// vim: filetype=html tabstop=73 background=light :
//#pragma GCC optimize("Ofast,no-stack-protector")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,tune=native")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2")
//#pragma GCC optimize("unroll-loops")
//#pragma GCC optimize("fast-math")
//#pragma GCC optimize("section-anchors")
//#pragma GCC optimize("profile-values,profile-reorder-functions,tracer")
//#pragma GCC optimize("vpt")
//#pragma GCC optimize("rename-registers")
//#pragma GCC optimize("move-loop-invariants")
//#pragma GCC optimize("unswitch-loops")
//#pragma GCC optimize("function-sections")
//#pragma GCC optimize("data-sections")
//#pragma GCC optimize("branch-target-load-optimize")
//#pragma GCC optimize("branch-target-load-optimize2")
//#pragma GCC optimize("btr-bb-exclusive")
//#pragma GCC optimize("O3")

#ifndef __APPLE__
#pragma GCC diagnostic ignored "-Wsign-compare"
#pragma GCC diagnostic ignored "-Wmaybe-uninitialized"
#endif

//#include <bits/stdc++.h>

#include <iostream>
#include <vector>
#include <cmath>
#include <algorithm>
#include <string>
#include <queue>
#include <set>
#include <map>
#include <iomanip>
#include <deque>
#include <map>
#include <fstream>
#include <utility>
#include <stack>
#include <unordered_map>
#include <unordered_set>
#include <numeric>
#include <random>
#include <math.h>
#include <cassert>
#include <bitset>
#include <chrono>
#include <sstream>
#include <array>
#include <list>
#include <functional>
#include <complex>
//#include <Python/Python.h>

using namespace std;

#define DEBUG_VIVOD " SHTO-TO POSHLO NE TAK\n"
//#define all(x) x.begin(), x.end()
//#define rall(x) x.rbegin(), x.rend()
//#define pb push_back
//#define pf push_front
//#define _USE_MATH_DEFINES
#define filin(x) freopen(x, "r", stdin)
#define filout(x) freopen(x, "w", stdout)
//#define deq deque
//#define vec vector
//#define umap unordered_map
//#define uset unordered_set
#define nan nullptr
#define endl "\n"
#define INF (2e9 + 2)
//#define INF ((int64_t)1e18)
#define INF_LL ((int64_t)1e18)
//#define int int64_t

//typedef long long ll;
typedef int64_t ll;
//typedef __int128 ll;
//typedef unsigned long long ull;
//typedef long long ull
typedef long double ull;
//typedef __float128 ull;
//typedef __int128 ull;
typedef long double ld;
typedef unsigned long long ui;

void solve() {
    int n; cin >> n;
    ll mod = 1e9 + 7;
    vector<ll> fac(n + 1);
    fac[0] = 1;
    int k2 = (1 << 30) - 1;
    map<int, int> kk;
    for (int i = 1; i <= n; ++i) {
        fac[i] = (fac[i - 1] * (ll)i) % mod;
        int tmp; cin >> tmp;
        kk[tmp]++;
        k2 &= tmp;
    }
    cout << ((((ll)kk[k2] * (ll)(kk[k2] - 1)) % mod) * fac[n - 2]) % mod << "\n";
}

signed main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    int q = 1;
    cin >> q;
    while (q--) solve();
}

### Prompt

Please create a solution in Cpp 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
// vim: filetype=html tabstop=73 background=light :
//#pragma GCC optimize("Ofast,no-stack-protector")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,tune=native")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2")
//#pragma GCC optimize("unroll-loops")
//#pragma GCC optimize("fast-math")
//#pragma GCC optimize("section-anchors")
//#pragma GCC optimize("profile-values,profile-reorder-functions,tracer")
//#pragma GCC optimize("vpt")
//#pragma GCC optimize("rename-registers")
//#pragma GCC optimize("move-loop-invariants")
//#pragma GCC optimize("unswitch-loops")
//#pragma GCC optimize("function-sections")
//#pragma GCC optimize("data-sections")
//#pragma GCC optimize("branch-target-load-optimize")
//#pragma GCC optimize("branch-target-load-optimize2")
//#pragma GCC optimize("btr-bb-exclusive")
//#pragma GCC optimize("O3")

#ifndef __APPLE__
#pragma GCC diagnostic ignored "-Wsign-compare"
#pragma GCC diagnostic ignored "-Wmaybe-uninitialized"
#endif

//#include <bits/stdc++.h>

#include <iostream>
#include <vector>
#include <cmath>
#include <algorithm>
#include <string>
#include <queue>
#include <set>
#include <map>
#include <iomanip>
#include <deque>
#include <map>
#include <fstream>
#include <utility>
#include <stack>
#include <unordered_map>
#include <unordered_set>
#include <numeric>
#include <random>
#include <math.h>
#include <cassert>
#include <bitset>
#include <chrono>
#include <sstream>
#include <array>
#include <list>
#include <functional>
#include <complex>
//#include <Python/Python.h>

using namespace std;

#define DEBUG_VIVOD " SHTO-TO POSHLO NE TAK\n"
//#define all(x) x.begin(), x.end()
//#define rall(x) x.rbegin(), x.rend()
//#define pb push_back
//#define pf push_front
//#define _USE_MATH_DEFINES
#define filin(x) freopen(x, "r", stdin)
#define filout(x) freopen(x, "w", stdout)
//#define deq deque
//#define vec vector
//#define umap unordered_map
//#define uset unordered_set
#define nan nullptr
#define endl "\n"
#define INF (2e9 + 2)
//#define INF ((int64_t)1e18)
#define INF_LL ((int64_t)1e18)
//#define int int64_t

//typedef long long ll;
typedef int64_t ll;
//typedef __int128 ll;
//typedef unsigned long long ull;
//typedef long long ull
typedef long double ull;
//typedef __float128 ull;
//typedef __int128 ull;
typedef long double ld;
typedef unsigned long long ui;

void solve() {
    int n; cin >> n;
    ll mod = 1e9 + 7;
    vector<ll> fac(n + 1);
    fac[0] = 1;
    int k2 = (1 << 30) - 1;
    map<int, int> kk;
    for (int i = 1; i <= n; ++i) {
        fac[i] = (fac[i - 1] * (ll)i) % mod;
        int tmp; cin >> tmp;
        kk[tmp]++;
        k2 &= tmp;
    }
    cout << ((((ll)kk[k2] * (ll)(kk[k2] - 1)) % mod) * fac[n - 2]) % mod << "\n";
}

signed main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    int q = 1;
    cin >> q;
    while (q--) solve();
}

```