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

T=int(input())

def base(B):

    L=len(B)
    flag=1
    
    while flag:
        B.sort(reverse=True)
        
        flag=0

        for i in range(L):
            for j in range(i+1,L):
                if B[i]^B[j]<B[i]:
                    B[i]=B[i]^B[j]
                    flag=1
                    break
            if flag:
                break
    return B     

def rep(x):
    flag=1

    while flag:
        flag=0
        for b in B:
            if b^x<x:
                x=b^x
                flag=1
                break
    return x

for tests in range(T):
    N=int(input())
    A=list(map(int,input().split()))
    B=[]
    S=input().strip()

    flag=1

    for i in range(N-1,-1,-1):
        if flag==0:
            break
        if S[i]=="0":
            v=rep(A[i])

            if v==0:
                continue
            B.append(v)
            B=base(B)

        else:
            if rep(A[i])!=0:
                print(1)
                flag=0
                break

    if flag:
        print(0)