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:
T = int(input())
ans = []
for _ in range(T):
    N = int(input())
    A = [int(_) for _ in input().split()]
    S = input()
    dp = set([0])
    for a, s in zip(A[::-1], S[::-1]):
        for b in dp:
            a = min(a, a ^ b)
        if s == '1':
            if a:
                dp = set()
                break
        else:
            dp2 = set([a])
            for b in dp:
                dp2.add(min(b, a ^ b))
            dp = dp2
    ans += [0 if 0 in dp else 1]
print(*ans, sep='\n')