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.
import sys,io,os
from os import path
if(path.exists('input.txt')):
     sys.stdin = open('input.txt','r')
     sys.stdout = open('output.txt','w')
else:
     #input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
     pass
def main():
    n=int(input())
    a=[]
    dist=[[] for i in range(n)]
    disk=[[] for i in range(n)]
    for i in range(n):
        b=list(map(int,input().split()))
        
        dist[b[0]-1].append(b[1]-1)
        disk[b[1]-1].append(b[0]-1)
        a.append([b[0]-1,b[1]-1])
    a.sort()
    dic1=[0]*n
    dic2=[0]*n
    for i in range(n):
            dic1[a[i][0]]+=1
            dic2[a[i][1]]+=1
    rep1=[]
    for i in range(n):
        if dic1[i]>1:
            rep1.append(i)
    sum=0
    for i in range(len(rep1)):
        for j in dist[rep1[i]]:
            if len(disk[j])>1:
                sum+=1
    
    print(int(n*(n-1)*(n-2)/6)-sum)




for _ in range(int(input())):
    main()
