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 matmul(a, b, mod):
    m = len(a)
    l = len(a[0])
    n = len(b[0])
    ret = [[0] * n for _ in range(m)]
    for i in range(m):
        for j in range(n):
            e = 0
            for k in range(l):
                e = (e + a[i][k] * b[k][j]) % 2
            ret[i][j] = e
    return ret

def calc(X, v, r):
    rr = 0
    for i in range(r, D):
        if v[i][0] == 1:
            rr = i
            break
    v[rr], v[r] = v[r], v[rr]
    X[rr], X[r] = X[r], X[rr]
    for i in range(D):
        if i == r or v[i][0] == 0:
            continue
        for c in range(D):
            X[i][c] = (X[i][c] + X[r][c]) % 2

T = int(input())
D = 64
for _ in range(T):
    N = int(input())
    A = list(map(int, input().split()))
    S = input().rstrip()
    X = [[int(i == j) for j in range(D)] for i in range(D)]
    r = 0
    for i in range(N)[::-1]:
        v = [[A[i] >> j & 1] for j in range(D)]
        if S[i] == '0':
            v = matmul(X, v, 2)
            if any(v[j][0] == 1 for j in range(r, D)):
                calc(X, v, r)
                r += 1
        else:
            v = matmul(X, v, 2)
            if any(v[j][0] == 1 for j in range(r, D)):
                print(1)
                break
    else:
        print(0)