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)] #基準(par = parentのpar)
    self.n   = num

  def find_set(self, x):
    if self.par[x] == x:
      return x
    else:
      self.par[x] = self.find_set(self.par[x]) #自分じゃなきゃ親を探す
      return self.par[x]

  def union(self, x, y):
    x = self.find_set(x)
    y = self.find_set(y)
    if x == y:
      return
    if self.rank[x] > self.rank[y]: #ランクの高い方に基準を合わせる
      self.par[y] = x
    else:
      self.par[x] = y
      if self.rank[x] == self.rank[y]:
        self.rank[y] += 1

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

N, Q = map(int, input().split())
uf = UnionFind(N)

for i in range(Q):
  C, X, Y = map(int, input().split())

  if C == 0:
    uf.union(X, Y)

  elif C == 1:
    print(1 if uf.same(X, Y) else 0)
  else:
    print(uf.find_set(X))

#計算量O(logn)経路圧縮とrankを用いた計算量
#-経路圧縮：葉から根へたどる際に通過したノードの親ポインタを根にする
#-rank：木を合併する際に、ノードの高さの高い方に低い方が結合しにいく

#処理の流れ
#same:  入力受け取り→親が同じ？→true/false
#unite: 高さがどっちが高いか？→高い方へ結合