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)

_, Q = gets.split.map &:to_i
$parent = []

def trace_parent i
  stack = []
  t = i
  while $parent[t]
    stack << t
    t = $parent[t]
  end
  stack.each{|e|
    $parent[e] = t
  }
  t
end

Q.times{
  com, s, t = gets.split.map &:to_i
  if com == 0
    if $parent[s] == nil
      if $parent[t] == nil
        $parent[t] = s
      else
        root = trace_parent t
        $parent[s] = root unless s == root
      end
    elsif $parent[t] == nil
      root = trace_parent s
      $parent[t] = root unless t == root
    else
      s_root = trace_parent s
      t_root = trace_parent t
      $parent[t_root] = s_root unless s_root == t_root
    end
  else
    puts trace_parent(s) == trace_parent(t) ? 1 : 0
  end
}