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:
#!python3

import sys
iim = lambda: map(int, sys.stdin.readline().rstrip().split())

X = (10**18).bit_length()

def f(a, s, n):
    if s[-1] == "1":
        return 1

    B = [None] * X
    for i in range(n-1, -1, -1):
        ai, si = a[i], s[i]

        if si == "0":
            while True:
                x = ai.bit_length() - 1
                if B[x] == ai: break
                elif B[x] == None:
                    B[x] = ai
                    break
                ai ^= B[x]
        else:
            while True:
                x = ai.bit_length() - 1
                if B[x] == ai: break
                elif B[x] == None:
                    return 1
                ai ^= B[x]
    return 0


def resolve():
    T = int(input())

    ans = []
    for i in range(T):
        N = int(input())
        A = list(iim())
        S  = input()

        ans.append(f(A, S, N))

    print(*ans, sep="\n")

if __name__ == "__main__":
    resolve()