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 <bits/stdc++.h>
using namespace std;
int main(){
  int T;
  cin >> T;
  for (int i = 0; i < T; i++){
    int N;
    cin >> N;
    vector<long long> A(N);
    for (int j = 0; j < N; j++){
      cin >> A[j];
    }
    string S;
    cin >> S;
    bool ok = true;
    for (int j = N - 1; j >= 0; j--){
      for (int k = N - 1; k > j; k--){
        A[j] = min(A[j], A[j] ^ A[k]);
      }
      if (S[j] == '1' && A[j] != 0){
        ok = false;
      }
    }
    if (ok){
      cout << 0 << endl;
    } else {
      cout << 1 << endl;
    }
  }
}