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 gauss_jordan(A):
  m=len(A)
  n=len(A[0])
  rank=0
  for col in range(n):
    pivot=-1
    for row in range(rank,m):
      if A[row][col]!=0:
        pivot=row
        break
    if pivot==-1:
      continue
    A[pivot],A[rank]=A[rank],A[pivot]
    for row in range(m):
      if row!=rank and A[row][col]!=0:
        for col2 in range(n):
          A[row][col2]^=A[rank][col2]      
    rank+=1
  if rank==len(A):
    return True
  else:
    return False

def make_vector(val):
  ret=[]
  for i in range(60,-1,-1):
    if val&(1<<i):
      ret.append(1)
    else:
      ret.append(0)
  return ret

t=int(input())
for _ in range(t):
  n=int(input())
  arr=list(map(int,input().split()))
  s=input()
  if s[-1]=='1':
    print(1)
    continue
  A=[make_vector(arr[-1])]
  for i in range(n-2,-1,-1):
    vector=make_vector(arr[i])
    if gauss_jordan(A+[vector]):
      if s[i]=='1':
        print(1)
        break
      if s[i]=='0':
        A.append(vector)
  else:
    print(0)