Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

3
2
1 2
10
2
1 1
10
6
2 3 4 5 6 7
111000

Sample Output 1

1
0
0

In the first test case, if Person 1 replaces x with 0 \oplus 1=1, we surely have x \neq 0 at the end of the game, regardless of the choice of Person 0.

In the second test case, regardless of the choice of Person 1, Person 0 can make x=0 with a suitable choice.

Solution in Java (OpenJDK 11.0.6) (judge verdict: Runtime Error)

import java.util.Scanner;
import java.util.HashSet;
import java.util.Set;


public class Main{
 public static void main(String[] args) {
   Scanner kbd =new Scanner(System.in);
   int t=kbd.nextInt();

   for(int k=0;k<t;k++){
   int n=kbd.nextInt();
   int[] A= new int[n];
   for(int i=0;i<n;i++){
     A[i]=kbd.nextInt();
   }
   String S=kbd.next();

   Set<Character> set = new HashSet<>();
    for (int i = 0; i < S.length(); i++) {
    if(A[i]-1<S.length()){set.add(S.charAt(A[i]-1));}
    }
    if(set.size()==n){
  System.out.println("1");
}else{
  System.out.println("0");
}

 }
}
}