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.Linq;
using System.Text;
using System;
using System.Collections;
using System.Collections.Generic;
using System.Globalization;
using System.IO;
using System.Numerics;

namespace AtCoder
{
    class Program
    {

        const int BiggestMod = 1000000007;

        public static void Main()
        {

            var ans = new List<int>();

            for (int num = 0, numT = int.Parse(Console.ReadLine()); num < numT; num++)
            {

                int numN = int.Parse(Console.ReadLine());
                var args = Console.ReadLine().Split(' ').ToList().ConvertAll(x => long.Parse(x));
                var turn = Console.ReadLine().ToArray();

                var dp = new List<long>[numN + 1];

                dp[numN] = new List<long>() { 0 };

                for (int i = numN - 1; -1 < i; i--)
                    if (turn[i] == '0')
                    {

                        dp[i] = new List<long>(dp[i + 1]);
                        foreach (var arg in dp[i + 1])
                        {

                            var buf = arg ^ args[i];
                            if (!dp[i].Contains(buf)) dp[i].Add(buf);
                        }

                    }
                    else
                    {
                        if (dp[i + 1].Contains(args[i])) dp[i] = dp[i + 1];
                        else
                        {

                            ans.Add(1);
                            break;

                        }
                    }

                if (ans.Count == num)
                    ans.Add(dp[0].Contains(0) ? 0 : 1);
                
            }

            foreach (var buf in ans) Console.WriteLine(buf);

        }

    }

}