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 find(x):
    if(p[x] == x):return x
    else: 
        p[x] = find(p[x])
        return p[x]
def unite(x,y):
    x = find(x)
    y = find(y)

    if x==y:return
    if rank[x] < rank[y]:
        p[x] = y
    else:
        p[y] = x
        if rank[x] == rank[y]:
            rank[x]+=1

def same(x,y):
    if find(x) == find(y):
        return 1
    else: return 0

if __name__=='__main__':
    n, q = (int(x) for x in input().split())
    p = [i for i in range(n)]
    rank = [0 for i in range(n)]
        
    for i in range(q):
        com, x, y = (int(x) for x in input().split())
        if com == 0:unite(x,y)
        else:print(same(x,y))