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

def findset(x,element):
    if(x != element[x]):
        element[x] = findset(element[x],element)
    return element[x]

def union(x,y,rank,element):
    link(findset(x,element),findset(y,element),rank,element)

def link(x,y,rank,element):
    if(rank[x] > rank[y]):
        element[y] = x
    else:
        element[x] = y
        if(rank[x] == rank[y]):
            rank[y]+=1

n,q = map(int, input().split());

element = [i for i in range(n)]
rank = [0 for i in range(n)]

for i in range(q):
    query,x,y = map(int, input().split());
    if(query == 0):
        union(x,y,rank,element)
    else :
        if(findset(x,element) == findset(y,element)):
            print(1)
        else:
            print(0)