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

f_i = sys.stdin

n, q = map(int, f_i.readline().split())

S = set([frozenset([i]) for i in range(n)])

def unite(sets, v1, v2):
    s1 = None
    s2 = None
    for s in sets:
        if v1 in s and v2 in s:
            return None
        elif v1 in s:
            s1 = s
        elif v2 in s:
            s2 = s
        if s1 and s2:
            break
    sets.discard(s1)
    sets.discard(s2)
    s3 = s1.union(s2)
    sets.add(s3)

def same(sets, v1, v2):
    for s in sets:
        if v1 in s and v2 in s:
            print(1)
            break
        elif v1 in s or v2 in s:
            print(0)
            break

for l in f_i:
    com, x, y = map(int, l.split())
    if com == 0:
        unite(S, x, y)
    else:
        same(S, x, y)