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:

def search_root(x):
    i = x
    while True:
        if i == nodes[i]:
            nodes[x] = i
            return i
        else:
            i = nodes[i]

def unite(x,y):
    nodes[search_root(x)] = search_root(y)

def same(x,y):
    if search_root(x) == search_root(y):
        print(1)
    else:
        print(0)


n, q = map(int, input().split())
nodes = [i for i in range(n)]
commands = []
for _ in range(q):
    commands.append(input())
for cmd in commands:
    c,x,y = map(int,cmd.split())
    if c == 0:
        unite(x,y)
    else:
        same(x,y)