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:
# coding: utf-8


def solve(*args: str) -> str:
    t = int(args[0])
    ret = []
    for i in range(1, 3*t+1, 3):
        n = int(args[i])
        A = tuple(map(int, args[i+1].split()))
        S = tuple(map(int, tuple(args[i+2])))

        ans = False
        dp = [0]*(max(A).bit_length()+1)
        for a, s in reversed(tuple(zip(A, S))):
            m = a.bit_length()
            if s == 0:
                while 0 < a and 0 < dp[m]:
                    a ^= dp[m]
                    m = a.bit_length()
                if 0 < a:
                    dp[m] = a
            elif s == 1:
                while 0 < a:
                    if 0 < dp[m]:
                        a ^= dp[m]
                        m = a.bit_length()
                    else:
                        ans = True
                        break

        ret.append(1*ans)

    return '\n'.join(map(str, ret))


if __name__ == "__main__":
    print(solve(*(open(0).read().splitlines())))