Contest Duration: - (local time) (110 minutes) Back to Home
C - Squared Graph /

Time Limit: 2 sec / Memory Limit: 256 MB

### 問題文

• 元のグラフにおいて aa' の間および bb' の間の両方に辺があるとき，またそのときに限り，(a, b)(a', b') の間に辺を張る．

このようにして作ったグラフの連結成分の個数を求めてください．

### 制約

• 2 \leq N \leq 100,000
• 0 \leq M \leq 200,000
• 1 \leq u_i < v_i \leq N
• u_i = u_j かつ v_i = v_j を満たすような異なる i, j の組は存在しない

N M
u_1 v_1
u_2 v_2
:
u_M v_M

3 1
1 2

7

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

### 出力例 2

18

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.

3 1
1 2

### Sample Output 1

7

The graph constructed by Takahashi is as follows.

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

18