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

class BaseXor:
    def __init__(self):
        self.size = 0
        self.base = []
    
    def base_calculate(self, x, b):
        return min(x, x ^ b)

    def make_base(self, x):
        for b in self.base:
            x = self.base_calculate(x, b)
        return x
    
    def change_base(self, x):
        for i in range(self.size):
            self.base[i] = self.base_calculate(self.base[i], x)

    def add_base(self, x):
        x = self.make_base(x)
        if x == 0:
            return False
        self.change_base(x)
        self.base.append(x)
        self.base.sort()
        self.size += 1
        return True
    
    def judge_linearly_dependent(self, x):
        for b in self.base:
            x = self.base_calculate(x, b)
        res = True if x else False
        return res

def solve(n, a, s):
    base = BaseXor()
    judge = False
    for i in range(n-1, -1, -1):
        x = s[i]
        if x == "0":
            base.add_base(a[i])
        else:
            judge = base.judge_linearly_dependent(a[i])
            if judge:
                break
    
    res = 1 if judge else 0
    return res

def main():
    t = int(input())
    ans = [0]*t
    for i in range(t):
        n = int(input())
        a = list(map(int, input().split()))
        s = input()
        res = solve(n, a, s)
        ans[i] = res
    print(*ans, sep="\n")
    
if __name__ == "__main__":
    main()