Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

3
2
1 2
10
2
1 1
10
6
2 3 4 5 6 7
111000

Sample Output 1

1
0
0

In the first test case, if Person 1 replaces x with 0 \oplus 1=1, we surely have x \neq 0 at the end of the game, regardless of the choice of Person 0.

In the second test case, regardless of the choice of Person 1, Person 0 can make x=0 with a suitable choice.

Solution in Python (3.8.2) (judge verdict: Time Limit Exceeded)

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

for ti in range(t):
  n,a,s = ls[ti]
  z = set()
  o = set()
  for i in range(n):
    if s[i] == "0":
      tmp = set()
      for e in z:
        tmp.add(a[i]^e)
      z = z | tmp
      z.add(a[i])
      #print("z: {}".format(z))
    if s[i] == "1":
      tmp = set()
      for e in o:
        tmp.add(a[i]^e)
      o = o | tmp
      o.add(a[i])
      #print("o: {}".format(o))
  #print(o)
  #print(z)
  #print(o <= z)
  if o<=z:
    print(0)
  else:
    print(1)