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:
import sys
 
f_i = sys.stdin
 
n, q = map(int, f_i.readline().split())

class DisjointSets:
    def __init__(self, size):
        # negative values are roots(representatives of each tree)
        # positive values represent the parent element
        self.table = [-1 for _ in range(size)]

    def _find(self, x):
        while self.table[x] >= 0:
            x = self.table[x]
        return x

    def union(self, x, y):
        s1 = self._find(x)
        s2 = self._find(y)
        if s1 != s2:
            if self.table[s1] < self.table[s2]: # the smaller has more elements
                self.table[s1] += self.table[s2]
                self.table[s2] = s1
            else:
                self.table[s2] += self.table[s1]
                self.table[s1] = s2

    def isSameSet(self, x, y):
        if self._find(x) == self._find(y):
            print(1)
        else:
            print(0)

S = DisjointSets(n)

for l in f_i:
    com, x, y = map(int, l.split())
    if com == 0:
        S.union(x, y)
    else:
        S.isSameSet(x, y)