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 C# (Mono-csc 3.5.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AtCoder {
    class XorBattle {
        static void Main(string[] args) {
            var T = int.Parse(Console.ReadLine());
            for (int t = 0; t < T; t++) {
                int N = int.Parse(Console.ReadLine());
                long[] A = new long[N];
                var parts = Console.ReadLine().Split(' ');
                for (int i = 0; i < N; i++) {
                    A[i] = long.Parse(parts[i]);
                }
                string S = Console.ReadLine();

                bool canWin = true;
                for (int bit = 0; bit < 60; bit++) {
                    int[] AA = new int[N];
                    for (int i = 0; i < N; i++) {
                        AA[i] = (A[i] & (1L << bit)) != 0 ? 1 : 0;
                    }

                    bool[][] dp = new bool[N + 1][];
                    for (int i = 0; i <= N; i++) {
                        dp[i] = new bool[2];
                    }

                    dp[N][0] = true;

                    for (int i = N - 1; i >= 0; i--) {
                        for (int j = 0; j < 2; j++) {
                            if (S[i] == '0') {
                                dp[i][j] = dp[i + 1][j] | dp[i + 1][j ^ AA[i]];
                            } else {
                                dp[i][j] = dp[i + 1][j] & dp[i + 1][j ^ AA[i]];
                            }
                        }
                    }

                    if (!dp[0][0]) {
                        canWin = false;
                        break;
                    }
                }

                Console.WriteLine(canWin ? "0" : "1");
            }
        }
    }
}