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:
#!python3

import sys
iim = lambda: map(int, input().rstrip().split())

def resolve():
    N, Q = iim()

    S = [[i] for i in range(N)]

    def find(i):
        x = S[i]
        while True:
            k = S[i][0]
            if k == i:
                x[0] = i
                return i
            S[i] = x
            i = k
    def union(i, j):
        ai = find(i)
        aj = find(j)
        if ai != aj:
            S[aj][0] = S[ai][0]
            S[aj] = S[ai]

    def same(i, j):
        ai = find(i)
        aj = find(j)
        return ai == aj

    ans = []
    for com, x, y in (map(int, line.split()) for line in sys.stdin):

        if com == 0:
            union(x, y)
            #print(x, y, *tuple(map(lambda x: (x, hex(id(x))[-4:]), S)))
        elif com == 1:
            ans.append(1 if same(x, y) else 0)
        else:
            raise 1
    print(*ans, sep="\n")


if __name__ == "__main__":
    resolve()