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 <stdio.h>

int main()
{
	int i, j, k, t, T, N, d, base[60], p[60];
	long long A[201], bit[60];
	char S[202];
	scanf("%d", &T);
	for (i = 1, bit[0] = 1; i < 60; i++) bit[i] = bit[i-1] << 1;
	
	for (t = 1; t <= T; t++) {
		scanf("%d", &N);
		for (i = 1; i <= N; i++) scanf("%lld\n", &(A[i]));
		scanf("%s", &(S[1]));
		
		for (i = N, d = 0; i >= 1; i--) {
			for (j = 0; j < d; j++) if ((A[i] | bit[p[j]]) == A[i]) A[i] ^= A[base[j]];
			if (A[i] != 0) {
				if (S[i] == '1') break;
				base[d] = i;
				for (j = 0; j < 60; j++) if ((A[i] | bit[j]) == A[i]) break;
				p[d++] = j;
			}
		}
		
		if (i == 0) printf("0\n");
		else printf("1\n");
	}

	fflush(stdout);
	return 0;
}