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

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

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

import sys
f = sys.stdin

n, q = map(int, f.readline().split())
uf = union_find(n)

op = (uf.union, lambda x, y:print(1 if uf.find(x) == uf.find(y) else 0))

for com, x, y in (map(int, f.readline().split()) for _ in range(q)):
    op[com](x, y)