Poor Turkeys

AtCoder

IDagc016_e

Time2000ms

Memory256MB

Difficulty—

There are $N$ turkeys. We number them from $1$ through $N$. $M$ men will visit here one by one. The $i$\-th man to visit will take the following action: * If both turkeys $x_i$ and $y_i$ are alive: selects one of them with equal probability, then eats it. * If either turkey $x_i$ or $y_i$ is alive (but not both): eats the alive one. * If neither turkey $x_i$ nor $y_i$ is alive: does nothing. Find the number of pairs $(i,\ j)$ ($1 ≤ i < j ≤ N$) such that the following condition is held: * The probability of both turkeys $i$ and $j$ being alive after all the men took actions, is greater than $0$. ## Constraints * $2 ≤ N ≤ 400$ * $1 ≤ M ≤ 10^5$ * $1 ≤ x_i < y_i ≤ N$ ## Input Input is given from Standard Input in the following format: $N$ $M$ $x_1$ $y_1$ $x_2$ $y_2$ $:$ $x_M$ $y_M$ [samples]

Samples

Input #1

3 1
1 2

Output #1

2

$(i,\ j) = (1,\ 3), (2,\ 3)$ satisfy the condition.

Input #2

Output #2

1

$(i,\ j) = (1,\ 4)$ satisfies the condition. Both turkeys $1$ and $4$ are alive if:

*   The first man eats turkey $2$.
*   The second man eats turkey $3$.
*   The third man does nothing.

Input #3

3 2
1 2
1 2

Output #3

Input #4

Output #4

API Response (JSON)

{
  "problem": {
    "name": "Poor Turkeys",
    "description": {
      "content": "There are $N$ turkeys. We number them from $1$ through $N$. $M$ men will visit here one by one. The $i$\\-th man to visit will take the following action: *   If both turkeys $x_i$ and $y_i$ are alive:",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc016_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ turkeys. We number them from $1$ through $N$.\n$M$ men will visit here one by one. The $i$\\-th man to visit will take the following action:\n\n*   If both turkeys $x_i$ and $y_i$ are alive:...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments