) — the number of problems that Monocarp have.

In the i-th of the following n lines, there are two integers a_i and b_i (1 ≤ a_i, b_i ≤ n) — the topic and the difficulty of the i-th problem.

It is guaranteed that there are no two problems that have the same topic and difficulty at the same time.

The sum of n over all testcases doesn't exceed 2 ⋅ 10^5.

Output

Print the number of ways to select three training problems that meet either of the requirements described in the statement.

Example

Input

2
4
2 4
3 4
2 1
1 3
5
1 5
2 4
3 3
4 2
5 1

Output

3
10

Note

In the first example, you can take the following sets of three problems:

  * problems 1, 2, 4.

  * problems 1, 3, 4.

  * problems 2, 3, 4. 


Thus, the number of ways is equal to three.":
assistant
#Here is Python program to determine the number of ways to select three problems for the problemset.
 def solve():
    n = int(input())
    arr = []
    a = [0] * (n + 1)
    b = [0] * (n + 1)
    for i in range(n):
        x, y = map(int, input().split())
        arr.append((x, y))
        a[x] += 1
        b[y] += 1
    res = ((n - 2) * (n - 1) * n) // 6
    for i in range(n):
        x, y = arr[i]
        res -= (a[x] - 1) * (b[y] - 1)
    print(res)


q = int(input())
for _ in range(q):
    solve()