Security Camera

AtCoder

IDabc220_h

Time2000ms

Memory256MB

Difficulty—

AtCoder Town has $N$ intersections and $M$ roads. Road $i$ connects Intersections $A_i$ and $B_i$. Takahashi, the mayor, has decided to install zero or more surveillance cameras at the intersections. Each intersection can be installed with zero or one surveillance camera. How many of the $2^N$ ways to install surveillance cameras monitor an even number of roads? Here, Road $i$ is said to be monitored when the following condition is satisfied: > a surveillance camera is installed at one or both of Intersections $A_i$ and $B_i$. ## Constraints * $2 \leq N \leq 40$ * $1 \leq M \leq \frac{N(N-1)}{2}$ * $1 \leq A_i \lt B_i \leq N$ * $(A_i,B_i) \neq (A_j,B_j)$ if $i \neq j$. * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $M$ $A_1$ $B_1$ $A_2$ $B_2$ $\vdots$ $A_M$ $B_M$ [samples]

Samples

Input #1

3 2
1 2
2 3

Output #1

6

The sets of towns to install surveillance cameras to satisfy the condition are: ${ } , { 2 } , { 1,2 } ,{1,3},{2,3},{1,2,3}$.  
Note that it is allowed to install no surveillance camera.

Input #2

Output #2

458752

The town may not be connected.

API Response (JSON)

{
  "problem": {
    "name": "Security Camera",
    "description": {
      "content": "AtCoder Town has $N$ intersections and $M$ roads.   Road $i$ connects Intersections $A_i$ and $B_i$. Takahashi, the mayor, has decided to install zero or more surveillance cameras at the intersections",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc220_h"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "AtCoder Town has $N$ intersections and $M$ roads.  \nRoad $i$ connects Intersections $A_i$ and $B_i$.\nTakahashi, the mayor, has decided to install zero or more surveillance cameras at the intersections...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments