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():
    T = int(input())
    for _ in range(T):
        N = int(input())
        A = list(map(int, input().split()))
        S = input()
        L = max(A).bit_length()
        s = [0]*L

        def check(x):
            for i in range(L-1, -1, -1):
                if (x >> i) % 2:
                    x ^= s[i]
            return(x == 0)

        def update(x):
            for i in range(L-1, -1, -1):
                if (x >> i) % 2:
                    x ^= s[i]
            id = x.bit_length() - 1
            if id >= 0:
                s[id] = x

        res = 0
        L2 = 0
        for i in range(N-1, -1, -1):
            k = int(S[i])
            if k:
                if check(A[i]):
                    continue
                else:
                    res = 1
                    break
            else:
                L2 = max(L2, A[i].bit_length())
                update(A[i])
        print(res)
main()