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 Ruby (2.7.1) (judge verdict: Wrong Answer)

t = gets.chomp.to_i
a = Array.new(t)
n = []
s = Array.new(t)

i = 0

t.times do
  n << gets.chomp.to_i
  a[i] = Array.new(n)
  s[i] = Array.new(n)
  a[i] = gets.chomp.split.map(&:to_i)
  s[i] = gets.chomp.chars
  i += 1
end

def x_or(x, a, s)
  # x ⊕ Ai
  # puts "x:#{x}, a:#{a}, s:#{s}"

  if s.to_i == 0
    # 0にしたい
    x = 0 if x ^ a === 0
  elsif s.to_i == 1
    # !0にしたい
    x = a if x ^ a === 1
  end
  x
end

k = 0
t.times do
  # 初期化
  x = 0

  i = 0
  n[k].times do
    x = x_or(x, a[k][i], s[k][i])
    # puts "x : #{x}"
    i += 1
  end

  if x == 0
    puts "0"
  else
    puts "1"
  end

  k += 1
end