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:
# -*- coding: utf-8 -*-
import sys
sys.setrecursionlimit(10000)

N, Q = tuple(map(int, input().split()))

tree = [[-1, 1]  for _ in range(N)] # [next, rank]

def find(i):
    if tree[i][0] == -1:
        group = i
    else:
        group = find(tree[i][0])    
    return group

def unite(x, y):
    px = find(x)
    py = find(y)
    
    if tree[px][1] == tree[py][1]: # rank is same
        tree[py][0] = px
        tree[px][1] += 1
    else:
        if tree[px][1] < tree[py][1]:
            px, py = py, px
        tree[py][0] = px

for _ in range(Q):
    com, x, y = tuple(map(int, input().split()))
    if com: # same
        print(int(find(x) == find(y)))
    else: # unite
        if not int(find(x) == find(y)):
            unite(x, y)