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:




class Node:
    def __init__(self, num):
        self.num = num
        self.parent = self
        self.rank = 0
    
def findSet(node):
    tmp = []
    while node.parent != node:
        tmp.append(node)
        node = node.parent
    
    while tmp:
        tmp.pop().parent = node
    return node

def unite(x, y):
    node1 = findSet(nodes[x])
    node2 = findSet(nodes[y])
    if node1.rank == node2.rank:
        node2.parent = node1
        node1.rank += 1
    elif node1.rank > node2.rank:
        node2.parent = node1
    else:
        node1.parent = node2

def same(x, y):
    node1 = findSet(nodes[x])
    node2 = findSet(nodes[y])
    return node1.parent == node2.parent

nums=list(map(int,input().split()))
n = nums[0]
q = nums[1]

nodes = []
for i in range(n):
    nodes.append(Node(i))

for i in range(q):
    nums=list(map(int,input().split()))
    if nums[0] == 0:
        unite(nums[1], nums[2])
    else:
        if same(nums[1], nums[2]):
            print(1)
        else:
            print(0)