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>
typedef long long ll;
using namespace std;

void solve(){
  int n;
  cin>>n;
  vector<ll> arr(n);
  for(int i=0;i<n;i++)
    cin>>arr[i];
  
  char s[n+1];
  cin>>s;
  assert(int(strlen(s)==n));
  vector<ll> base;
  
  for(int i=n-1;i>=0;i--){
    ll ans=arr[i];
    for(ll x: base){
      ans=min(ans,ans^x);
    }
    if(ans==0)
      continue;
    if(s[i]=='0')
      base.push_back(ans);
    else{
      cout<<"1";
      return;
    }
  }
	cout<<"0";
}

int main(){
  int t;
  cin>>t;
  while(t--){
    solve();
    cout<<endl;
  }
  return 0;
}