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)

import math

def kosu(kitei, k):
    n=len(kitei)
    lim = [0]*n
    for i in range(1, n):
        lim[i] = lim[i-1]|kitei[i-1]
    dp = [0]*(2**17)
    tmp = dp[:]
    dp[k] = 1
    for i in range(len(kitei))[::-1]:
        for j in range(lim[i]+1):
            tmp[j] = (dp[j^kitei[i]] + dp[j]) % (10**9+7)
        dp, tmp = tmp, dp
    return dp[0]
    
def solve(n, alist, s):
    kitei=[0]
    answer=0
    for i in range(n):
        teban=s[n-i-1]
        now=alist[n-i-1]
        if teban=='0':
            if kosu(kitei, now)>0:
                pass
            else:
                kitei.append(now)
        else:
            if kosu(kitei, now)>0:
                pass
            else:
                answer=1
    return answer

t=int(input())
for i in range(t):
    n=int(input())
    alist = list(map(int, input().split()))
    s=input()
    print(solve(n, alist, s))