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: Time Limit Exceeded)

import java.math.BigInteger;
import java.util.LinkedList;
import java.util.Queue;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		int numTimes = scan.nextInt();
		for(int i = 0; i < numTimes; i++) {
			int N = scan.nextInt();
			long[] A = new long[N];
			for(int index = 0; index < N; index++) {
				A[index] = scan.nextLong();
			}
			scan.nextLine();
			BigInteger X = BigInteger.ZERO;
			String[] S = scan.nextLine().split("");
			
			X = getSolution(S, A);
			
			if(!X.equals(BigInteger.ZERO)) {
				System.out.println(1);
			}
			else {
				System.out.println(0);
			}
		}
	}
	public static BigInteger getSolution(String[] S, long[] A) {
		BigInteger X = BigInteger.ONE;
		
		Queue<Number> queue = new LinkedList<Number>();
		boolean found = false;
		queue.add(new Number(BigInteger.ZERO, 0L));
		

		while(queue.size() != 0 || found) {

			Number curr = queue.poll();
			BigInteger currA = curr.current;
			long currMoves = curr.numMoves;

			
			if(currA.equals(BigInteger.ZERO) && currMoves == (S.length)) {
				found = true;
				X = BigInteger.ZERO;
				break;
			}
			if(currMoves+1 <= S.length) {
				BigInteger optionOne = currA.xor(BigInteger.valueOf(A[(int) (currMoves)]));
				if(S[(int) currMoves].equals("1")) {
					if(!currA.equals(BigInteger.ZERO)) {
						queue.add(new Number(currA, currMoves+1));
					}
					else {
						if(!optionOne.equals(BigInteger.ZERO)) {
							queue.add(new Number(optionOne, currMoves+1));
						}
					}
				}
				else {
					
					queue.add(new Number(optionOne, currMoves+1));
					queue.add(new Number(currA, currMoves+1));
				}
			}
		}
		
		return X;
	}
}
class Number {
		public BigInteger current;
		public long numMoves;

		public Number(BigInteger current, long numMoves) {
			this.current = current;
			this.numMoves = numMoves;
		}
	}