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 bisect
from itertools import accumulate

T = int(input())

for _ in range(T):
    N = int(input())
    As = list(map(int, input().split()))
    S = input()
    possible_xor = []
    if S[-1] == '1':
        print(1)
        continue
    flg = True
    for c, A in reversed(list(zip(S, As))):
        if c == '0':
            for xor in possible_xor[::-1]:
                if A.bit_length() == xor.bit_length():
                    A ^= xor
                elif A > xor:
                    break
            possible_xor.insert(bisect.bisect_left(possible_xor, A), A)
        else:
            for xor in possible_xor[::-1]:
                if A.bit_length() == xor.bit_length():
                    A ^= xor
            if A != 0:
                flg = False
                break
    if flg:
        print(0)
    else:
        print(1)