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)

#!/bin/ruby

class UnionFindTree
  def initialize(size)
    @array = Array.new(size) { |i| i }
  end

  def union(x, y)
    @array[root(x)] = root(y)
  end

  def print_same(x, y)
    puts same?(x, y) ? 1 : 0
  end

  def same?(x, y)
    root(x) == root(y)
  end

  def root(n)
    @array[n] == n ? n : root(@array[n])
  end
end

n, q = gets.split.map(&:to_i)
tree = UnionFindTree.new(n)
q.times do
  com, x, y = gets.split.map(&:to_i)
  com == 0 ? tree.union(x, y) : tree.print_same(x, y)
end