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:
(n,q), *cxy = [list(map(int, s.split())) for s in open(0)]

class UnionFind:
    def __init__(self, n):
        self.parent = {i:i for i in range(n)}
        
    def find_root(self, x):
        parent = self.parent[x]
        if x != parent:
            result = self.find_root(parent)
            self.parent[x] = result
            return result
        else:
            return x

    def unite(self, x, y):
        if x == y:
            return
        
        x, y = min(x,y), max(x,y)
        x = self.find_root(x)
        y = self.find_root(y)
        
        if x == y:
            return
        elif x > y:
            x = self.find_root(x)
            if x == y:
                return
            x, y = min(x,y), max(x,y)
        self.parent[y] = x

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

u = UnionFind(n)

for c,x,y in cxy:
    if c:
        print(int(u.same(x,y)))
    else:
        u.unite(x,y)