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 <cstdio>
#include <vector>

int main()
{
  int T;
  scanf("%d",&T);
  while(T--){
    int n;
    scanf("%d",&n);
    std::vector<long long> a(n);
    for(int i=0;i<n;i++){
      scanf("%lld",&a[i]);
    }
    char s[300];
    scanf("%s",s);
    std::vector<long long> bs(64);
    std::vector<int> tp(64);
    int dim=0;
    bool ans=true;
    for(int i=n-1;i>=0;i--){
      long long v=a[i];
      int t=0;
      while(t<dim){
	if((v&((1ll<<tp[t])-1))!=0){
	  break;
	}
	//printf(" %lld %d %d %lld\n",v,t,tp[t],bs[t]);
	if(v&(1ll<<tp[t])){
	  v^=bs[t];
	}
	t++;
      }
      //printf("%d %lld %d %d\n",i,v,dim,t);
      if(v!=0){
	if(s[i]=='0'){
	  for(int x=dim;x>t;x--){
	    bs[x]=bs[x-1];
	    tp[x]=tp[x-1];
	  }
	  bs[t]=v;
	  tp[t]=0;
	  while((v&(1ll<<tp[t]))==0){
	    tp[t]++;
	  }
	  dim++;
	}
	else{
	  ans=false;
	  break;
	}
      }
    }
    puts(ans?"0":"1");
  }
  return 0;
}