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# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

using System;
using System.Linq;
using System.Collections.Generic;
using System.IO;
using static Scanner;

class Program
{
    static void Main()
    {
        new Program().Solve();
    }

    public void Solve()
    {
        int t = ReadInt();
        for (int testcase = 0; testcase < t; testcase++)
        {
            int n = ReadInt();
            long[] a = ReadLong(n).ToArray();
            string s = Read();

            var last = new int[64];

            for (int i = 0; i < n; i++)
            {
                string s2 = Convert.ToString(a[i], 2).PadLeft(64, '0');

                for (int j = 0; j < 64; j++)
                {
                    if (s2[j] == '1')
                    {
                        if (s[i] == '0')
                        {
                            last[j] = 0;
                        }
                        else
                        {
                            last[j] = 1;
                        }
                    }
                }
            }

            if (last.Any(x => x == 1))
            {
                Console.WriteLine(1);
            }
            else
            {
                Console.WriteLine(0);
            }
        }
    }
}

static class Scanner
{
    static Queue<string> que = new Queue<string>();

    static void Scan()
    {
        var line = Console.ReadLine();
        if (line == null) throw new EndOfStreamException();
        foreach (var s in line.Split()) que.Enqueue(s);
    }

    public static string Read()
    {
        if (!que.Any()) Scan();
        return que.Dequeue();
    }
    public static int ReadInt() => int.Parse(Read());
    public static long ReadLong() => long.Parse(Read());
    public static double ReadDouble() => double.Parse(Read());
    public static decimal ReadDecimal() => decimal.Parse(Read());

    // 以下遅延実行に注意
    // ToArray() 等と組み合わせると安全
    public static IEnumerable<string> Read(long n)
    {
        for (long i = 0; i < n; i++) yield return Read();
    }
    public static IEnumerable<int> ReadInt(long n) => Read(n).Select(int.Parse);
    public static IEnumerable<long> ReadLong(long n) => Read(n).Select(long.Parse);
    public static IEnumerable<double> ReadDouble(long n) => Read(n).Select(double.Parse);
    public static IEnumerable<decimal> ReadDecimal(long n) => Read(n).Select(decimal.Parse);
}