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:
def kosu(kitei, aaa, tuika):
    global now_ret
    ret = 0
    n=len(kitei)
    ret2=0
    kitei.append(aaa)
    n+=1
    for i in range(n):
        if kitei[i]:
            ret2 += 1
            x = 0
            while (2**(x+1)) <= kitei[i]:
                x += 1
            for y in range(i+1, n, 1):
                if kitei[y] & (2 ** x):
                    kitei[y] ^= kitei[i]
    
    if now_ret==ret2:
        return 1
    else:
        if tuika==1:
            now_ret+=1
        return 0
 
 
def solve(n, alist, s):
    kitei=[0]
    answer=0
    for i in range(n):
        teban=s[n-i-1]
        now=alist[n-i-1]
        if teban=='0':
            if kosu(kitei, now, 1)>0:
                pass
            else:
                kitei.append(now)
        else:
            if kosu(kitei, now, 0)>0:
                pass
            else:
                answer=1
        #print(kitei)
    return answer
 
t=int(input())
for i in range(t):
    now_ret=0
    n=int(input())
    alist = list(map(int, input().split()))
    s=input()
    print(solve(n, alist, s))