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 collections
import math
import itertools
import  sys
import time
import random

def fast_input():
    return sys.stdin.readline().strip()

input = fast_input

def ints_input():
    return list(int(x) for x in input().split())

def int_input():
    return int(input())



def solve():
    n = int_input()
    a = [None for _ in range(n)]
    b = [None for _ in range(n)]
    for i in range(n):
        a[i], b[i] = ints_input()
    a_counts = collections.Counter(a)
    b_counts = collections.Counter(b)
    a_two_families = 0
    a_three_families = 0
    b_two_families = 0
    b_three_families = 0
    two_overlaps = 0
    for i in range(n):
        a_count = a_counts[a[i]]
        b_count = b_counts[b[i]]
        a_two_families += (a_count - 1) * (n - a_count)
        b_two_families += (b_count - 1) * (n - b_count)
        a_three_families += (a_count - 1) * (a_count - 2) // 2
        b_three_families += (b_count - 1) * (b_count - 2) // 2
        two_overlaps += (a_count - 1) * (b_count - 1)
    good = (n * (n-1) * (n-2)) // 6 - two_overlaps
    print(good)





if True:
    for _ in range(int_input()):
        solve()
else:
    solve()