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:
rank = {}
p = {}
        
def makeSet(x):
    p[x] = x
    rank[x] = 0

def link(x, y):
    if  rank[x] > rank[y]:
        p[y] = x
    else:
        p[x] = y
    if  rank[x] == rank[y]:
        rank[y] += 1

def union(x, y):
    link(findSet(x), findSet(y))
    
def findSet(x):
    if  x != p[x]:
        p[x] = findSet(p[x])
    return p[x]
    
def isSameSet(x, y):
    return findSet(x) == findSet(y)

n, q = map(int, input().split())
for x in range(n):
    makeSet(x)

for i in range(q):
    a,x,y = map(int, input().split())
    ret = (union if a == 0 else isSameSet)(x,y)
    if ret is None: continue
    if ret == True: print(1)
    else: print(0)