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, num):
    self.rank = [0]*num
    self.par = [i for i in range(num)]
    self.n = num
    self.size = [1]*num
  
  def find(self, x):
    if self.par[x] == x:
      return x
    else:
      self.par[x] = self.find(self.par[x])
      return self.par[x]
    
  def union(self, x, y):
    x = self.find(x)
    y = self.find(y)
    if x == y:
      return 
    if self.rank[x] > self.rank[y]:
      self.par[y] = x
      self.size[x] += self.size[y]
      self.size[y] = 0
    else:
      self.par[x] = y
      self.size[y] += self.size[x]
      self.size[x] = 0
      if self.rank[x] == self.rank[y]:
        self.rank[y] += 1
    
  def same(self, x, y):
    return self.find(x) == self.find(y)
  
  def all_find(self):
    ls = []
    for i in range(len(self.par)):
      ls.append(self.find(i))
    return ls
    
n, q = map(int, input().split())

uf = UnionFind(n)

for _ in range(q):
  com, x, y = map(int, input().split())

  if com == 0:
    uf.union(x, y)
  else:
    print(int(uf.same(x,y)))