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>
#define ll long long
using namespace std;

void solve(){
  int n;
  cin>>n;
  ll vec[n];
  for(int i=0;i<n;i++){
    cin>>vec[i];
  }
  string s;
  cin>>s;
  if(s[n-1]=='1'){
    cout<<1<<endl;
    return;
  }
  reverse(vec,vec+n);
  reverse(s.begin(),s.end());
  vector<ll> bases;
  for(int i=0;i<n;i++){
    for(ll base:bases){
      vec[i]=min(vec[i],vec[i]^base);
    }
    if(vec[i]){
      if(s[i]=='0'){
        bases.push_back(vec[i]);
      }
      else{
        cout<<1<<endl;
        return;
      }
    }
  }
  cout<<0<<endl;
}

int main(){
  int t;
  cin>>t;
  while(t--){
    solve();
  }
}