Score : $300$ points

Problem Statement

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?

Constraints

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

Input

Input is given from Standard Input in the following format:

$N$

$A_1$ $\ldots$ $A_N$

Output

Print the maximum number of oranges Takahashi can eat.

6
2 4 4 9 4 9

20

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

6
200 4 4 9 4 9

200

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