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:
# coding: utf-8
class UnionFind:
    def __init__(self, node_num):
        self._rank = [0] * node_num
        self._par  = [i for i in range(node_num)]
        self.N    =  node_num

    def _find(self, x):
        if self._par[x] == x:
            return x
        else:
            self._par[x] = self._find(self._par[x])
            return self._par[x]

    def merge(self, x, y):
        x = self._find(x)
        y = self._find(y)
        if x == y: return

        if self._rank[x] < self._rank[y]:
            self._par[x] = y
        else:
            self._par[y] = x
            if self._rank[x] == self._rank[y]:
                self._rank[y] += 1

    def is_same(self, x, y):
        return self._find(x) == self._find(y)


N, Q = map(int, input().split())
uf = UnionFind(N)
for _ in range(Q):
    C, X, Y = map(int, input().split())

    if C == 0:
        uf.merge(X, Y)
    else:
        print(1 if uf.is_same(X, Y) else 0)