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>

using namespace std;

#define FOE(i, s, t) for (int i = s; i <= t; i++)
#define FOR(i, s, t) for (int i = s; i < t; i++)
#define FOD(i, s, t) for (int i = s; i >= t; i--)

#define LL long long
#define mp make_pair
#define pb push_back

#define K 601

int t;

int n;
LL a[K];
int b[K];
string s;

LL c[K];
int cnt;

void add(LL mask) {
	FOD(i, 61, 0) {
		if ((mask & ((LL)1 << i)) == 0) continue;

		if (!c[i]) {
			c[i] = mask;
			
			FOD(j, i - 1, 0) if (c[i] & ((LL)1 << j)) c[i] ^= c[j];
			FOE(j, i + 1, 61) if (c[j] & ((LL)1 << i)) c[j] ^= c[i];
	
			return;
		}

		mask ^= c[i];
		
	}
}

bool verify(LL u) {
	FOD(i, 61, 0) if (u & c[i]) u ^= c[i];
	return (u == 0);
}	

void solve() {
	scanf("%d", &n);
	
	FOE(i, 1, n) scanf("%lld", &a[i]);

	cin >> s;
	FOE(i, 1, n) b[i] = (s[i - 1] == '0' ? 0 : 1);
	FOE(i, 0, 99) c[i] = 0;
	
	FOD(i, n, 1) {
		if (b[i] == 1) {
			if (verify(a[i]) == false) {
				printf("1\n");
				return;
			}
		} else {
			add(a[i]);	
		}
	}
	
	printf("0\n");
}

int main() {
	scanf("%d", &t);
	while (t--) solve();
}