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: Accepted)

class UnionFind
  def initialize
    @obj_to_node = {}
  end

  class UnionFind::Node
    def initialize(obj)
      @obj = obj
      @parent = self
      @rank = 0
    end

    def root
      return self if @parent == self
      @parent = @parent.root
    end  

    attr_accessor :parent, :rank
  end

  def unite(x, y)
    u = (@obj_to_node[x] ||= UnionFind::Node.new(x)).root
    v = (@obj_to_node[y] ||= UnionFind::Node.new(y)).root
    return if u == v
    if u.rank > v.rank
      v.parent = u
    elsif v.rank > u.rank
      u.parent = v
    else
      u.parent = v
      v.rank += 1
    end
  end

  def same?(x, y)
    return false unless u = @obj_to_node[x]
    return false unless v = @obj_to_node[y]
    u.root == v.root
  end
end

n, q = gets.split.map(&:to_i)
uf = UnionFind.new
q.times do
  c, x, y = gets.split.map(&:to_i)
  if c == 0
    uf.unite(x, y)
  else
    puts uf.same?(x, y) ? '1' : '0'
  end
end