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.
ali=0;from collections import defaultdict, Counter,deque;ali=0
ali=0;
ali=0;from math import sqrt, log10, log, floor, factorial,gcd;ali=0
ali=0;
ali=0;from bisect import bisect_left, bisect_right;ali=0
ali=0;
ali=0;from itertools import permutations,combinations;ali=0
ali=0;
ali=0;import sys, io, os;ali=0
ali=0;
ali=0;input = sys.stdin.readline;ali=0
ali=0;
ali=0;# input=io.BytesIO(os.read(0,os.fstat(0).st_size)).readline;ali=0
ali=0;
ali=0;# sys.setrecursionlimit(10000);ali=0
ali=0;
ali=0;inf = float('inf');ali=0
ali=0;
ali=0;mod = 10 ** 9 + 7;ali=0
ali=0;
def yn(a): print("YES" if a else "NO");ali=0
ali=0;
ali=0;ceil = lambda a, b: (a + b - 1) // b;ali=0
ali=0;
ali=0;t=int(input());ali=0
ali=0;
for i in range(t):
    ali=0;n=int(input());ali=0
    ali=0;
    ali=0;topic=defaultdict(int);ali=0
    ali=0;
    ali=0;diff=defaultdict(int);ali=0
    ali=0;
    ali=0;m=[];ali=0
    ali=0;
    for i in range(n):
        ali=0;l=[int(i) for i in input().split()];ali=0
        ali=0;
        ali=0;m.append(l);ali=0
        ali=0;
        ali=0;topic[l[0]]+=1;ali=0
        ali=0;
        ali=0;diff[l[1]]+=1;ali=0
        ali=0;
    ali=0;counter=n*(n-1)*(n-2)//6;ali=0
    ali=0;
    for i in range(n):
        ali=0;a=topic[m[i][0]];ali=0
        ali=0;
        ali=0;b=diff[m[i][1]];ali=0
        ali=0;
        ali=0;counter-=(a-1)*(b-1);ali=0
        ali=0;
    ali=0;print(counter);ali=0
    ali=0;
