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:
def root(x):
    path = []
    while P[x] != x:
        path.append(x)
        x = P[x]
    for node in path:
        P[node] = x
    return x
def check(x,y):
    if root(x) == root(y):
        return 1
    else:
        return 0
def unite(x,y):
    P[root(x)] = root(y)        
 
n,q = map(int,input().split())
P = [i for i in range(n)]
for j in range(q):
    s = list(map(int,input().split()))
    if s[0] == 0:
        unite(s[1],s[2])
    else:
        print(check(s[1],s[2]))
    #print(P)