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:

class UnionFind:
    def __init__(self,n):
        self.n = n
        self.p = [i for i in range(n)]
        self.rank = [0]*n

    def same(self,x,y):
        return self.root(x)==self.root(y)

    def root(self,x):
        if x!=self.p[x]:self.p[x] = self.root(self.p[x])
        return self.p[x]

    def unite(self,x,y):
        x = self.root(x)
        y = self.root(y)
        if self.rank[y]<self.rank[x]:
            self.p[y] = x
        else:
            self.p[x] = y
            if self.rank[y]==self.rank[x]:
                self.rank[y]+=1

def main():
    n,q = map(int,input().split())
    UF = UnionFind(n)
    for _ in range(q):
        a,b,c = map(int,input().split())
        if a == 0:UF.unite(b,c)
        else:
            if UF.same(b,c):print(1)
            else           :print(0)


if __name__ == '__main__':
    main()