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:
n, q = map(int, input().split())

tree = [i for i in range(n)]
def root(x):
    pre = []
    while x != tree[x]:
        pre.append(x)
        x = tree[x]
    for node in pre:
        tree[node] = x
    return x
def unite(x, y):
    X, Y = root(x), root(y)
    if X != Y:
        tree[X] = Y
def same(x, y):
    if root(x) == root(y):
        return print(1)
    else:
        return print(0)

for _ in range(q):
    c, x, y = map(int, input().split())
    if c == 0:
        unite(x, y)
    else:
        same(x, y)