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
def judge(mat,x,pivot):
  b = x.bit_length()
  cnt = 0
  for i in range(b)[::-1]:
    if x&1<<i:
      if i not in pivot:
        return False
      for j in range(cnt,len(mat)):
        if mat[j]&1<<i:
          x ^= mat[j]
          cnt = j+1
          break
  if x == 0:
    return True
  else:
    return False
def add(mat,x,pivot):
  b = x.bit_length()
  cnt = 0
  for i in range(b)[::-1]:
    if x&1<<i:
      if i in pivot:
        for j in range(cnt,len(mat)):
          if mat[j]&1<<i:
            x ^= mat[j]
            cnt = j+1
            break
      else:
        pivot.add(i)
        for j in range(len(mat)):
          if mat[j] < x:
            mat.insert(j,x)
            for k in range(i)[::-1]:
              if mat[j]&1<<k and k in pivot:
                for l in range(j+1,len(mat)):
                  if mat[l]&1<<k:
                    mat[j] ^= mat[l]
            x = mat[j]
            break
        else:
          mat.append(x)
        for j in range(len(mat)):
          if mat[j] > x and mat[j]&1<<i:
            mat[j] ^= x
        break
t = int(input())
for _ in range(t):
  n = int(input())
  a = list(map(int,input().split()))
  s = input().rstrip()
  pivot = set()
  mat = []
  for i in range(n)[::-1]:

    x = a[i]
    if s[i] == "0":
      if judge(mat,x,pivot):
        continue
      else:
        add(mat,x,pivot)
    else:
      if judge(mat,x,pivot):
        continue
      else:
        print(1)
        break
  else:
    print(0)