Contest Duration: - (local time) (100 minutes) Back to Home
E - Count Simple Paths /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 制約

• 1 \leq N \leq 2 \times 10^5
• 0 \leq M \leq \min \left(2 \times 10^5, \frac{N(N-1)}{2}\right)
• 1 \leq u_i, v_i \leq N
• 入力で与えられるグラフは単純グラフ
• 入力で与えられるグラフの頂点の次数はすべて 10 以下
• 入力される値は全て整数

### 入力

N M
u_1 v_1
u_2 v_2
\vdots
u_M v_M


### 入力例 1

4 2
1 2
2 3


### 出力例 1

3


• 頂点 1
• 頂点 1, 頂点 2
• 頂点 1, 頂点 2, 頂点 3

### 入力例 2

4 6
1 2
1 3
1 4
2 3
2 4
3 4


### 出力例 2

16


### 入力例 3

8 21
2 6
1 3
5 6
3 8
3 6
4 7
4 6
3 4
1 5
2 4
1 2
2 7
1 4
3 5
2 5
2 3
4 5
3 7
6 7
5 7
2 8


### 出力例 3

2023


Score : 500 points

### Problem Statement

You are given a simple undirected graph with N vertices numbered 1 to N and M edges numbered 1 to M. Edge i connects vertex u_i and vertex v_i. The degree of each vertex is at most 10.
Let K be the number of simple paths (paths without repeated vertices) starting from vertex 1. Print \min(K, 10^6).

### Constraints

• 1 \leq N \leq 2 \times 10^5
• 0 \leq M \leq \min \left(2 \times 10^5, \frac{N(N-1)}{2}\right)
• 1 \leq u_i, v_i \leq N
• The given graph is simple.
• The degree of each vertex in the given graph is at most 10.
• All values in the input are integers.

### Input

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

N M
u_1 v_1
u_2 v_2
\vdots
u_M v_M


### Sample Input 1

4 2
1 2
2 3


### Sample Output 1

3


We have the following three paths that count. (Note that a path of length 0 also counts.)

• Vertex 1;
• vertex 1, vertex 2;
• vertex 1, vertex 2, vertex 3.

### Sample Input 2

4 6
1 2
1 3
1 4
2 3
2 4
3 4


### Sample Output 2

16


### Sample Input 3

8 21
2 6
1 3
5 6
3 8
3 6
4 7
4 6
3 4
1 5
2 4
1 2
2 7
1 4
3 5
2 5
2 3
4 5
3 7
6 7
5 7
2 8


### Sample Output 3

2023