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: Wrong Answer)

def LI():
    return list(map(int,input().split()))

from collections import deque

def main():
    n=int(input())
    a=LI()
    s=[int(ss) for ss in list(input())]
    b=deque(sorted([bin(q)[::-1] for q in a]))
    x=0
    print(b)
    for q in range(n):
        # x^=q
        if s[q]==0:
            tmp=b.popleft()
            if tmp[0]=="1":continue
            tmp=int(tmp[::-1],0)
            x^=tmp
        else:
            tmp=b.pop()
            if tmp[0]=="0":continue
            tmp=int(tmp[::-1],0)
            x^=tmp
        
    print(0 if x==0 else 1)

t=int(input())
for _ in range(t):
    main()

# 入力例1でしんでるけど