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.data = [ -1 for i in range(n) ]
    
  def root(self, x):
    if self.data[x] < 0:
      return x
    else:
      self.data[x] = self.root(self.data[x])
      return self.data[x]
    
  def same(self, l, r):
    return self.root(l) == self.root(r)
  
  def join(self, l, r):
    l = self.root(l)
    r = self.root(r)
    if l == r:
      return False
    if self.data[l] > self.data[r]:
      l, r = r, l
    self.data[l] += self.data[r]
    self.data[r] = l
    return True
  
n,q,*l = map(int,open(0).read().split())
uf = unionfind(n)
for c,x,y in zip(*[iter(l)]*3):
  if c:
    print(int(uf.same(x,y)))
  else:
    uf.join(x,y)