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;

void solve() {
  int N;
  cin >> N;
  vector<int64_t> A(N);
  for (auto&& e : A) {
    cin >> e;
  }
  string S;
  cin >> S;
  vector<int64_t> B;
  for (int i = N - 1; i > -1; i--) {
    int64_t x = A[i];
    for (auto b : B) {
      x = min(x, x ^ b);
    }
    if (S[i] == '0') {
      if (x > 0) B.emplace_back(x);
    } else if (x > 0) {
      cout << 1 << '\n';
      return;
    }
  }
  cout << 0 << '\n';
}

int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  int T;
  cin >> T;
  for (int i = 0; i < T; i++) {
    solve();
  }
  return 0;
}