#include <bits/stdc++.h>
#define ll          long long int
#define uu          first
#define vv          second
#define pii         pair<int,int>
#define pll         pair<ll,ll>
#define tp          tuple<int,int,int>
#define fastio      ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0)
using namespace std;
const int INF = 1e9;
const ll MOD = 1e9 + 7;

const int N = 1e6 + 6;

int main()  {
    fastio;

    int t;
    cin>>t;
    while(t--) {
        int n;
        cin>>n;
        vector<int>vec(n);

        for(int i =0 ; i < n; i++ ) cin>>vec[i];
        int xx = vec[0];
        for(auto x : vec) xx &= x;
        for(auto &x: vec) x ^= xx;
        ll zero = 0;
        for(auto x : vec) zero += (x == 0);
        ll baki = n - zero;

        ll ans = ( zero * (zero-1) ) %MOD;
        baki += zero - 2;

        for(ll i = 1 ; i <= baki ; i++) {
            ans *= i;
            ans %= MOD;
        }

        cout<<ans<<'\n';
    }
    return 0;
}
### Prompt

Generate a CPP solution to the following problem:

A sequence of n non-negative integers (n ≥ 2) a_1, a_2, ..., a_n is called good if for all i from 1 to n-1 the following condition holds true: $$$a_1 \: \& \: a_2 \: \& \: ... \: \& \: a_i = a_{i+1} \: \& \: a_{i+2} \: \& \: ... \: \& \: a_n, where \&$$$ denotes the [bitwise AND operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND).

You are given an array a of size n (n ≥ 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 ≤ t ≤ 10^4), denoting the number of test cases.

The first line of each test case contains a single integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the size of the array.

The second line of each test case contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ 10^9) — the elements of the array.

It is guaranteed that the sum of n over all test cases doesn't exceed 2 ⋅ 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.

Example

Input


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

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. 

### Response

```cpp
#include <bits/stdc++.h>
#define ll          long long int
#define uu          first
#define vv          second
#define pii         pair<int,int>
#define pll         pair<ll,ll>
#define tp          tuple<int,int,int>
#define fastio      ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0)
using namespace std;
const int INF = 1e9;
const ll MOD = 1e9 + 7;

const int N = 1e6 + 6;

int main()  {
    fastio;

    int t;
    cin>>t;
    while(t--) {
        int n;
        cin>>n;
        vector<int>vec(n);

        for(int i =0 ; i < n; i++ ) cin>>vec[i];
        int xx = vec[0];
        for(auto x : vec) xx &= x;
        for(auto &x: vec) x ^= xx;
        ll zero = 0;
        for(auto x : vec) zero += (x == 0);
        ll baki = n - zero;

        ll ans = ( zero * (zero-1) ) %MOD;
        baki += zero - 2;

        for(ll i = 1 ; i <= baki ; i++) {
            ans *= i;
            ans %= MOD;
        }

        cout<<ans<<'\n';
    }
    return 0;
}
```