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: Time Limit Exceeded)

# xor battle

def Normalize(A):
    A.sort(reverse=True)
    start_point = 0
    for i in range(60, -1, -1):
        X = 1 << i
        for j in range(start_point, len(A)):
            if A[j] >> i & 1:
                A[start_point], A[j] = A[j], A[start_point]
                for k in range(len(A)):
                    if A[k] >> i & 1 and k != start_point:
                        A[k] ^= A[start_point]
                start_point += 1
                break

# 最高位のbit を取得

def highest_bit(X):
    cnt = 0
    V = X
    while V & 1 == 0:
        cnt += 1
        V >>= 1
    return cnt


def solve():
    N = int(input())
    a = list(map(int, input().split()))
    player = input()

    p0, p1 = [], []

    for i in range(N):
        if player[i] == "0":
            p0.append(a[i])
        else:
            p1.append(a[i])
    Normalize(p0)
    Normalize(p1)

    for v in p0:
        bit = highest_bit(v)
        for j in range(len(p1)):
            if (v >> bit) & (p1[j] >> bit):
                p1[j] ^= v

    res = 0

    for x in p1:
        res ^= x

    print(res & 1)
    
    return


def main():
    T = int(input())
    for i in range(T):
        solve()
    return


if __name__ == "__main__":
    main()