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 DisjointSet:
    def __init__(self,size):
        self.rank = [None]*size
        self.p = [None]*size
        for i in range(size):
            self.make_set(i)
        return
    
    def make_set(self,x):
        self.p[x] = x
        self.rank[x] = 0
        return
    
    def same(self,x,y):
        return self.find_set(x) == self.find_set(y)
        
    def unite(self,x,y):
        self.link(self.find_set(x),self.find_set(y))
        return
    
    def link(self,x,y):
        if self.rank[x]>self.rank[y]:
            self.p[y] = x
        else:
            self.p[x] = y
            if self.rank[x]==self.rank[y]:
                self.rank[y] += 1
                
    def find_set(self,x):
        if x != self.p[x]:
            self.p[x] = self.find_set(self.p[x])
        return self.p[x]
        
n,q = map(int,input().split())
djs = DisjointSet(n)

for i in range(q):
    com,x,y = map(int,input().split())
    if com == 0:
        djs.unite(x,y)
    else:
        print(int(djs.same(x,y)))