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 PYTHON):

Solution:
# coding: utf-8

"""
def makeSet(x, p, rank):
    p[x] = x
    rank[x] = 0
"""

def union(x, y, p, rank):
    link( findSet(x, p, rank), findSet(y, p, rank), p, rank)
    
def findSet(x, p, rank):
    if  x != p[x] :
        p[x] = findSet(p[x], p, rank)
    return p[x]
    
def isSameSet(x, y, p, rank): # Union Find
    if findSet(x, p, rank) == findSet(y, p, rank): print 1
    else: print 0   
    
def link(x, y, p, rank):
    if  rank[x] > rank[y]:
        p[y] = x
    else:
        p[x] = y
        if  rank[x] == rank[y]  :
            rank[y] += 1

n,q = map(int,raw_input().split())
p = [i for i in range(n)] # pointer
rank = [0 for i in range(n)]
for i in range(q):
    com, x, y = map(int,raw_input().split())
    if com: # same
        isSameSet(x, y, p, rank)
    else: # unite
        union(x, y ,p , rank)