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:
printn = lambda x: print(x,end='')
inn = lambda : int(input())
inl   = lambda: list(map(int, input().split()))
inm   = lambda:      map(int, input().split())
ins = lambda : input().strip()
DBG = True # and False
BIG = 10**18

def ddprint(x):
  if DBG:
    print(x)

def cover0(c,d):
    m = len(c)
    for i in range(m):
        if c[i]==0:
            continue
        k = -1
        for j in range(62):
            b = 1<<j
            if c[i]&b != 0:
                k = j
                break
        for j in range(i+1,m):
            if c[j]&b != 0:
                c[j] ^= c[i]
        for j in range(len(d)):
            if d[j]&b != 0:
                d[j] ^= c[i]
    return sum(d)==0

t = inn()
for tt in range(t):
    n = inn()
    a = inl()
    s = ins()
    top = n
    to0 = []
    to1 = []
    done = False
    while top>0:
        prev0 = top
        while top>0 and s[top-1]=='0':
            top -= 1
        top0 = top
        to0.extend(a[top0:prev0])
        prev1 = top
        while top>0 and s[top-1]=='1':
            top -= 1
        top1 = top
        to1.extend(a[top1:prev1])
        cc = [x for x in to0]
        dd = [x for x in to1]
        if not cover0(cc,dd):
            print(1)
            done = True
            break
    if not done:
        print(0)