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:
n, q = map(int, input().split(" "))
parent = [i for i in range(n)]
rank = [0] * len(parent)

def root(s):
    if parent[s] == s:
        return s
    else:
        parent[s] = root(parent[s])
        return parent[s]

def same(s1, s2):
    if root(s1) == root(s2):
        print("1")
    else:
        print("0")

def unite(s1, s2):
    s1 = root(s1)
    s2 = root(s2)

    if s1 == s2:
        return

    if rank[s1] < rank[s2]:
        parent[s1] = s2
    else:
        parent[s2] = s1
        if rank[s1] == rank[s2]:
            rank[s1] += 1

for i in range(q):
    query, item1, item2 = input().split(" ")
    item1, item2 = int(item1), int(item2)

    if query == "0":
        unite(item1, item2)
    else:
        same(item1, item2)