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:
T = int(input())

def hakidasi(L):
  n = len(bin(max(L))) - 2
  k, end = 0, len(L)
  for i in range(n - 1, -1, -1):
    for j in range(k, end):
      if (L[j] >> i) & 1:
        L[k], L[j] = L[j], L[k]
        break
    else:
      continue
    k += 1
    for j in range(end):
      if j == k - 1: continue
      if (L[j] >> i) & 1:
        L[j] ^= L[k - 1]
  return L

def judge(L, x):
  if L == []:
    return False
  n = len(bin(max(L))) - 2
  m = len(L)
  for i in range(m):
    a = len(bin(x))
    b = len(bin(L[i]))
    if a == b:
      x ^= L[i]
    elif a > b:
      return False
    if x == 0:
      return True
  return False

def main():
  N = int(input())
  A = list(map(int, input().split()))
  S = input()
  U = 60
  
  L = []
  for i in range(N - 1, -1, -1):
    if A[i] == 0:
      continue
    n = int(S[i])
    if n == 0:
      L.append(A[i])
      L = hakidasi(L)
      if L[-1] == 0:
        L.pop()
    else:
      m = judge(L, A[i])
      if m == False:
        return 1
  return 0

for i in range(T):
  print(main())