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:
class VectorSpace:
    def __init__(self, k):
        self.k = k
        self.E = [0] * k
    
    def chk(self, n):
        for i in range(self.k)[::-1]:
            n = min(n, n ^ self.E[i])
        return 1 if n == 0 else 0
    
    def add(self, n):
        for i in range(self.k)[::-1]:
            n = min(n, n ^ self.E[i])
        if n: self.E[n.bit_length() - 1] = n
        return 1 if n == 0 else 0
    
    def dimension(self):
        return len(self.E)

T = int(input())
for _ in range(T):
    N = int(input())
    A = [int(a) for a in input().split()]
    S = [int(a) for a in input()]
    vs = VectorSpace(60)
    for i in range(N)[::-1]:
        a = vs.add(A[i])
        if S[i] and a == 0:
            print(1)
            break
    else:
        print(0)