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 UnionFindTree:
  def __init__(self, n: int):
    self.__parent = [i for i in range(n)]
    self.__rank = [0 for i in range(n)]

  def unite(self, x, y):
    self.__link(self.__find_set(x), self.__find_set(y))

  def same(self, x, y):
    return self.__find_set(x) == self.__find_set(y)

  def __find_set(self, x):
    if x != self.__parent[x]:
      self.__parent[x] = self.__find_set(self.__parent[x])
    return self.__parent[x]

  def __link(self, x, y):
    if self.__rank[x] < self.__rank[y]:
      self.__parent[x] = y
    else:
      if self.__rank[x] == self.__rank[y]:
        self.__rank[x] += 1
      self.__parent[y] = x


N, Q = map(int, input().split())
t = UnionFindTree(N)
for i in range(Q):
  command, x, y = map(int, input().split())
  if command == 0:
    t.unite(x, y)
  if command == 1:
    if t.same(x, y):
      print(1)
    else:
      print(0)