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:
# F_2 ^nの基底クラス
class F2n:
    # LISTを受け取ってbasisを生成する.(掃き出し法)
    def __init__(self,LIST):
        self.basis = []
        for ele in LIST:
            for vec in self.basis:
                ele = min(ele, vec^ele)
            if ele:
                self.basis.append(ele)
    # basisに要素eleを追加できるなら追加しTrueを返す. 追加できないなら何もせず,Falseを返す.
    def Add(self, ele):
        for vec in self.basis:
            ele = min(ele, ele^vec)
        if ele:
            self.basis.append(ele)
            return True
        else:
            return False

def solve():
    n=int(input())
    a=list(map(int,input().split()))[::-1]
    s=input()[::-1]
    h=F2n([])
    for i in range(n):
        if h.Add(a[i]):
            if s[i]=="1":
                print(1)
                return
    print(0)
t=int(input())
for _ in range(t):
    solve()