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:
from sys import stdin


class DisjointSet():
    def __init__(self):
        self.parent = None
        self.ancestor = self


def ancestor(elems, x):
    s = elems[x].ancestor
    while s.parent is not None:
        s = s.parent
    elems[x].ancestor = s
    return s


def unite(elems, x, y):
    ax = ancestor(elems, x)
    ay = ancestor(elems, y)
    if ax is not ay:
        parent = DisjointSet()
        ax.parent = ay.parent = parent


def same(elems, x, y):
    return ancestor(elems, x) is ancestor(elems, y)


def main():
    n, q = [int(x) for x in input().split()]
    elems = [DisjointSet() for _ in range(n)]

    for _ in range(q):
        com, x, y = [int(x) for x in input().split()]
        if com == 0:
            unite(elems, x, y)
        else:
            print(1 if same(elems, x, y) else 0)


if __name__ == '__main__':
    main()