﻿

### Problem Statement

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

Based on this graph, Takahashi is now constructing a new graph with N2 vertices, where each vertex is labeled with a pair of integers (a, b) (1 ≤ a ≤ N, 1 ≤ b ≤ 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 ≤ N ≤ 100,000
• 0 ≤ M ≤ 200,000
• 1 ≤ ui < vi ≤ N
• There exists no pair of distinct integers i and j such that ui = uj and vi = vj.

### Input

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

```N M
u1 v1
u2 v2
:
uM vM
```

### 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
```

### Submitting .cpp to 'Square Graph'

Time Limit: 2 Seconds
Memory Limit: 1024MB