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 union(x, y):
    link(findSet(x), findSet(y))

def link(x, y):
    if r[x] > r[y]:
        p[y] = x
    else:
        p[x] = y
        if r[x] == r[y]: r[y] = r[y] + 1

def findSet(x):
    if x != p[x]:
        p[x] = findSet(p[x])
    return p[x]


if __name__ == '__main__':

    p = [];
    r = [];

    n_set, n_quare = map(int, input().split())

    for i in range(n_set):
        p.append(i)
        r.append(0)


    for i in range(n_quare):
        q, x, y = map(int, input().split())

        if q == 0:
            union(x, y)

        else:
            print(int(findSet(x) == findSet(y)))