#include <bits/stdc++.h>
using namespace std;
void debug_all() { cerr << "]\n"; }
template <typename T, typename... Types>
void debug_all(T var1, Types... var2) {
  cerr << ' ' << var1 << ' ';
  debug_all(var2...);
}
long long int binomialCoeff(int n, int k) {
  long long int C[n + 1][k + 1];
  int i, j;
  for (i = 0; i <= n; i++) {
    for (j = 0; j <= min(i, k); j++) {
      if (j == 0 || j == i)
        C[i][j] = 1;
      else
        C[i][j] = C[i - 1][j - 1] + C[i - 1][j];
    }
  }
  return C[n][k];
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long int tc, n, z, o, ans;
  cin >> tc;
  while (tc--) {
    cin >> n;
    vector<long long int> a(n);
    z = o = 0;
    for (int i = 0; i < n; i++) {
      cin >> a[i];
      if (a[i] == 0) {
        z++;
      } else if (a[i] == 1) {
        o++;
      }
    }
    ans = o;
    for (int i = 1; i <= z; i++) {
      ans += o * (binomialCoeff(z, i));
    }
    cout << ans << endl;
  }
  return 0;
}

### Prompt

Your challenge is to write a Cpp solution to the following problem:

Luntik came out for a morning stroll and found an array a of length n. He calculated the sum s of the elements of the array (s= ∑_{i=1}^{n} a_i). Luntik calls a subsequence of the array a nearly full if the sum of the numbers in that subsequence is equal to s-1.

Luntik really wants to know the number of nearly full subsequences of the array a. But he needs to come home so he asks you to solve that problem!

A sequence x is a subsequence of a sequence y if x can be obtained from y by deletion of several (possibly, zero or all) elements.

Input

The first line contains a single integer t (1 ≤ t ≤ 1000) — the number of test cases. The next 2 ⋅ t lines contain descriptions of test cases. The description of each test case consists of two lines.

The first line of each test case contains a single integer n (1 ≤ n ≤ 60) — the length of the array.

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

Output

For each test case print the number of nearly full subsequences of the array.

Example

Input


5
5
1 2 3 4 5
2
1000 1000
2
1 0
5
3 0 2 1 1
5
2 1 0 3 0


Output


1
0
2
4
4

Note

In the first test case, s=1+2+3+4+5=15, only (2,3,4,5) is a nearly full subsequence among all subsequences, the sum in it is equal to 2+3+4+5=14=15-1.

In the second test case, there are no nearly full subsequences.

In the third test case, s=1+0=1, the nearly full subsequences are (0) and () (the sum of an empty subsequence is 0).

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
void debug_all() { cerr << "]\n"; }
template <typename T, typename... Types>
void debug_all(T var1, Types... var2) {
  cerr << ' ' << var1 << ' ';
  debug_all(var2...);
}
long long int binomialCoeff(int n, int k) {
  long long int C[n + 1][k + 1];
  int i, j;
  for (i = 0; i <= n; i++) {
    for (j = 0; j <= min(i, k); j++) {
      if (j == 0 || j == i)
        C[i][j] = 1;
      else
        C[i][j] = C[i - 1][j - 1] + C[i - 1][j];
    }
  }
  return C[n][k];
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long int tc, n, z, o, ans;
  cin >> tc;
  while (tc--) {
    cin >> n;
    vector<long long int> a(n);
    z = o = 0;
    for (int i = 0; i < n; i++) {
      cin >> a[i];
      if (a[i] == 0) {
        z++;
      } else if (a[i] == 1) {
        o++;
      }
    }
    ans = o;
    for (int i = 1; i <= z; i++) {
      ans += o * (binomialCoeff(z, i));
    }
    cout << ans << endl;
  }
  return 0;
}

```