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)

require 'set'; require 'prime'; require 'pp'
INF=Float::INFINITY; MOD=10**9+7
t = gets.chomp.to_i

def solve(index, x)
  return @memo[index][x] if @memo[index][x]
  if index == @n
    return @memo[index][x] ||= x == 0
  end
  cur = @s[index]
  num = @a[index]
  if cur
    @memo[index][x] ||= solve(index+1, x) || solve(index+1, x ^ num)
  else
    @memo[index][x] ||= !(!solve(index+1, x) || !solve(index+1, x ^ num))
  end
end

t.times do |ti|
  @n = gets.chomp.to_i
  @a = gets.chomp.split.map(&:to_i)
  @s = gets.chomp.split(//).map{|c| c == '0'}
  @memo = Array.new(@n+1){Hash.new}
  if solve(0, 0)
    puts '0'
  else
    puts '1'
  end
end