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:
def solve():
    base = [] # 基底の初期化
    for a, s in zip(A[::-1], S[::-1]):
        # print(f'a: {a}, s: {s}')
        # for i, y in enumerate(base):
        #     print('base{:d} {:3d}: {:05b}'.format(i, y, y))

       # 従属関係を確認
        x = a
        for y in base:
            x = min(x, x ^ y)

        # A_iがA_{i+1:N}で表現可能ならx=0になっている
        if x:
            if s == "0":
                # print('=>add {:3d}: {:05b}'.format(x, x))
                base.append(x)
            else:
                return 1
    return 0


t = int(input())
for _ in range(t):
    n = int(input())
    *A, = map(int, input().split())
    S = input()
    # print(f'A: {A}, S: {S}')
    print(solve())
    # print('-'*32)