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() {
  constexpr int d = 60;
  int t;
  cin >> t;
  for (int i = 0; i < t; i++) {
    int n, ans = 0;
    cin >> n;
    vector<uint64_t> a(n), w(d);
    for (int j = 0; j < n; j++) {
      cin >> a.at(j);
    }
    string s;
    cin >> s;
    for (int j = n - 1; j >= 0; j--) {
      if (s.at(j) == '1') {
        uint64_t m = a.at(j);
        for (int k = 0; k < d; k++) {
          if ((m >> k) & 1ul) m ^= w.at(k);
        }
        if (m) {
          ans = 1;
        }
      } else {
        uint64_t m = a.at(j);
        for (int k = 0; k < d; k++) {
          if ((m >> k) & 1ul) {
            if (w.at(k) == 0) {
              w.at(k) = m;
            }
            m ^= w.at(k);
          }
        }
      }
    }
    cout << ans << "\n";
  }
}