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: Wrong Answer)

import java.util.Scanner;
import java.util.ArrayList; 

class Calc{
    void solve(ArrayList<ArrayList<Long>> a,ArrayList<String> s,int t){
	for(int i=0;i<t;i++){
	    int w = 0;
	    //System.out.println(s.get(i).length());
	    for(int j=0;j<s.size();j++){
		//System.out.println(a);
		//System.out.println(s.get(j));
		//System.out.println(s.get(j).length()-1);
		for(int k=s.get(i).length()-1;k>=0;k--){
		    //System.out.println(a.get(i).size());
		    //System.out.println(s.get(i).charAt(k));
		    if(s.get(i).charAt(k)=='0'){
			//System.out.println("0のターン");
			if(a.get(i).get(k)==1){
			    break;
			}
		    }else{
			//System.out.println("1のターン");
			if(a.get(i).get(k)==1){
			    w = 1;
			    break;
			}
		    }
		}
	    }
	    System.out.println(w);
	}
    }
}

class Main{
      public static void main(String args[]){
	Scanner sc = new Scanner(System.in);
	//System.out.println("t?");
	int t = sc.nextInt();
	ArrayList<ArrayList<Long>>ai = new ArrayList<>();
	ArrayList<String> p = new ArrayList<>();
	for(int i=0;i<t;i++){
	    ai.add(new ArrayList<Long>());
	    //System.out.println("n?");
	    int n = sc.nextInt();
	    for(int j=0;j<n;j++){
		//System.out.println("ai?");
		ai.get(i).add(sc.nextLong()%2);
	    }
	    //System.out.println("s?");
	    p.add(sc.next());
	}
	Calc calc = new Calc();
	calc.solve(ai,p,t);
	sc.close();
      }
}