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<stdio.h>
long long IN(void)
{
  long long x=0;short f=0,c=getchar();while(c<48||c>57){f^=c==45,c=getchar();}
  while(c>47&&c<58){x=x*10+c-48,c=getchar();}return f?-x:x;
}
void sub(void)
{
  int N=IN(),S[200],sz=0;long long A[200],x,y[200];
  for(int i=0;i<N;i++){A[i]=IN();}
  for(int i=0;i<N;i++){S[i]=getchar()-'0';}
  for(int i=N-1;i>=0;i--)
  {
    x=A[i];
    if(sz){for(int j=0;j<sz;j++){x=(x<(x^y[j]))?x:x^y[j];}}
    if(x){if(S[i]){puts("1");return;}y[sz++]=x;}
  }
  puts("0");
}
signed main(void){int T=IN();while(T--){sub();}}