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.parent = [-1] * N  

    def findset(self, A):  
        if (self.parent[A] < 0):
            return A
        self.parent[A] = self.findset(self.parent[A])  
        return self.parent[A]

    def size(self, A):  
        return -self.parent[self.findset(A)]

    def unite(self, A, B):
        A = self.findset(A)
        B = self.findset(B)

        if (A == B):
            return False

        if (self.size(A) < self.size(B)):
            A, B = B, A

        self.parent[A] += self.parent[B]  
        self.parent[B] = A  

        return True

    def is_in_same(self, A, B):
        return self.findset(A) == self.findset(B)


N, Q = map(int, input().split())
ds = UnionFind(N)
for q in range(Q):
    com, x, y = map(int, input().split())
    if com == 0:
        ds.unite(x, y)
    elif com == 1:

        print(1 if ds.is_in_same(x, y) else 0)