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.parent = [-1] * n

    def root(self, a):
        if self.parent[a] < 0:
            return a
        else:
            self.parent[a] = self.root(self.parent[a])
            return self.parent[a]

    def size(self, a):
        return -self.parent[self.root(a)]

    def connect(self, a, b) -> bool:
        a = self.root(a)
        b = self.root(b)

        if a == b:
            return False

        if self.size(a) < self.size(b):
            a, b = b, a

        self.parent[a] += self.parent[b]

        self.parent[b] = a

        return True


n, q = map(int, input().split())
unif = UnionFind(n)
for _ in range(q):
    com, x, y = map(int, input().split())
    if com == 0:
        unif.connect(x, y)
    else:
        print(1 if unif.root(x) == unif.root(y) else 0)