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:
T = int(input())

def check_base(bases, A):
	for n, b in bases:
		if A & (1 << n) != 0:
			A ^= b
	if A == 0:
		return None
	n = 0
	d = 1
	while True:
		if A & d != 0:
			return n, A
		n += 1
		d <<= 1

def append_base(bases, A):
	pair = check_base(bases, A)
	if pair != None:
		bases.append(pair)

def check(N, A_list, S):
	bases = []
	for i in range(N - 1, -1, -1):
		A = A_list[i]
		if S[i] == "0":
			append_base(bases, A)
		else:
			if check_base(bases, A):
				return False
	return True

for i in range(T):
	N = int(input())
	A_list = list(map(int, input().split()))
	S = input().strip()
	
	if check(N, A_list, S):
		print("0")
	else:
		print("1")