N-Rock-Paper-Scissors

Dohun, a game enthusiast, wanted to make rock-paper-scissors more fun, so he invented a new game called N-Rock-Paper-Scissors. The rules are as follows.

• $N+1$ players each start with cards numbered from $1$ to $N$, one card each.
• Each player plays one round against each of the other $N$ players, for $N$ rounds in total. In each round, the two players each play one of their cards.
• If two players play cards $i$ and $i+1$, the player who played card $i$ wins, and the player who played card $i+1$ loses. $(1\le i\le N-1)$
• If two players play card $N$ and card $1$, the player who played card $N$ wins, and the player who played card $1$ loses.
• All other matchups are draws.
• Once a round is decided as a win, loss, or draw, the played card is discarded, and the next round is played with the remaining cards.

Dohun designed these rules. He wants to know the maximum number of draws possible in the next $N$ rounds, given the list of cards the opponent will play in those rounds.

The first line contains the number of rounds $N$. $(3\le N\le 200\,000)$

The second line contains the cards $A_1, A_2, \cdots, A_N$ that the opponent will play in order, separated by spaces. $(1 \le A_i \le N)$

Print the maximum number of draws you can get by playing cards appropriately in the $N$ rounds.