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
input = sys.stdin.readline

class UnionFind():
    def __init__(self,n):
        self.n = n
        self.parents = [i for i in range(n)]
        self.rank = [0 for _ in range(n)]
    def find(self,x):
        root = x
        while self.parents[root] != root:
            root = self.parents[root]
        while self.parents[x] != root:
            parent = self.parents[x]
            self.parents[x] = root
            x = parent
        return root
    def unite(self,x,y):
        xroot,yroot = self.find(x),self.find(y)
        if xroot == yroot:
            return
        xrank,yrank = self.rank[xroot],self.rank[yroot]
        if xrank < yrank:
            self.parents[xroot] = yroot
        elif xrank == yrank:
            self.parents[yroot] = xroot
            self.rank[yroot] += 1
        else:
            self.parents[yroot] = xroot

N,Q = map(int,input().split())
uf = UnionFind(N)

for _ in range(Q):
    com,x,y = map(int,input().split())
    if com == 0:
        uf.unite(x,y)
    else:
        print(1 if uf.find(x)==uf.find(y) else 0)