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 main():
    def sweep(arr):
        col = max(arr).bit_length()
        row = len(arr)

        rank = 0
        for c in range(col-1, -1, -1):
            piv = -1
            for r in range(rank, row):
                if arr[r] >> c & 1:
                    piv = r
            if piv == -1:
                continue

            arr[piv], arr[rank] = arr[rank], arr[piv]

            for r in range(row):
                if r == rank:
                    continue
                if arr[r] >> c & 1:
                    arr[r] ^= arr[rank]

            rank += 1

        return sorted(arr[:rank], reverse=True)

    def solve():
        N = int(input())
        A = list(map(int, input().split()))[::-1]
        S = input()[::-1]
        B0 = []

        for a, s in zip(A, S):
            if s == '1':
                for b0 in B0:
                    if a >> b0.bit_length()-1 & 1:
                        a ^= b0
                if a:
                    return 1
            else:
                B0 = sweep(B0+[a])

        return 0

    for _ in [0]*int(input()):
        print(solve())


if __name__ == '__main__':
    main()