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 PYTHON):

Solution:
class UnionFind:
    def __init__(self,n):
        self.parent = {}
        for i in range(n):
            self.parent[i] = i

    def get_root(self,x):
        r = x
        depth = 0
        path = [r]
        while self.parent[r]!=r:
            r = self.parent[r]
            path.append(r)
            depth += 1
        for n in path:
            self.parent[n] = r
        return r,depth

    def unite(self,x,y):
        rx,dx = self.get_root(x)
        ry,dy = self.get_root(y)
        if rx!=ry:
            if dx > dy:
                self.parent[ry] = rx
            else:
                self.parent[rx] = ry

    def same(self,x,y):
        rx,_ = self.get_root(x)
        ry,_ = self.get_root(y)
        if rx==ry: return 1
        else: return 0


n,q = map(int,raw_input().split(' '))
tree = UnionFind(n)

answers = []
for _ in range(q):
    com,x,y = map(int,raw_input().split(' '))
    if com==0:
        tree.unite(x,y)
    elif com==1:
        answers.append(tree.same(x,y))

for a in answers:
    print a