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 typing import Union, List
import sys

sys.setrecursionlimit(100000)

# 木の根を返す
def find(x: int, S: List[int]) -> int:
    if S[x] == x:
        return x
    else:
        S[x] = find(S[x], S)
        return S[x]

# xとyが同じ集合に属すかの判定
def same(x: int, y: int, S: List[int]) -> bool:
    return find(x, S) == find(y, S)

# xとyの属する集合を結合
def unite(x: int, y: int, S: List[int]) -> None:
    rx = find(x, S)
    ry = find(y, S)
    if rx == ry:
        return None
    else:
        S[rx] = ry

if __name__ == '__main__':
    [n, q] = [int(i) for i in input().split()]

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

    for i in range(q):
        [com, x, y] = [int(i) for i in input().split()]
        if com == 0:
            unite(x, y, S)
        elif com == 1:
            if same(x, y, S):
                print('1')
            else:
                print('0')
        else:
            raise ValueError('value error')