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
input = sys.stdin.readline

class UnionFind:
    N = 0
    cost = 0
    par = []
    
    def init(N):
        UnionFind.N = N
        UnionFind.par = [i for i in range(N)]

    def find(v):
        c = 0
        u = v
        while v != UnionFind.par[v]:
            v = UnionFind.par[v]
            c += 1

        if c > 10:
            while u != v: u, UnionFind.par[u] = UnionFind.par[u], v

        return v

    def union(v, u, c=0):
        vr = UnionFind.find(v)
        ur = UnionFind.find(u)

        if vr == ur: return True

        UnionFind.par[ur] = vr
        UnionFind.cost += c

        return False
            
    def get_cost():
        return UnionFind.cost

    def same(v, u):
        return UnionFind.find(v) == UnionFind.find(u)

def main():    
    n, q = list(map(int, input().split()))
    UnionFind.init(n)

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

        if com == 0: UnionFind.union(x, y)
        else: 
            if UnionFind.same(x, y): print(1)
            else: print(0)

if __name__ == '__main__':
    main()