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;

#ifdef LOCAL
#include "debug.h"
#else
#define DEBUG(...)
#endif

int main() {
  cin.tie(nullptr);
  ios::sync_with_stdio(false);
  int tt;
  cin >> tt;
  while (tt--) {
    int n;
    cin >> n;
    vector<long long> a(n);
    for (auto&& e : a) cin >> e;
    string s;
    cin >> s;
    vector<long long> v;
    auto add = [&](long long x) -> bool {
      for (auto e : v) {
        x = min(x, x ^ e);
      }
      if (x) {
        v.push_back(x);
        return true;
      }
      return false;
    };
    int res = 0;
    for (int i = n; i--; ) {
      if (s[i] == '0') {
        add(a[i]);
      } else {
        if (add(a[i])) {
          res = 1;
          break;
        }
      }
    }
    cout << res << '\n';
  }
}