Problem: 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.

Constraints

* 1 ≤ n ≤ 10000
* 1 ≤ q ≤ 100000
* x ≠ y

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.

Example

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


Output

0
0
1
1
1
0
1
1

Solution (in PYTHON3):

Solution:
class UnionFind:
  def __init__(self, n):
    self.parent = [i for i in range(n)]
    self.height = [0 for i in range(n)]
        
  def get_root(self, i):
    if self.parent[i] == i:
      return i
    else:
      self.parent[i] = self.get_root(self.parent[i])
      return self.parent[i]
            
  def unite(self, i, j):
    root_i = self.get_root(i)
    root_j = self.get_root(j)
    if root_i != root_j:
      if self.height[root_i] < self.height[root_j]:
        self.parent[root_i] = root_j
      else:
        self.parent[root_j] = root_i
        if self.height[root_i] == self.height[root_j]:
          self.height[root_i] += 1
                
  def is_in_group(self, i, j):
    if self.get_root(i) == self.get_root(j):
      return 1
    else:
      return 0

n, q = map(int, input().split())
uf = UnionFind(n)
for i in range(q):
  a, b, c = map(int, input().split())
  if(a == 0):
    uf.unite(b, c)
  else:
    print(uf.is_in_group(b, c))