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 UnionSet:
    def __init__(self, nmax: int) -> None:
        self.size = [1] * nmax
        self.id = [i for i in range(nmax)]

    def root(self, i: int) -> int:
        while (i != self.id[i]):
            self.id[i] = self.id[self.id[i]]
            i = self.id[i]
        return i

    def connected(self, p: int, q: int) -> bool:
        return self.root(p) == self.root(q)

    def unite(self, p: int, q: int) -> None:
        i, j = self.root(p), self.root(q)
        if (i == j):
            return
        if self.size[i] < self.size[j]:
            self.id[i] = j
            self.size[j] += self.size[i]
        else:
            self.id[j] = i
            self.size[i] += self.size[j]


if __name__ == "__main__":
    n, q = map(int, input().split())

    u = UnionSet(n)
    for _ in range(q):
        op, x, y = map(lambda x: int(x), input().split())
        if (0 == op):
            u.unite(x, y)
        else:
            print(f"{1 if u.connected(x, y) else 0}")