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:
import sys
input = sys.stdin.readline
sys.setrecursionlimit(pow(10, 6))


class UnionFind:
  def __init__(self, size):
    self.size = size
    self.parent = [i for i in range(size)]
    self.size = [1 for _ in range(size)]
    self.height = [1 for _ in range(size)]

  def root(self, i):
    if i != self.parent[i]:
      self.parent[i] = self.root(self.parent[i])
    return self.parent[i]

  def union(self, i, j):
    pi, pj = self.root(i), self.root(j)
    if pi == pj:
      return
    if self.height[pi] < self.height[pj]:
      self.parent[pi] = pj
      self.size[pj] += self.size[pi]
    else:
      self.parent[pj] = pi
      self.size[pi] += self.size[pj]
      if self.height[pi] == self.height[pj]:
        self.height[pi] += 1

  def is_same(self, i, j):
    return self.root(i) == self.root(j)


def main():
  n, q = map(int, input().split())
  uf = UnionFind(n)
  for _ in range(q):
    c, x, y = map(int, input().split())
    if c == 1:
      if uf.is_same(x, y):
        print(1)
      else:
        print(0)
    else:
      uf.union(x, y)


if __name__ == '__main__':
  main()