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B. AND Sequences

Description

A 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 \(10^9+7\).

Input:

The 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 \(2 \cdot 10^5\).

Output:

Output t lines, where the i-th line contains the number of good permutations in the i-th test case modulo 10^9 + 7.

standard input

4
3
1 1 1
5
1 2 3 4 5
5
0 2 0 3 0
4
1 3 5 1

standard output

6
0
36
4

Note

Note

In 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

  • \(s_1 = s_2 \: \& \: s_3 \: \& \: s_4 \: \& \: s_5 = 0\),
  • \(s_1 \: \& \: s_2 = s_3 \: \& \: s_4 \: \& \: s_5 = 0\),
  • \(s_1 \: \& \: s_2 \: \& \: s_3 = s_4 \: \& \: s_5 = 0\),
  • \(s_1 \: \& \: s_2 \: \& \: s_3 \: \& \: s_4 = s_5 = 0\).