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 PyPy3 (7.3.0) (judge verdict: Runtime Error)

# -*- coding: utf-8 -*-
import sys
# sys.setrecursionlimit(10**6)
# buff_readline = sys.stdin.buffer.readline
buff_readline = sys.stdin.readline
readline = sys.stdin.readline

INF = 2**62-1


def read_int():
    return int(buff_readline())


def read_int_n():
    return list(map(int, buff_readline().split()))


def read_float():
    return float(buff_readline())


def read_float_n():
    return list(map(float, buff_readline().split()))


def read_str():
    return readline().strip()


def read_str_n():
    return readline().strip().split()

def error_print(*args):
    print(*args, file=sys.stderr)


def mt(f):
    import time

    def wrap(*args, **kwargs):
        s = time.time()
        ret = f(*args, **kwargs)
        e = time.time()

        error_print(e - s, 'sec')
        return ret

    return wrap


# @mt
def ref(N, A, S):
    if S[-1] == '1':
        return 1

    def f(i, x):
        if i == N:
            if x == 0:
                return 0
            else:
                return 1
        p = int(S[i])
        if f(i+1, x ^ A[i]) == p:
            return p
        if f(i+1, x) == p:
            return p
        return p ^ 1

    return f(0, 0)

def slv(N, A, S):
    if S[-1] == '1':
        return 1
    from random import choices
    al = [[], []]
    for s, a in zip(S, A):
        al[int(s)].append(a)

    al[0] = []
    for i in range(N-1, -1, -1):
        if S[i] == '1':
            break
        al[0].append(A[i])


    a0 = set(choices(list(set(al[0])), k=10))
    a1 = set(choices(list(set(al[1])), k=10))
    p0 = set([0])
    for a in a0:
        t = set()
        for v in p0:
            t.add(v ^ a)
        p0 |= t

    p1 = set([0])
    for a in a1:
        t = set()
        for v in p1:
            t.add(v ^ a)
        p1 |= t

    for v in p1:
        if v not in p0:
            return 1
    return 0


def main():
    T = read_int()
    for _ in range(T):
        N = read_int()
        A = read_int_n()
        S = read_str()
        print(slv(N, A, S))


    # import random
    # N = 35
    # A = [random.randint(1, 10**18) for _ in range(N)]
    # S = random.choices('01', k=N-1)
    # S.append('0')
    # print(ref(N, A, S))

    # while True:
    #     N = 30
    #     A = [random.randint(1, 1<<4) for _ in range(N)]
    #     S = random.choices('01', k=N-1)
    #     S.append('0')


    #     # A = [4, 16, 2, 10, 3, 13, 6, 4, 1, 3]
    #     # S = ['0', '0', '1', '0', '0', '0', '0', '0', '0', '0']
    #     print(A)
    #     print(S)
    #     a = slv(N, A, S)
    #     b = ref(N, A, S)
    #     if a != b:
    #         print(a, b)
    #         break


if __name__ == '__main__':
    main()