Score : $300$ points

Problem Statement

$2N$ 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:

$N$ $A$ $B$

Output

Print the smallest number of rounds after which the friends can get to play a match against each other.

5 2 4

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.

5 2 3

2

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