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: Wrong Answer)

#include <bits/stdc++.h>
#define int long long
#define db long double
#define x first
#define y second
#define mp make_pair
#define pb push_back
#define all(a) a.begin(), a.end()

using namespace std;

void solve() {

	int n;
	cin >> n;

	vector<int> v(n);
	for (int i = 0; i < n; ++i) cin >> v[i];

	string s;
	cin >> s;

	vector<int> gauss(60, -1);

	for (int i = v.size() - 1; i >= 0; i--) {

		if (s[i] == '0') {
			int cur = v[i];
			for (int j = 59; j >= 0; j--) {
				if (!((1LL<<j)&cur)) continue;
				if (gauss[j] == -1) {
					gauss[j] = cur;
					continue;
				}

				cur ^= gauss[j];
			}
		}

		else {
			int cur = v[i];
			for (int j = 59; j >= 0; j--) {
				if (!((1LL<<j)&cur)) continue;
				if (gauss[j] == -1) {
					cout << "1\n";
					return;
				}

				cur ^= gauss[j];
			}
		}
	}

	cout << "0\n";

}

main(){
#ifdef LOCAL
	freopen("G_input.txt", "r", stdin);
	//freopen("G_output.txt", "w", stdout);
#endif
	ios_base::sync_with_stdio(0);
	cin.tie(0);

	int t;
	cin >> t;

	for (int i = 0; i < t; ++i) solve();

}