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:
from sys import stdin
high = [0] * 10000
par = [i for i in range(10000)]
def findSet(x):
    if par[x] == x: return x
    par[x] = findSet(par[x])
    return par[x]
def unite(x, y):
    x = findSet(x)
    y = findSet(y)
    if x == y: return
    if high[x] > high[y]: par[y] = x;
    else:
        par[x] = y
        if high[x] == high[y]: high[y] += 1
def same(x, y):
    return findSet(x) == findSet(y)
n, q = map(int, stdin.readline().split())
for i in range(q):
    t, a, b = map(int, stdin.readline().split())
    if t == 0: unite(a, b);
    elif t == 1: print(1 if same(a, b) else 0)