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 PYTHON):

Solution:
#!/usr/bin/env python
from __future__ import division, print_function
from sys import stdin


def main():
    n, q = (int(s) for s in stdin.readline().split())
    s = [{i} for i in range(n)]

    for _ in range(q):
        com, x, y = (int(s) for s in stdin.readline().split())
        if com:
            if x in s[x] and y in s[x]:
                print(1)
            else:
                print(0)
        else:
            a = s[x]
            b = s[y]
            if a is not b:
                a |= b
                for i in a:
                    s[i] = a


main()