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):
        self.data = {}
        self.rank = {}

    def make_set(self,x):
        if not x in self.data:
            self.data[x] = x
            self.rank[x] = 0

    def find_set(self,x):
        path = []
        while self.data[x] != x:
            path.append(x)
            x = self.data[x]
        for y in path:
            self.data[y] = x
        return x

    def same(self,x,y):
        if self.find_set(x) == self.find_set(y):
            return True
        else:
            return False

    def unite(self,x,y):
        rx = self.find_set(x)
        ry = self.find_set(y)
        if not rx == ry:
            if self.rank[rx] > self.rank[ry]:
                self.data[ry] = rx
            elif self.rank[rx] < self.rank[ry]:
                self.data[rx] = ry
            else:
                self.data[rx] = ry
                self.rank[rx] += 1

n,q = map(int, raw_input().split(' '))
s = UnionFind()
for i in range(n):
    s.make_set(i)
for i in range(q):
    c,x,y = map(int,raw_input().split(' '))
    if c == 0:
        s.unite(x,y)
    else:
        if s.same(x,y):
            print 1
        else:
            print 0