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:
import sys
input = sys.stdin.readline

def standard_form(A):
    C = A[:]
    L = 60
    E = []
    ids = []
    for i in range(L):
        e = j0 = None
        mask = (1 << i)-1
        for j, a in enumerate(C):
            if (a >> i) & 1 and (a & mask) == 0:
                e = a
                j0 = j
                break
        else:
            continue
        ids.append(j0)
        for j, a in enumerate(C):
            if j0 == j:
                continue
            if (a >> i) & 1:
                C[j] ^= e
    return [C[e] for e in ids]


t = int(input())
for _ in range(t):
    n = int(input())
    a = list(map(int, input().split()))
    s = input()
    A = []
    B = []

    task = set([0])

    now = s[n-1]
    if now == "1":
        print(1)
        continue


    q = []
    win = "0"
    for i in range(n-1, -1, -1):
        if now == "0":
            if s[i] == "0":
                q.append(a[i])
            else:
                q = standard_form(q)
                task = task | set(q)
                task = set(standard_form(list(task)))
                q = [a[i]]
                now = "1"
        else:
            if s[i] == "1":
                q.append(a[i])
            else:
                q = standard_form(q)
                q = set(q) | task
                q = set(standard_form(list(q)))
                if task != task | q:
                    win = "1"
                    break

                q = [a[i]]
                now = "0"

    if now == "1":
        q = standard_form(list(q))
        q = set(q) | task
        q = standard_form(list(q))
        q = set(q)
        if task != task | q:
            win = "1"

    print(win)