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;
using i64 = long long;
#define endl "\n"

int main()
{
  i64 T;
  cin >> T;
  while (T--)
  {
    i64 N;
    cin >> N;
    vector<i64> A(N);
    for (i64 i = 0; i < N; i++)
      cin >> A[i];
    string S;
    cin >> S;
    vector<i64> b;
    for (i64 i = N; 0 <= i; i--)
    {
      i64 x = A[i];
      for (i64 j : b)
        x = min(x, j ^ x);
      if (x != 0)
      {
        if (S[i] == '1')
        {
          cout << "1" << endl;
          goto fin;
        }
        b.push_back(x);
      }
    }
    cout << "0" << endl;
  fin:;
  }
  return 0;
}