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.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.HashSet;
import java.util.List;
import java.util.Scanner;
import java.util.Set;

public final class Main {

    public static void main(String[] args) {
        final Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        final int t = Integer.parseInt(in.nextLine());
        for (int x = 0; x < t; x++) {
            final int n = Integer.parseInt(in.nextLine());
            final long[] arr = new long[n];
            final String[] w = in.nextLine().split(" ");
            for (int i = 0; i < w.length; i++) {
                arr[i] = Long.parseLong(w[i]);
            }
            final String s = in.nextLine();
            final List<Long> left = new ArrayList<>();
            final List<Long> right = new ArrayList<>();
            for (int j = 0; j < s.length(); j++) {
                if (s.charAt(j) == '1') {
                    left.add(arr[j]);
                } else {
                    right.add(arr[j]);
                }
            }
            final Set<Long> set = new HashSet<>();
            dfs(left, set, 0, 0, true);
            dfs(right, set, 0, 0, false);
            System.out.println(set.isEmpty() ? 0 : 1);
        }
    }

    public static void dfs(List<Long> nums, Set<Long> res, long curr, int idx, boolean turn) {
        if (turn) {
            res.add(curr);
        } else {
            res.remove(curr);
        }
        for (int i = idx; i < nums.size(); i++) {
            curr ^= nums.get(i);
            dfs(nums, res, curr, i + 1, turn);
            curr ^= nums.get(i);
        }
    }
}