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: Wrong Answer)

class Disjoint_set
  attr_accessor :next, :me, :rank
  def initialize(n,m)
    @next = n
    @me = m
    @rank = 0
  end
  def find_set(x)
    temp = x
    if x != $ps[x].next
      temp = $ps[$ps[x].next].find_set($ps[x].next)
    end
    return temp
  end
  def print_all()
    puts "next:#{@next}"
    puts "me:#{@me}"
    puts "rank:#{@rank}"
    puts
  end
end
def union(xroot, yroot)
  if $ps[xroot].rank < $ps[yroot].rank
    $ps[yroot].next = xroot
  else
    $ps[xroot].next = yroot
    if $ps[xroot].rank == $ps[yroot].rank
      $ps[yroot].rank+=1
    end
  end
end
$ps = []
n,q = gets.split.map(&:to_i)
n.times{|i|
  $ps << Disjoint_set.new(i,i)
}
q.times{|i|
  com, x, y = gets.split.map(&:to_i)

  xroot = $ps[x].find_set(x)
  yroot = $ps[y].find_set(y)

  if com == 0
    if xroot != yroot
      union(x, y)
    end
#    $ps[x].print_all
#    $ps[y].print_all
  else
#    puts "xroot:#{xroot}"
#    puts "yroot:#{yroot}"

    if xroot == yroot
      puts "1"
    else
      puts "0"
    end
  end
}