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++ (GCC 9.2.1) (judge verdict: Runtime Error)

#include <bits/stdc++.h>
using namespace std;
 
int main() {
  int T;
  cin >> T;
  for(int i = 0; i < T; i++){
    int N;
    cin >> N;
    long long A[N],cnt0 = 0, cnt1 = 0;
    string S;
    for(int j = 0; j < N; j++) cin >> A[j];
    cin >> S;
    for(int j = 0; j < S.length(); j++){
      string check = S.substr(j,1);
      if(check == "0") cnt0 += A[j];
      else cnt1 += A[j];
    }
    if((cnt0 != 0 && cnt1 != 1 && (cnt0 % cnt1 == 0 || cnt1 % cnt0 == 0)) || cnt0 == cnt1) cout << "0" << endl;
    else cout << "1" << endl;
  }
}