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 1.8.0) (judge verdict: Runtime Error)

import java.util.Scanner;

class Main{
	public static void main(String[] args){
      	int x = 0;
    	Scanner sc = new Scanner(System.in);
      	int T = sc.nextInt();
      	for(int j = 0; j < T; j++){

        	int N = sc.nextInt();
          	int[] A;
          	A = new int[N];
          	for(int i=0;i<N;i++){
              //Nラウンド繰り返す
            	A[i] = sc.nextInt();
                }
          	String S = sc.next();
          	for(int i=0;i<N;i++){
              char SI = S.charAt(i);
              if(SI=='0'){
              	if(x==0){
                	
                }else{
                	x = x ^ A[i];
                }
              }
              if(SI=='1'){
              	if(x==0){
                	x = x ^ A[i];
                }else{
                	
                }
              }
              }
           if(x == 0){System.out.println(0);}else{System.out.println(1);}
            }
            }
        }