Problem: There are two persons, numbered 0 and 1, and a variable x whose initial value is 0. The two persons now play a game. The game is played in N rounds. The following should be done in the i-th round (1 \leq i \leq N):

* Person S_i does one of the following:
* Replace x with x \oplus A_i, where \oplus represents bitwise XOR.
* Do nothing.



Person 0 aims to have x=0 at the end of the game, while Person 1 aims to have x \neq 0 at the end of the game.

Determine whether x becomes 0 at the end of the game when the two persons play optimally.

Solve T test cases for each input file.

Constraints

* 1 \leq T \leq 100
* 1 \leq N \leq 200
* 1 \leq A_i \leq 10^{18}
* S is a string of length N consisting of `0` and `1`.
* All numbers in input are integers.

Input

Input is given from Standard Input in the following format. The first line is as follows:


T


Then, T test cases follow. Each test case is given in the following format:


N
A_1 A_2 \cdots A_N
S


Output

For each test case, print a line containing `0` if x becomes 0 at the end of the game, and `1` otherwise.

Example

Input

3
2
1 2
10
2
1 1
10
6
2 3 4 5 6 7
111000


Output

1
0
0

Solution (in CPP):

Solution:
#include <iostream>
#include <vector>

using namespace std;

using ull = unsigned long long;

#define Rep(i, n) for(int i = 0; i < (int)(n); ++i)

int solve() {
  int N;
  cin >> N;

  vector<ull> A(N);
  Rep(n, N) cin >> A[n];

  string S;
  cin >> S;

  vector<ull> basis;
  for (int n = N - 1; n >= 0; n--) {
    ull a = A[n];
    for (auto b : basis) {
      a = min(a, a ^ b);
    }
    if (a != 0) {
      if (S[n] == '0') {
        basis.push_back(a);
      } else if (S[n] == '1') {
        return 1;
      } else {
        abort();
      }
    }
  }

  return 0;
}

int main() {
  int T;
  cin >> T;
  Rep(t, T) {
    cout << solve() << endl;
  }
  return 0;
}