human
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.
Using python3 can you solve the prior task?
 Can you provide a Python code to determine the number of ways to select three problems for the problemset?
assistant
#Here is Python code to determine the number of ways to select three problems for the problemset.

try:
        import sys
        from functools import lru_cache, cmp_to_key
        from heapq import merge, heapify, heappop, heappush
        # from math import *
        from collections import defaultdict as dd, deque, Counter as C
        from itertools import combinations as comb, permutations as perm
        from bisect import bisect_left as bl, bisect_right as br, bisect, insort
        from time import perf_counter
        from fractions import Fraction
        import copy
        from copy import deepcopy
        import time
        starttime = time.time()
        mod = int(pow(10, 9) + 7)
        mod2 = 998244353

        def data(): return sys.stdin.readline().strip()
        def out(*var, end="\n"): sys.stdout.write(' '.join(map(str, var))+end)
        def L(): return list(sp())
        def sl(): return list(ssp())
        def sp(): return map(int, data().split())
        def ssp(): return map(str, data().split())
        def l1d(n, val=0): return [val for i in range(n)]
        def l2d(n, m, val=0): return [l1d(n, val) for j in range(m)]
        def A2(n,m): return [[0]*m for i in range(n)]
        def A(n):return [0]*n
        # sys.setrecursionlimit(int(pow(10,6)))
        # from sys import stdin
        # input = stdin.buffer.readline
        # I = lambda : list(map(int,input().split()))
        # import sys
        # input=sys.stdin.readline
        

        sys.stdin = open("input.txt", "r")
        sys.stdout = open("output.txt", "w")
except:
        pass

import sys
input=sys.stdin.readline
for _ in range(L()[0]):
        n = L()[0]
        
        X = [L() for  i in range(n)]

        par = [i for i in range(n+1)]

        
        Y = [[X[i][0],i+1] for i in range(n)]
        Y.sort()
        d = dd(int)
        for i in range(n):
                x,y = Y[i]
                if x not in d:
                        d[x]=par[y]
                else:
                        par[y]=d[x]


        par1 = par[::]
        par = [i for i in range(n+1)]



        Y = [[X[i][1],i+1] for i in...