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( ))
tag = [i for i in range(n)]
for _ in range(q):
    cmmd,x,y =map(int, input().split( ))
    if cmmd == 0:
        chng1 = []
        chng2 = []
        chng1.append(x)
        x = tag[x]
        chng2.append(y)
        y = tag[y]
        while x != tag[x]:
            chng1.append(x)
            x = tag[x]
        chng1.append(x)
        while y != tag[y]:
            chng2.append(y)
            y = tag[y]
        chng2.append(y)
        if x != y:
            if len(chng1) < len(chng2):
                for x_ in chng1:
                    tag[x_] = y
            else:
                for y_ in chng2:
                    tag[y_] = x
 
    else:
        while x != tag[x]:
            x = tag[x]
        while y != tag[y]:
            y = tag[y]
        if x != y:
            print(0)
        else:
            print(1)