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.par=[i for i in range(N)]
        self.siz=[1 for _ in range(N)]
        self.rank=[0 for _ in range(N)]
    def find(self,x):
        if self.par[x]==x:
            return x
        else:
            self.par[x]=self.find(self.par[x])
            return self.par[x]
    def union(self,a,b):
        a=self.find(a)
        b=self.find(b)
        if a==b:
            return 0
        else:
            if self.rank[a]>self.rank[b]:
                self.par[b]=a
                self.siz[a]+=self.siz[b]
            else:
                self.par[a]=b
                self.siz[b]+=self.siz[a]
                if self.rank[a]==self.rank[b]:
                    self.rank[b]+=1
    def size(self,a):
        return self.siz[self.find(a)]
    def same(self,a,b):
        return self.find(a)==self.find(b)

n,q=map(int,input().split())
uf=UnionFind(n)
for i in range(q):
    com,x,y=map(int,input().split())
    x,y=x-1,y-1
    if com:
        print(1 if uf.same(x,y) else 0)
    else:
        uf.union(x,y)