Problem:
Score : 800 points

Problem Statement

Takahashi has received an undirected graph with N vertices, numbered 1, 2, ..., N.
The edges in this graph are represented by (u_i, v_i).
There are no self-loops and multiple edges in this graph.

Based on this graph, Takahashi is now constructing a new graph with N^2 vertices, where each vertex is labeled with a pair of integers (a, b) (1 \leq a \leq N, 1 \leq b \leq N).
The edges in this new graph are generated by the following rule:

Span an edge between vertices (a, b) and (a', b') if and only if both of the following two edges exist in the original graph: an edge between vertices a and a', and an edge between vertices b and b'.

How many connected components are there in this new graph?

Constraints

2 \leq N \leq 100,000

0 \leq M \leq 200,000

1 \leq u_i < v_i \leq N

There exists no pair of distinct integers i and j such that u_i = u_j and v_i = v_j.

Input

The input is given from Standard Input in the following format:

N M
u_1 v_1
u_2 v_2
:
u_M v_M

Output

Print the number of the connected components in the graph constructed by Takahashi.

Sample Input 1

3 1
1 2

Sample Output 1

7

The graph constructed by Takahashi is as follows.

Sample Input 2

7 5
1 2
3 4
3 5
4 5
2 6

Sample Output 2

18

Solution in Ruby (2.3.3) (judge verdict: Wrong Answer)

#!/usr/bin/ruby
def dfs(c)
	$h[c].each{|d|
		if $v[d]==0
			$v[d]=3-$v[c]
			return false if !dfs(d)
		elsif $v[d]==$v[c]
			return false
		end
	}
	true
end
n,m=gets.split.map &:to_i
$h=Hash.new{|h,k|h[k]=[]}
m.times{a,b=gets.split.map &:to_i;$h[a-1]<<b-1;$h[b-1]<<a-1}
$v=Hash.new 0
a=b=c=0
n.times{|i|
	next if $v[i]>0
	if $h[i].empty?
		c+=1
	else
		$v[i]=1
		if dfs(i)
			a+=1
		else
			b+=1
		end
	end
}
p a*a*2+a*b*2+b*b+(n*n-(n-c)*(n-c))