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 = lambda : sys.stdin.readline().rstrip()
sys.setrecursionlimit(max(1000, 10**9))
write = lambda x: sys.stdout.write(x+"\n")


class BaseF2:
    def  __init__(self, vs=None):
        """vs: list of vecotr in F2
        """
        self.base = []
        if vs is not None:
            for v in vs:
                tmp = v
                for u in self.base:
                    tmp = min(tmp, tmp^u)
                if tmp>0:
                    self.base.append(tmp)
    def insert(self, v):
        for u in self.base:
            v = min(v, v^u)
        if v>0:
            self.base.append(v)
    def check(self, v):
        for u in self.base:
            v = min(v, v^u)
        return v==0
    def clear(self):
        self.base = []
    
    
t = int(input())
for _ in range(t):
    n = int(input())
    a = list(map(int, input().split()))
    s = input()
    b0 = BaseF2()
    b1 = BaseF2()
    done = False
    for i in range(n-1, -1, -1):
        if s[i]=="1":
            b1.insert(a[i])
        else:
            b0.insert(a[i])
        for item in b1.base:
            if not b0.check(item):
                print(1)
                done = True
                break
        if done:
            break
    else:
        print(0)