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 Python (3.8.2) (judge verdict: Accepted)

import sys

readline = sys.stdin.readline
readall = sys.stdin.read
ns = lambda: readline().rstrip()
ni = lambda: int(readline().rstrip())
nm = lambda: map(int, readline().split())
nl = lambda: list(map(int, readline().split()))
prn = lambda x: print(*x, sep='\n')

def solve():
    INT_BITS = 64
    n = ni()
    a = nl()[::-1]
    s = ns()[::-1]
    lis = [0]*64
    for i in range(n):
        if s[i] == '1':
            c = a[i]
            for x in lis[::-1]:
                if x == 0:
                    continue
                if c & (1 << (x.bit_length() - 1)):
                    c ^= x
            if c:
                print(1)
                return
        else:
            c = a[i]
            for x in lis[::-1]:
                if x == 0:
                    continue
                if c & (1 << (x.bit_length() - 1)):
                    c ^= x
            if c:
                lis[c.bit_length() - 1] = c
    print(0)
    return

T = ni()
for _ in range(T):
    solve()