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:
import sys

def solve():
    n, q = map(int, sys.stdin.readline().split())
    ds = [[i] for i in range(n)]
    n2s = [i for i in range(n)]
    ans = []

    for lp in range(q):
        c, x, y = map(int, sys.stdin.readline().split())

        if c == 0:
            merge(ds, n2s, x, y)
        else:
            ans.append(1 if n2s[x] == n2s[y] else 0)

    print(*ans, sep='\n')

def merge(ds, n2s, x, y):
    u = n2s[x]
    v = n2s[y]

    if u == v:
        return None

    if len(ds[u]) < len(ds[v]):
        ds[v].extend(ds[u])
        for w in ds[u]:
            n2s[w] = v
        del ds[u][:]
    else:
        ds[u].extend(ds[v])
        for w in ds[v]:
            n2s[w] = u
        del ds[v][:]

def debug(x, table):
    for name, val in table.items():
        if x is val:
            print('DEBUG:{} -> {}'.format(name, val), file=sys.stderr)
            return None

if __name__ == '__main__':
    solve()