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

Difficulty: UNKNOWN_DIFFICULTY

Solutions:
sc = iter(open(0).read().split())
ni = lambda : int(next(sc))
ns = lambda : next(sc)
T = ni()
for _ in range(T):
	N = ni()
	A = [ni() for _ in range(N)]
	S = ns()
	B = []
	ans = 0
	for (a, s) in zip(reversed(A), reversed(S)):
		for b in B:
			a = min(a, a ^ b)
		if a:
			if s == '1':
				ans = 1
				break
			else:
				B.append(a)
	print(ans)