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 get_root(nodes, x: int) -> int:
    if nodes[x] < 0:
        return x
    else:
        nodes[x] = get_root(nodes, nodes[x])
        return nodes[x]


def unite(nodes, x: int, y: int) -> None:
    root_x, root_y = get_root(nodes, x), get_root(nodes, y)
    if root_x != root_y:
        bigroot, smallroot = \
            (root_x, root_y) if nodes[root_x] < nodes[root_y] else (root_y, root_x)
        nodes[bigroot] += nodes[smallroot]
        nodes[smallroot] = bigroot


if __name__ == "__main__":
    import sys
    N, Q = map(int, input().split())
    nodes = [-1]*N
    result = []
    append = result.append

    for p, a, b in (map(int, l.split()) for l in sys.stdin):
        if not p:
            unite(nodes, a, b)
        else:
            append(1 if get_root(nodes, a) == get_root(nodes, b) else 0)

    print(*result, sep="\n")