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: Time Limit Exceeded)

def xor(a, b)
  bigger = a < b ? b : a
  size = bigger.to_s(2).length
  as = a.to_s(2).rjust(size, '0').chars
  bs = b.to_s(2).rjust(size, '0').chars
  as.zip(bs).map do |ai, bi|
    ai == bi ? '0' : '1'
  end.join.to_i(2)
end

t = gets.to_i
t.times do
  n = gets.to_i
  a = gets.split.map(&:to_i)
  list_zero = []
  list_one = []
  s = gets.chop.chars
  if s.last == '1'
    puts 1
    next
  end
  s.each.with_index do |c, idx|
    case c
    when '0'
      list_zero.push(a[idx])
    when '1'
      list_one.push(a[idx])
    end
  end

  zero_avalables = []
  (1..list_zero.length).each do |zn|
    zero_avalables << list_zero.combination(zn).map{_1.inject(0){ |acc, cur| xor(acc, cur) }}
  end
  puts list_one.all?{ zero_avalables.flatten.include?(_1) } ? '0' : '1'
end