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;
typedef int64_t ll;

int main(){
  int t,n;
  cin>>t;
  for(int i=0;i<t;i++){
    cin>>n;
    ll a[n];
    string s;
    for(int j=0;j<n;j++){
      cin>>a[j];
    }
    cin>>s;
    for(int j=n-1;j>=0;j--){
      if(a[j]>0){
        if(s[j]-'0'==1){cout<<1<<endl;break;}
        for(int k=0;k<62;k++){
          if((a[j]>>k)&1){
            for(int l=j-1;l>=0;l--){
              if((a[l]>>k)&1)a[l]^=a[j];
            }
            break;
          }
        }
      }
      if(j==0)cout<<0<<endl;
    }
  }
}