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 battle
  n = gets.to_i
  a = gets.split.map!(&:to_i)
  s = gets.chomp.chars.map!(&:to_i)

  a0, a1 = a.zip(s).partition { |ai, si| si == 0 }.map! do |as|
    aa = as.map!(&:first)
    h = aa.group_by(&:bit_length)
    h.default_proc = ->(h, k) { h[k] = [] }
    h
  end

  a0max = a0.keys.max
  a1max = a1.keys.max
  if a0max < a1max
    puts 1
    return
  end

  a0max.downto(1) do |k|
    a0vals = a0[k].tap(&:uniq!)
    a1vals = a1[k].tap(&:uniq!) - a0vals

    if a0vals.empty? && !a1vals.empty?
      puts 1
      return
    end

    a0vals.combination(2) { |x, y| z = x ^ y; a0[z.bit_length] << z }
    a0vals.product(a1vals) { |x, y| z = x ^ y; a0[z.bit_length] << z }
  end

  puts 0
end

t = gets.to_i
t.times { battle }