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:
#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
signed main() { 
  ios::sync_with_stdio(false); cin.tie(0);
  auto solve = [] () {
    int n;
    cin >> n;
    vector<long long> a(n);
    for (int i = 0; i < n; i++) cin >> a[i];
    string s;
    cin >> s;
    vector<long long> base(61);
    for (int i = n - 1; i >= 0; i--) {
      long long cur = a[i];
      for (int j = 0; j < 61; j++) {
        if (cur & (1LL << j)) {
          cur ^= base[j];
        }
      }
      if (s[i] == '0') {
        if (cur != 0) {
          int id = 0;
          while (true) {
            if (cur & (1LL << id)) {
              break;
            }
            id++;
          }
          base[id] = cur;
        }
      } else if (cur != 0) {
        return 1;
      }
    }
    return 0;
  };
  int t;
  cin >> t;
  while (t--) cout << solve() << '\n';
  return 0;
}