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: Wrong Answer)

t=int(input())
res=list()

def ea(lst):
    flag=1
    while flag==1:
        flag=0
        for i in range(len(lst)):
            for j in range(i+1,len(lst)):
                if  lst[i]^lst[j] < lst[i] and lst[i]^lst[j]!=0:
                    flag=1
                    lst[i]=lst[i]^lst[j]
                if lst[i]^lst[j] < lst[j] and lst[i]^lst[j]!=0:
                    flag=1
                    lst[j]=lst[i]^lst[j]
    return(lst)
        
for i in range(t):
    n=int(input())
    a=list(map(int,input().split()))
    s=str(input())
    black=list()
    white=list()
    for i in range(n):
        if s[i]=="1":
            black.append(a[i])
        else:
            white.append(a[i])
    black=ea(black)
    white=ea(white)
    for item in black:
        if item in white:
            black.remove(item)
    black.extend(white)
    black=ea(black)
    ans=0
    for item in black:
        if (not item in white):
            f=0
            for i in range(len(white)):
                if item^white[i] in white:
                    f=1
            if f==0:
                ans=1
    res.append(ans)
    
for i in res:
    print(i)