B. AND Sequencestime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputA sequence of n non-negative integers (n \ge 2) a_1, a_2, \dots, a_n is called good if for all i from 1 to n-1 the following condition holds true: a_1 \: \& \: a_2 \: \& \: \dots \: \& \: a_i = a_{i+1} \: \& \: a_{i+2} \: \& \: \dots \: \& \: a_n, where \& denotes the bitwise AND operation.You are given an array a of size n (n \geq 2). Find the number of permutations p of numbers ranging from 1 to n, for which the sequence a_{p_1}, a_{p_2}, ... ,a_{p_n} is good. Since this number can be large, output it modulo 10^9+7.InputThe first line contains a single integer t (1 \leq t \leq 10^4), denoting the number of test cases.The first line of each test case contains a single integer n (2 \le n \le 2 \cdot 10^5) — the size of the array.The second line of each test case contains n integers a_1, a_2, \ldots, a_n (0 \le a_i \le 10^9) — the elements of the array.It is guaranteed that the sum of n over all test cases doesn't exceed 2 \cdot 10^5.OutputOutput t lines, where the i-th line contains the number of good permutations in the i-th test case modulo 10^9 + 7.ExampleInput
4
3
1 1 1
5
1 2 3 4 5
5
0 2 0 3 0
4
1 3 5 1
Output
6
0
36
4
NoteIn the first test case, since all the numbers are equal, whatever permutation we take, the sequence is good. There are a total of 6 permutations possible with numbers from 1 to 3: [1,2,3], [1,3,2], [2,1,3], [2,3,1], [3,1,2], [3,2,1].In the second test case, it can be proved that no permutation exists for which the sequence is good.In the third test case, there are a total of 36 permutations for which the sequence is good. One of them is the permutation [1,5,4,2,3] which results in the sequence s=[0,0,3,2,0]. This is a good sequence because    s_1 = s_2 \: \& \: s_3 \: \& \: s_4 \: \& \: s_5 = 0,   s_1 \: \& \: s_2 = s_3 \: \& \: s_4 \: \& \: s_5 = 0,   s_1 \: \& \: s_2 \: \& \: s_3 = s_4 \: \& \: s_5 = 0,   s_1 \: \& \: s_2 \: \& \: s_3 \: \& \: s_4 = s_5 = 0.  
4
3
1 1 1
5
1 2 3 4 5
5
0 2 0 3 0
4
1 3 5 1

6 0 36 4 
['bitmasks', 'combinatorics', 'constructive algorithms', 'math', '*1400']