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.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Runtime.InteropServices.ComTypes;
using CompLib.Util;

public class Program
{

    public void Solve()
    {
        var sc = new Scanner();
        int t = sc.NextInt();
        Console.SetOut(new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });


        for (int i = 0; i < t; i++)
        {
            Console.WriteLine(Q(sc.NextInt(), sc.LongArray(), sc.Next()));
        }
        Console.Out.Flush();
    }

    string Q(int n, long[] a, string s)
    {
        // 1の操作だけでできる数　∈ 0の人の操作だけでできる数
        // なら0
        // else 1
        // 
        // 1の人のそれぞれを消せる 0の操作があるなら0

        var one = new List<long>();
        var zero = new List<long>();
        for (int i = 0; i < n; i++)
        {
            if (s[i] == '0') zero.Add(a[i]);
            else one.Add(a[i]);
        }
        var zz = zero.ToArray();

        foreach (var l in one)
        {
            if (!SubsetXor(zz, l))
            {
                return "1";
            }
        }
        return "0";
    }

    bool SubsetXor(long[] ar, long target)
    {
        if (target == 0) return true;

        var a = new int[60][];
        var ans = new int[60];

        for (int i = 0; i < 60; i++)
        {
            long bit = 1L << i;
            ans[i] = (target & bit) == 0 ? 0 : 1;
            a[i] = new int[ar.Length];
            for (int j = 0; j < ar.Length; j++)
            {
                a[i][j] = (ar[j] & bit) == 0 ? 0 : 1;
            }
        }

        int index = 0;
        for (int d = 0; d < ar.Length - 1 && index < 60 - 1; d++)
        {
            int j;
            bool f = false;
            for (j = index; j < 60; j++)
            {
                if (a[j][d] == 1)
                {
                    f = true;
                    break;
                }
            }
            if (!f) continue;

            if (index != j)
            {
                var t = a[index];
                a[index] = a[j];
                a[j] = t;

                var t2 = ans[index];
                ans[index] = ans[j];
                ans[j] = t2;
            }

            for (int k = index + 1; k < 60; k++)
            {
                if (a[k][d] == 0) continue;
                for (int l = d; l < ar.Length; l++)
                {
                    a[k][l] = (a[k][l] + a[index][l]) % 2;
                }
                ans[k] = (ans[k] + ans[index]) % 2;
            }

            index++;
        }

        return ans[index] == 0 || a[index].Count(i => i == 1) > 0;
    }

    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();
    }
}