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.n = n
        self.par = [-1] * (n + 1)
        self.size = [1] * (n + 1)

    def root(self, idx):
        if self.par[idx] == -1:
            return idx

        self.par[idx] = self.root(self.par[idx])
        return self.par[idx]

    def unite(self, idx1, idx2):
        idx1_par = self.root(idx1)
        idx2_par = self.root(idx2)

        if idx1_par == idx2_par:
            return

        if self.size[idx1_par] >= self.size[idx2_par]:
            self.size[idx1_par] += self.size[idx2_par]
            self.par[idx2_par] = idx1_par
        else:
            self.size[idx2_par] += self.size[idx1_par]
            self.par[idx1_par] = idx2_par

    def same(self, idx1, idx2):
        return self.root(idx1) == self.root(idx2)


n, q = map(int, input().split())

uf = UnionFind(n)

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