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:
import sys

readline = sys.stdin.readline
MOD = 10 ** 9 + 7
INF = float('INF')
sys.setrecursionlimit(10 ** 5)


def main():
    def calc():
        n = int(readline())
        a = list(map(int, readline().split()))
        s = input()
        b = [-1] * 61

        for i in range(n - 1, -1, -1):
            x = a[i]
            if s[i] == "0":
                l = x.bit_length()
                if b[l - 1] == -1:
                    b[l - 1] = x
                else:
                    while b[l - 1] != -1 and x > 0:
                        x ^= b[l - 1]
                        l = x.bit_length()
                    if x != 0:
                        b[l - 1] = x
            else:
                xb = format(x, "b")[::-1]
                l = len(xb)
                cur = 0
                for j in range(l - 1, -1, -1):
                    bit = int(xb[j])
                    cur_bit = int(format(cur,"b").zfill(l)[::-1][j])
                    if bit ^ cur_bit == 1:
                        if b[j] != -1:
                            cur ^= b[j]
                        else:
                            return print(1)
        return print(0)

    t = int(readline())
    for _ in range(t):
        calc()


if __name__ == '__main__':
    main()