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 solve(n, a_list, s):

    for i in range(n - 1, -1, -1):
        if s[i] == "0":
            if a_list[i] == 0:
                continue
            r = 2 ** (a_list[i].bit_length() - 1)
            for j in range(i):
                if a_list[j] & r > 0:
                    a_list[j] = a_list[i] ^ a_list[j]
        else:
            if a_list[i] > 0:
                return 1
    return 0


def main():
    t = int(input())
    res_list = []
    for _ in range(t):
        n = int(input())
        a_list = list(map(int, input().split()))
        s = input()
        res = solve(n, a_list, s)
        res_list.append(res)
    for res in res_list:
        print(res)


def test():
    assert solve(2, [1, 2], "10") == 1
    assert solve(2, [1, 1], "10") == 0
    assert solve(6, [2, 3, 4, 5, 6, 7], "111000") == 0


if __name__ == "__main__":
    test()
    main()