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(N, A, S):
    
    # s == 0 のa を組み合わせて s==1 の任意のa を張ることができれば0
    # 下から
    
    if int(S[-1]) == 1:
        return 1
    
    B = [None] * max(A).bit_length()
    for i in reversed(range(N)):
        a = A[i]
        s = int(S[i])
        
        if s == 0: #基底生成
            while a:
                l = a.bit_length()-1
                if B[l] == None:
                    B[l] = a
                    break
                a ^= B[l]
        else: # i以上の基底で張れなければ 1
            while a:
                l = a.bit_length()-1
                if B[l] == None:
                    return 1
                a ^= B[l]
    return 0

T = int(input())
for i in range(T):
    N = int(input())
    A = list(map(int, input().split()))
    S = input()
    print(solve(N, A, S))