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)

# coding: utf-8
class UnionFind
  attr :id, :rank

  def initialize(n)
    @id   = (0..n).to_a
    @rank = Array.new(n,0)
  end

  def root(i)
    if @id[i] == i or i == @id[@id[i]]
      i
    else
      @id[i] = root(@id[i])
      @id[i]
    end
  end

  # find, check if p and q has the same root
  def same?(p, q)
    root(p) == root(q)
  end

  # union, to merge components containing p and q
  # set id of p's root to the id of q's root
  def unite(p, q)

    i = root(p)
    j = root(q)

    return if i == j

    if @rank[i] < @rank[j]
      @id[i] = j
    else
      @id[j] = i;
      @rank[i]+=1  if @rank[i] == @rank[j]
    end
  end
end


lines = $stdin.read
array = lines.split("\n")

n = array[0].split(" ")[0].to_i
q = array[0].split(" ")[1].to_i

un = UnionFind.new(n)

for i in 1..q
  com = array[i].split(" ")[0]
  x   = array[i].split(" ")[1].to_i
  y   = array[i].split(" ")[2].to_i

  if com == '0'
    # unite(4,3) id[4] = 3, 4の頭を3にする
    un.unite(x, y)
  else
    # same
    puts un.same?(x, y) ? "1" : "0"
  end
end