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,rt):
    if rt[x] == x:
        return x
    else:
        while rt[x] != x:
            rt[x] = root(rt[x],rt)
            return rt[x]
def union(x,y,rt,rank):
    rootx = root(x,rt)
    rooty = root(y,rt)
    if rootx == rooty:
        return 0
    else:
        if rank[rootx] < rank[rooty]:
            rt[rootx] = rooty
        else:
            rt[rooty] = rootx
            if rank[rootx] == rank[rooty]:
                rank[rootx] += 1

def issame(x,y,rt):
    return root(x,rt) == root(y,rt)

length,query = (int(n) for n in input().split(" "))
rootlist = [n for n in range(length)]
rank = [0 for n in range(length)]

for q in range(query):
    #print(root)
    com,x,y = (int(n) for n in input().split(" "))
    if com == 0:
        union(x,y,rootlist,rank)
    else:
        print(1 if issame(x,y,rootlist) else 0)