Table Tennis Training

AtCoder

IDagc041_a

Time2000ms

Memory256MB

Difficulty—

$2N$ players are running a competitive table tennis training on $N$ tables numbered from $1$ to $N$. The training consists of _rounds_. In each round, the players form $N$ pairs, one pair per table. In each pair, competitors play a match against each other. As a result, one of them wins and the other one loses. The winner of the match on table $X$ plays on table $X-1$ in the next round, except for the winner of the match on table $1$ who stays at table $1$. Similarly, the loser of the match on table $X$ plays on table $X+1$ in the next round, except for the loser of the match on table $N$ who stays at table $N$. Two friends are playing their first round matches on distinct tables $A$ and $B$. Let's assume that the friends are strong enough to win or lose any match at will. What is the smallest number of rounds after which the friends can get to play a match against each other? ## Constraints * $2 \leq N \leq 10^{18}$ * $1 \leq A < B \leq N$ * All input values are integers. ## Input Input is given from Standard Input in the following format: $N$ $A$ $B$ [samples]

Samples

Input #1

5 2 4

Output #1

1

If the first friend loses their match and the second friend wins their match, they will both move to table $3$ and play each other in the next round.

Input #2

5 2 3

Output #2

2

If both friends win two matches in a row, they will both move to table $1$.

API Response (JSON)

{
  "problem": {
    "name": "Table Tennis Training",
    "description": {
      "content": "$2N$ players are running a competitive table tennis training on $N$ tables numbered from $1$ to $N$. The training consists of _rounds_. In each round, the players form $N$ pairs, one pair per table. I",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc041_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "$2N$ players are running a competitive table tennis training on $N$ tables numbered from $1$ to $N$.\nThe training consists of _rounds_. In each round, the players form $N$ pairs, one pair per table. I...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments