Problem: 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.

Example

Input

3
2
1 2
10
2
1 1
10
6
2 3 4 5 6 7
111000


Output

1
0
0

Solution (in PYTHON3):

Solution:
import sys
readline = sys.stdin.readline
T = int(readline())
Ans = [None]*T
for qu in range(T):
    N = int(readline())
    A = list(map(int, readline().split()))
    S = list(map(int, readline().strip()))
    
    if len(set(A)) == 1:
        Ans[qu] = S[-1]
        continue
    
    if S[-1] == 1:
        Ans[qu] = 1
        continue
    
    stack = [0]*61
    for i in range(N-1, -1, -1):
        a = A[i]
        for j in range(60, -1, -1):
            if a&(1<<j):
                a ^= stack[j]
        
        if S[i] == 0:
            if a:
                stack[a.bit_length()-1] = a
            else:
                continue
        else:
            if a:
                Ans[qu] = 1
                break
    else:
        Ans[qu] = 0

print('\n'.join(map(str, Ans)))