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:
def collapse(A):
    R = []
    a = max(A)
    n = a.bit_length()
    B = [set() for _ in range(n)]
    for a in A:
        B[a.bit_length()].add(a)
    for i in reversed(range(n)):
        if not B[i]:
            continue
        b = B[i].pop()
        R.append(b)
        for k in B[i]:
            k ^= b
            B[k.bit_length()].add(k)
    return R

def solve(N, A, S):
    B = [0] * 64
    for a, s in zip(reversed(A), reversed(S)):
        if s == '1':
            n = a.bit_length() - 1
            while a != 0:
                if B[n] == 0:
                    return 1
                a ^= B[n]
                n = a.bit_length() - 1
        else:
            n = a.bit_length() - 1
            while a != 0 and B[n] != 0:
                a ^= B[n]
                n = a.bit_length() - 1
            if a == 0:
                continue
            B[n] = a
    return 0
    
def main():
    T = int(input())
    for _ in range(T):
        N = int(input())
        A = list(map(int, input().split()))
        S = input()
        print(solve(N, A, S))
main()