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:
# xor battle


def is_included(base, X):
    base.sort(reverse=True)
    V = X
    for x in base:
        V = min(V, V ^ x)
    return V


def solve():
    N = int(input())
    a = list(map(int, input().split()))[::-1]
    player = input()[::-1]
    basement = [0]
    for i in range(N):
        v = a[i]
        K = is_included(basement, v)
        if player[i] == "0":
            if K == 0:
                pass
            else:
                basement.append(K)
        else:
            if K == 0:
                pass
            else:
                return 1

    return 0


def main():
    T = int(input())
    for i in range(T):
        A = solve()
        print(A)
    return


if __name__ == "__main__":
    main()