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 base(a, f=False):
    k = 0
    for i in range(64):
        for ind in range(k, len(a)):
            j = a[ind]
            if (j >> i) & 1 == 1:
                break
        else:
            continue

        a[ind], a[k] = a[k], a[ind]
        for ind, j in enumerate(a):
            if ind == k:
                continue
            if (j >> i) & 1 == 1:
                a[ind] ^= a[k]
        k += 1
        if k >= len(a):
            break
    return a[:k]


t = int(input())
for _ in range(t):
    n = int(input())
    a = [int(i) for i in input().split()]
    s = input()

    b = []
    for i in reversed(range(n)):
        if s[i] == '0':
            b = base(b + [a[i]])

        else:
            c = base(b[:] + [a[i]])
            if len(c) != len(b):
                print(1)
                break

    else:
        print(0)