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 init(N, parent, rank):
    for i in range(N):
        parent.append(i)
        rank.append(0)
    return parent, rank

def find(parent, v):
    if parent[v] == v:
        return v
    else:
        parent[v] = find(parent, parent[v])
        return parent[v]

def unite(parent, rank, a, b):
    a = find(parent, a)
    b = find(parent, b)
    if a == b:
        return 
    elif rank[a] < rank[b]:
        parent[a] = b
        return parent
    elif rank[a] > b:
        parent[b] = a
        return parent
    else:
        parent[b] = a
        rank[a] += 1
        return parent, rank

def union_find():
    N, Q = [int(i) for i in input().split()]
    parent = []
    rank = []
    init(N, parent, rank)
    for i in range(Q):
        P, A, B = [int(i) for i in input().split()]
        if P == 0:
            unite(parent, rank, A, B)
        else:
            a = find(parent, A)
            b = find(parent, B)
            if a == b:
                print("1")
            else:
                print("0")

if __name__ == "__main__":
    union_find()