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(object):

    def __init__(self, size):
        self.table = [-1 for _ in xrange(size)]

    def find(self, x):
        if self.table[x] < 0:
            return x
        self.table[x] = self.find(self.table[x])
        return self.table[x]

    def same(self, x, y):
        return self.find(x) == self.find(y)

    def union(self, x, y):
        s1 = self.find(x)
        s2 = self.find(y)
        if s1 == s2:
            return False
        if self.table[s1] > self.table[s2]:
            s1, s2 = s2, s1
        self.table[s1] += self.table[s2]
        self.table[s2] = s1
        return True


def main():
    n, q = map(int, raw_input().split())
    uf = UnionFind(n)
    for _ in xrange(q):
        com, x, y = map(int, raw_input().split())
        if com == 0:
            uf.union(x, y)
        else:
            print 1 if uf.same(x, y) else 0

if __name__ == "__main__":
    main()