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 UF():
  def __init__(self, N):
    self.parents = [-1] * N

  def find(self, n):
    if self.parents[n] < 0:
      return n
    else:
      self.parents[n] = self.find(self.parents[n])
      return self.parents[n]

  def union(self, u,v):
    p1,p2 = self.find(u),self.find(v)
    if p1==p2: return
    if p1 > p2:
      p1,p2 = p2,p1
    self.parents[p1] += self.parents[p2]
    self.parents[p2] = p1

  def same(self, u,v):
    return self.find(u) == self.find(v)

n,q = map(int,input().split())
uf = UF(n)
for _ in range(q):
  i,u,v = map(int,input().split())
  if i==0:
    uf.union(u,v)
  else:
    if uf.same(u,v):
      print(1)
    else:
      print(0)