There is an empty sequence $X$ and an empty stack $S$. Also, you are given an integer sequence $A=(a_1,\ldots,a_N)$ of length $N$.  
For each $i=1,\ldots,N$ in this order, Takahashi will do one of the following operations:

-   Move the integer $a_i$ onto the top of $S$.
-   Discard the integer $a_i$ from $A$.

Additionally, Takahashi may do the following operation whenever $S$ is not empty:

-   Move the integer at the top of $S$ to the tail of $X$.

The score of the final $X$ is defined as follows.

-   If $X$ is non-decreasing, i.e. if $x_i \leq x_{i+1}$ holds for all integer $i(1 \leq i \lt |X|)$, where $X=(x_1,\ldots,x_{|X|})$, then the score is $|X|$ (where $|X|$ denotes the number of terms in $X$).
-   If $X$ is not non-decreasing, then the score is $0$.

Find the maximum possible score.

Input is given from Standard Input in the following format:

```
$N$
$a_1$ $\ldots$ $a_N$
```

Print the answer.

-   $1 \leq N \leq 50$
-   $1 \leq a_i \leq 50$
-   All values in input are integers.

5

The following operations make the final X equal (1,1,2,3,4), for a score of 5.

• Move $a_1=1$ onto the top of S.
• Move 1 at the top of S to the tail of X.
• Move $a_2=2$ onto the top of S.
• Discard $a_3=3$.
• Move $a_4=4$ onto the top of S.
• Move $a_5=1$ onto the top of S.
• Move 1 at the top of S to the tail of X.
• Move $a_6=2$ onto the top of S.
• Move 2 at the top of S to the tail of X.
• Move $a_7=3$ onto the top of S.
• Move 3 at the top of S to the tail of X.
• Move 4 at the top of S to the tail of X.

We cannot make the score 66 or greater, so the maximum possible score is 5.