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:
import sys
f = sys.stdin

def unite(x, y):
    global dat
    x, y = find(dat, x), find(dat, y)
    if x == y:
        return True
    if dat[y] < dat[x]:
        x, y = y, x
    dat[x] += dat[y]
    dat[y] = x
    return False
        

def same(x, y):
    global dat
    x, y = find(dat, x), find(dat, y)
    print(1 if x == y else 0)
def find(dat, x):
    if dat[x] < 0:
        return x
    dat[x] = find(dat, dat[x])
    return dat[x]

com = (unite, same)

n, q = map(int, f.readline().split())
dat = [-1] * n

for c, x, y in (map(int, f.readline().split()) for _ in range(q)):
    com[c](x, y)