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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using CompLib.Util;

public class Program
{
    public void Solve()
    {
        var sc = new Scanner();
        int t = sc.NextInt();
        Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) {AutoFlush = false});
        for (int i = 0; i < t; i++)
        {
            Q(sc);
        }

        Console.Out.Flush();
    }

    private int N;
    private long[] A;
    private string S;

    void Q(Scanner sc)
    {
        N = sc.NextInt();
        A = sc.LongArray();
        S = sc.Next();

        // ラウンドiの時点でtなら0にできる
        // tの集合
        var dp = new HashSet<long>();
        dp.Add(0);
        for (int i = N - 1; i >= 0; i--)
        {
            if (S[i] == '0')
            {
                List<long> add = new List<long>();
                foreach (long j in dp)
                {
                    add.Add(j ^ A[i]);
                }

                foreach (long l in add)
                {
                    dp.Add(l);
                }
            }
            else
            {
                // t^a_i,tの両方がdp[i+1]に含まれる
                List<long> rm = new List<long>();
                foreach (long j in dp)
                {
                    if (!dp.Contains(j ^ A[i])) rm.Add(j);
                }

                foreach (long l in rm)
                {
                    dp.Remove(l);
                }
            }
        }

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

    public static void Main(string[] args) => new Program().Solve();
}

namespace CompLib.Util
{
    using System;
    using System.Linq;

    class Scanner
    {
        private string[] _line;
        private int _index;
        private const char Separator = ' ';

        public Scanner()
        {
            _line = new string[0];
            _index = 0;
        }

        public string Next()
        {
            while (_index >= _line.Length)
            {
                _line = Console.ReadLine().Split(Separator);
                _index = 0;
            }

            return _line[_index++];
        }

        public int NextInt() => int.Parse(Next());
        public long NextLong() => long.Parse(Next());
        public double NextDouble() => double.Parse(Next());
        public decimal NextDecimal() => decimal.Parse(Next());
        public char NextChar() => Next()[0];
        public char[] NextCharArray() => Next().ToCharArray();

        public string[] Array()
        {
            _line = Console.ReadLine().Split(Separator);
            _index = _line.Length;
            return _line;
        }

        public int[] IntArray() => Array().Select(int.Parse).ToArray();
        public long[] LongArray() => Array().Select(long.Parse).ToArray();
        public double[] DoubleArray() => Array().Select(double.Parse).ToArray();
        public decimal[] DecimalArray() => Array().Select(decimal.Parse).ToArray();
    }
}