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
readall = sys.stdin.read
ns = lambda: readline().rstrip()
ni = lambda: int(readline().rstrip())
nm = lambda: map(int, readline().split())
nl = lambda: list(map(int, readline().split()))
prn = lambda x: print(*x, sep='\n')

def solve():
    INT_BITS = 64
    n = ni()
    a = nl()[::-1]
    s = ns()[::-1]
    lis = [0]*64
    for i in range(n):
        if s[i] == '1':
            c = a[i]
            for x in lis[::-1]:
                if x == 0:
                    continue
                if c & (1 << (x.bit_length() - 1)):
                    c ^= x
            if c:
                print(1)
                return
        else:
            c = a[i]
            for x in lis[::-1]:
                if x == 0:
                    continue
                if c & (1 << (x.bit_length() - 1)):
                    c ^= x
            if c:
                lis[c.bit_length() - 1] = c
    print(0)
    return

T = ni()
for _ in range(T):
    solve()