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 DisjointSet
  def initialize(n)
    @rank = Array.new(n){0}
    @p = (0...n).to_a
  end

  def same(x, y)
    find_set(x) == find_set(y)
  end

  def unite(x, y)
    link(find_set(x), find_set(y))
  end

  def link(x, y)
    if @rank[x] > @rank[y]
      @p[y] = x
    else
      @p[x] = y

      if @rank[x] == @rank[y]
        @rank[y] += 1
      end
    end
  end

  def find_set(x)
    @p[x] = find_set(@p[x]) if x != @p[x]
    @p[x]
  end
end

n, q = gets.split.map(&:to_i)

ds = DisjointSet.new(n)

(0...q).each do |i|
  t, a, b = gets.split.map(&:to_i)

  if t == 0
    ds.unite(a, b)
  elsif t == 1
    puts ds.same(a, b) ? 1 : 0
  end
end