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)

### SNIPPET
  # n = gets.split.map(&:to_i)
  # array = n.times.map { gets.split.map(&:to_i) }
  # [].all?(&:even?)
  # a = [*1..m].repeated_combination(n).to_a
  # [1,2,3,4,5].select { |num| num.even? }  # => [2, 4]
  # ["a","a","b"].group_by(&:itself).map{|k,v| [k, v.count]}.to_h #=> {"a"=>2, "b"=>1}
  # 切り捨て: .floor(2).to_f ,切り上げ： .ceil(2).to_f,四捨五入: round(2)
  # 3.upto(6) do |i|, 6.downto(3) do |i|
  # 公約数125.gcd(100)、公倍数125.lcm(100)
  # PI = Math::PI
  # 高さ = a * Math.sin(w / 180.0 * Math::PI), 底辺 = a * Math.cos(w / 180.0 * Math::PI)
  # def chmax(a, b) a > b ? a : b end
  # INF = Float::INFINITY
  # def chmin(a, b) a < b ? a : b end
DEBUG = false

t = gets.to_i

n = []
a = []
s = []
t.times do
  n << gets.to_i
  a << gets.split.map(&:to_i)
  s << gets.chomp.split("").map(&:to_i)
end

t.times do |i|
  x = 0
  ary = a[i]
  s[i].each_with_index do |player,index|
    if DEBUG
      puts "---"
      puts "x: #{x}"
      puts "player: #{player}"
      puts "ary[index]: #{ary[index]}"
    end
    if player == 0
      if x ^ ary[index] == 0
        x = x ^ ary[index]
      end
    elsif player == 1
      if x ^ ary[index] != 0
        x = x ^ ary[index]
      end
    end
    if DEBUG
      puts "change x: #{x}"
    end

  end

  puts x == 0 ? 0 : 1 
end