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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;

public class Main {

    public static void main(String[] args) throws IOException {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        int testCases = Integer.parseInt(reader.readLine().trim());


        while (testCases > 0) {
            reader.readLine();
            int[] arr = Arrays.stream(reader.readLine().split(" "))
                    .map(String::trim)
                    .mapToInt(Integer::parseInt)
                    .toArray();

            int[] turns = Arrays.stream(reader.readLine().split(""))
                    .map(String::trim)
                    .mapToInt(Integer::parseInt)
                    .toArray();

            int result = solve(arr, turns, 0);
            if (result > 0)
                System.out.println(1);
            else
                System.out.println(0);

            testCases--;
        }
    }

    private static int solve(int[] arr, int[] turns, int x) {
        for (int i = 0; i < turns.length; i++) {
            if (turns[i] == 0) {
                if ((x ^ arr[i]) == 0)
                    x = x ^ arr[i];
            } else {
                if ((x ^ arr[i]) > 0)
                    x = x ^ arr[i];
            }
        }

        return x;
    }
}