Straights

In poker, a *straight* is a continuous
sequence of cards, in this case of any length. Your friend John
makes up a game called straights which is played with
$N$ cards with numbers
that may repeat, between $1$ and $10^4$. In order to win, you must get
rid of all of your cards in as little turns as possible. The
only way to put down more than $1$ card at a time is if the cards are
strictly in *descending* or *ascending* order.

For example, given eight cards with the numbers: `1 8 3 6 5 7 2 1`, the minimum number of turns to
get rid of all of your cards would be: `3` because you would have 2 straights:
`1 2 3` and `5 6 7
8` and a single card: `1` left
over.

Can you find the minimum number of turns required for you to win?

Input consists of two lines. The first contains the number of cards that you are given $N$ ($1 \leq N \leq 10^4$). The second line consists of $N$ space separated integers each with a different value between $1$ and $10^4$.

Output the minimum number of turns to win.

Sample Input 1 | Sample Output 1 |
---|---|

8 1 8 3 6 5 7 2 1 |
3 |