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 makeSet(x):
    global p, rank
    p[x] = x
    rank[x] = 0

def union(x,y):
    link(findSet(x), findSet(y))

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

def isSame(x, y):
    global p
    if(findSet(x) == findSet(y)):
        return True
    else:
        return False

if __name__ == "__main__":
    N, Q = (int(z) for z in input().split())
    p = [None] * N
    rank = [None] * N

    for i in range(N):
        makeSet(i)

    for i in range(Q):
        com_i, x, y = (int(z) for z in input().split())
        if(com_i == 0):
            #print("union")
            union(x, y)
        if(com_i == 1):
            #print("isSame")
            if(isSame(x, y) == False):
                print("0")
            else:
                print("1")