Problem:
Disjoint Set

Write a program which manipulates a disjoint set S = {S1, S2, . . . , Sk}.

First of all, the program should read an integer n, then make a disjoint set where each element consists of 0, 1, ... n−1 respectively.

Next, the program should read an integer q and manipulate the set for q queries. There are two kinds of queries for different operations:

unite(x, y): unites sets that contain x and y, say Sx and Sy, into a new set.

same(x, y): determine whether x and y are in the same set.

Input

n q
com1 x1 y1
com2 x2 y2
...
comq xq yq

In the first line, n and q are given. Then, q queries are given where com represents the type of queries. '0' denotes unite and '1' denotes same operation.

Output

For each same operation, print 1 if x and y are in the same set, otherwise 0, in a line.

Constraints

1 ≤ n ≤ 10000

1 ≤ q ≤ 100000

x ≠ y

Sample Input

5 12
0 1 4
0 2 3
1 1 2
1 3 4
1 1 4
1 3 2
0 1 3
1 2 4
1 3 0
0 0 4
1 0 2
1 3 0

Sample Output

0
0
1
1
1
0
1
1

Solution in Ruby (judge verdict: Time Limit Exceeded)

class Factor
  attr_reader :id
  def initialize(id)
    @id = id
    @parent = self
  end

  def union
    if @parent != self
      @parent.union
    else
      self
    end
  end

  def unite(other)
    @parent.union.unite(other.union) if @parent != self
    @parent = other.union
  end

  def same(other)
    if union == other.union
      puts 1
    else
      puts 0
    end
  end

  def ==(other)
    @id == other.id
  end
  
end
class String
  def com(x, y)
    x.send(self, y)
  end
end
def main
  n, q = gets.split(" ").map(&:to_i)
  array = Array.new(n){|i|Factor.new(i)}
  comand = ["unite", "same"]
  q.times do
    arg = gets.split(" ").map(&:to_i)
    comand[arg[0]].com(array[arg[1]], array[arg[2]])
  end
end
main