There are $N$ dishes arranged in a row in front of Takahashi. The $i$-th dish from the left has $A_i$ oranges on it.

Takahashi will choose a triple of integers $(l, r, x)$ satisfying all of the following conditions:

-   $1\leq l \leq r \leq N$;
-   $1 \le x$;
-   for every integer $i$ between $l$ and $r$ (inclusive), $x \le A_i$.

He will then pick up and eat $x$ oranges from each of the $l$-th through $r$-th dishes from the left.

At most how many oranges can he eat by choosing the triple $(l, r, x)$ to maximize this number?

Input is given from Standard Input in the following format:

```
$N$
$A_1$ $\ldots$ $A_N$
```

Print the maximum number of oranges Takahashi can eat.

-   All values in input are integers.
-   $1 \leq N \leq 10^4$
-   $1 \leq A_i \leq 10^5$

20

By choosing (l,r,x)=(2,6,4), he can eat 20 oranges.

200

By choosing (l,r,x)=(1,1,200), he can eat 200 oranges.