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
input = sys.stdin.readline
def root(s):
    global pa
    if pa[s] == s:
        return s
    pa[s] = p = root(pa[s])
    return p

def unite(s, t):
    global pa
    a = root(s);b = root(t)
    if a == b:
        return 1
    elif rank[a] == rank[b]:
        pa[b] = a
        rank[a] += 1
    else:
        if rank[a] < rank[b]:
            pa[a] = b
        else:
            pa[b] = a

n, q = map(int, input().split())
pa = [i for i in range(n)]
rank = [1]*n
for i in range(q):
    a, b, c = map(int, input().split())
    if a == 0:unite(b,c)
    else:
        if root(b) == root(c):
            print(1)
        else:print(0)