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)

def makeSet(x)
  $ps << x
  $rank << 0
end
def union(x,y)
  link(findSet(x), findSet(y))
end
def link(x,y)
  if $rank[x] > $rank[y]
    $ps[y] = x
  else
    $ps[x] = y
    if $rank[x] == $rank[y]
      $rank[y] = $rank[y] + 1
    end
  end
end
def findSet(x)
  if x != $ps[x]
    $ps[x] = findSet($ps[x])
  end
  return $ps[x]
end
$ps = []
$rank = []

n,q = gets.split.map(&:to_i)
n.times{|i|
  makeSet(i)
}
q.times{|i|
  com, x, y = gets.split.map(&:to_i)
  if com == 0
    union(x,y)
  elsif com == 1
    puts findSet(x) == findSet(y) ? "1" : "0"
  end
}