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:
#coding:utf-8
import time

N,Q = map(int,input().split())
rank = [0 for i in range(N)]

class Tree:
    def __init__(self,par,key):
        self.par = par
        self.key = key

List = [Tree(i,i) for i in range(N)]

def unit(x,y):
    while List[x].par != x:
        x = List[x].par
    a = rank[x]
            
    while List[y].par != y:
        y = List[y].par
    b = rank[y]
    if a <= b:
        if a == b:
            rank[x] += 1
        List[y].par = x
    else:
        List[x].par = y



def Find(x,y):
    Q = []
    P = []
    while List[x].par != x:
        x = List[x].par
        Q.append(x)
            
    while List[y].par != y:
        y = List[y].par
        P.append(y)
    for xi in Q:
        List[xi].par = x
        rank[xi] = 1
    for yi in P:
        List[yi].par = y
        rank[yi] = 1
    if x == y:
        print(1)
    else:
        print(0)
    
        
for i in range(Q):
    com, x,y = map(int,input().split())

    if com == 0:
        unit(x,y)
            
    else:
        Find(x,y)