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 slv(n,a,s):
  base=[0]
  for i in range(n-1,-1,-1):
    v=a[i]
    for j in sorted(base,reverse=True):
      v=min(v,j^v)
    if v==0:
      pass
    else:
      if s[i]=='0':base.append(v)
      if s[i]=='1':return 1
  if base:return 0
  return 1

t=int(input())
n=[]
a=[]
s=[]
for _ in range(t):
  n.append(int(input()))
  a.append(list(map(int,input().split())))
  s.append(input())
for i in range(t):
  print(slv(n[i],a[i],s[i]))