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:
from collections import deque

def get_input():
  return list(map(int, input().split(' ')))

(n, q) = get_input()

d = [] # [{i} for i in range(n)]

for _ in range(q):
  c = get_input()
  if c[0] == 0: # unite(x, y)
    i1 = None
    i2 = None
    for i in range(len(d)):
      s = d[i]
      if c[1] in s or c[2] in s:
        if i1 != None:
          i2 = i
          d[i1] = d[i1] | s
          d.pop(i2)
          break
        else:
          i1 = i
    if i1 == None:
      d.append({c[1],c[2]})
    elif i2 == None:
      d[i1] = d[i1] | {c[1],c[2]}
  elif c[0] == 1: # same(x, y)
    p = False
    for s in d:
      if c[1] in s or c[2] in s:
        if c[1] in s and c[2] in s:
          print(1)
        else:
          print(0)
        p = True
        break
    if not p:
      print(0)