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())
for t in range(T):
    N=int(input())
    A=list(map(int,input().split()))[::-1]
    S=input()
    S=[1 if c=='1' else 0 for c in S][::-1]
    l=[]
    r=0
    for i,a in enumerate(A):
        if S[i]:
            for e in sorted(l)[::-1]:
                b=pow(2,e.bit_length()-1)
                if a&b:
                    a^=e
            if a:
                r=1
        else:
            for e in l:
                if a>e^a:
                    a^=e
            if a:
                l.append(a)
    print(r)