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:
def fg(x):
    if g[x] == x:
        return x
    re = fg(g[x])
    g[x] = re
    return re


def kg(x, y):
    x = fg(x)
    y = fg(y)
    if d[y] > d[x]:
        g[x] = y
    else:
        g[y] = x
    if d[x] == d[y]:
        d[x] += 1


n, q = map(int, input().split())
d = [0] * n
g = [x for x in range(n)]
for _ in range(q):
    c, x, y = map(int, input().split())
    if c:
        print((fg(x) == fg(y))*1)
    else:
        kg(x, y)