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: Accepted)

#include <bits/stdc++.h>

using namespace std;

#define ll long long
#define endl '\n'
const int N = 1e6 + 5;
ll a[N];
int main(){
        ios_base::sync_with_stdio(false);
        cin.tie(0);
        if (fopen("BONUS.INP", "r")){
                freopen("BONUS.INP", "r", stdin);
                freopen("BONUS.OUT", "w", stdout);
        }
        ll t;
        cin >> t;
        while (t--){
                ll n;
                cin >> n;
                for (int i = 0; i < n; i++){
                        cin >> a[i];
                }
                string s;
                cin >> s;
                vector<ll> now;
                bool flag = true;
                for (int i = n - 1; i >= 0; i--){
                        for (auto j : now) a[i] = min(a[i], a[i] ^ j);
                        now.push_back(a[i]);
                        if (s[i] == '1' && a[i]){
                                flag = false;
                                break;
                        }
                }
                if (flag) cout << 0 << endl;
                else cout << 1 << endl;
        }
}