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)

# https://onlinejudge.u-aizu.ac.jp/courses/library/3/DSL/1/DSL_1_A

class UnionFindWithRank
  def initialize(n)
    @parent = Array.new(n, -1)
    @rank = Array.new(n, 0)
    @size = n
  end

  def root(x)
    raise "UnionFindWithRank::IndexError" if x < 0 || @size <= x
    return x if @parent[x] == -1
    @parent[x] = root(@parent[x])
    return @parent[x]
  end

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

  def merge(x, y)
    x, y = root(x), root(y)
    return false if x == y
    x, y = y, x if @rank[x] < @rank[y]
    @rank[x] += 1 if @rank[x] == @rank[y]
    @parent[y] = x
    return true
  end
end

n, q = gets.split.map(&:to_i)
uf = UnionFindWithRank.new(n)
ans = []
q.times do |i|
  com, x, y = gets.split.map(&:to_i)
  if com == 0
    uf.merge(x, y)
  else
    ans << (uf.same?(x, y) ? 1 : 0)
  end
end
puts ans