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-mcs 6.8.0.105) (judge verdict: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;
class a{
  public static void Main(){
    int num_of_try = int.Parse(Console.ReadLine());
    for(int counter = 0; counter < num_of_try; counter++){
      int n = int.Parse(Console.ReadLine());
      int[] num = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
      String s = Console.ReadLine();
      List<int> p0 = new List<int>();
      List<int> p1 = new List<int>();
      p0.Add(0); p1.Add(0);
      int max;
      for(int i=0; i<n; i++){
        if(s[i] == '0'){
          max = p0.Count;
          for(int j=0; j<max; j++){
            p0.Add(p0[j]^num[i]);
          }
        }
        if(s[i] == '1'){
          max = p1.Count;
          for(int j=0; j<max; j++){
            p1.Add(p1[j]^num[i]);
          }
        }
      }
      bool ans = true;
      /*Console.WriteLine("p0-----------");
      Console.WriteLine(string.Join(" ",p0));
      Console.WriteLine("p1-----------");
      Console.WriteLine(string.Join(" ",p1));
      Console.WriteLine("--------------");*/
      for(int i=0; i<p1.Count; i++){
        if(!p0.Contains(p1[i])){
          ans = false;
          break;
        }
      }
      if(ans){
        Console.WriteLine(0);
      }
      else{
        Console.WriteLine(1);
      }
    }
  }
}