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:
#! python3
# disjoint_set_union_find_tree.py

n, q = [int(x) for x in input().split(' ')]

sets = [set([i]) for i in range(n)]

def unite(Sx, Sy):
    return Sx | Sy

def search(x):
    global sets
    flag = False
    for i in range(len(sets)):
        if x in sets[i]:
            flag = True
            break
    if flag:
        return i
    else:
        return None

def same(x, y):
    global sets
    flag = 0
    for set in sets:
        if x in set:
            if y in set:
                 flag = 1
            break
    return flag

for i in range(q):
    query, x, y = input().split(' ')
    x, y = int(x), int(y)
    if query == '0':
        # unite
        i_x = search(x)
        i_y = search(y)
        if i_x != None and i_y != None and i_x != i_y:
            sets[i_x] = unite(sets[i_x], sets[i_y])
            del sets[i_y]
    elif query == '1':
        # same
        print(same(x, y))