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 main():
    n, q = input().split()
    n = int(n)
    q = int(q)
    nums = [i for i in range(n)]
    rank = [0 for i in range(n)]

    def find_top(x):
        if (nums[x] != x):
            nums[x] = find_top(nums[x])
        return nums[x]

    def unite(x, y):
        x = find_top(x)
        y = find_top(y)
        if rank[x] > rank[y]:
            nums[y] = x
        else:
            nums[x] = y
            if (rank[x] == rank[y]):
                rank[y] += 1

    def same(x, y):
        return find_top(x) == find_top(y)

    for _ in range(q):
        query = input().split()
        com, x, y = tuple(map(int, query))
        if com == 0:
            unite(x, y)
        else:
            print(same(x, y) * 1)


if __name__ == "__main__":
    main()