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 _ in [0]*T:
    N = int(input())
    *A, = map(int,input().split())
    S = input()

    B = []
    ans = 0
    for s,a in zip(S[::-1],A[::-1]):
        if s=="0":
            B.append(a)
        else:
            # check
            C = B[:]
            for i in range(64):
                for b in C:
                    if (b >> i) & 1 == 1: break
                else:
                    continue
                if (a >> i) & 1 == 1: a ^= b
                for j,c in enumerate(C):
                    if (c >> i) & 1 == 1: C[j] ^= b
            if a!=0:
                ans = 1
                break
    print(ans)