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:
p=[]
rank=[]
answer=[]

def makeset(x):
    p[x] = x
    rank[x] = 0
    
def union(x,y):
    link(findset(x),findset(y))
    
def link(x,y):
    if rank[x] > rank[y]:
        p[y] = x
    else:
        p[x] = y
        if rank[x] == rank[y]:
            rank[y] = rank[y] + 1
def findset(x):
    if x != p[x]:
        p[x] = findset(p[x])
    return p[x]

t,s = map(int,input().split())
for i in range(t):
    p.append(None)
    rank.append(None)
while True:
    try:
        o,x,y = map(int,input().split())
    except:
        break
    else:
        if o == 0:
            if p[x] == None:
                makeset(x)
            if p[y] == None:
                makeset(y)
            union(x,y)
        else:
            if p[x] == None:
                makeset(x)
            if p[y] == None:
                makeset(y)
            if findset(x) == findset(y):
                answer.append(1)
            else:
                answer.append(0)
for i in range(len(answer)):
    print(answer[i])