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:
#! /usr/local/bin/python

class N:
	def __init__(self, n):
		self.parent = n
		self.rank = 0
		self.n = n

def find( n: int) -> N:
	if data[n].parent == n:
		return data[n]
	else:
		data[n].parent = find(data[n].parent).n
		return data[data[n].parent]

def union( a: int, b: int):
	A = find(a)
	B = find(b)
	if A.rank > B.rank:
		B.parent = A.n
	elif A.rank < B.rank:
		A.parent = B.n
	elif A.n != B.n:
		B.parent = A.n
		A.rank = A.rank + 1

# Start
n, p = input().split(" ")
data = [ N(i) for i in range(int(n))]
for i in range(int(p)):
	com, x, y = input().split(" ")
	if com == '0':
		union(int(x),int(y))
	else:
		if find(int(x)).n != find(int(y)).n:
			print(0)
		else:
			print(1)