Problem C
Bergur

Hot Yoga

Bergur has decided to go to a Hot Yoga class to burn some fat. Bergur doesn’t think it’s good enough to just regularly attend Hot Yoga classes, he wants to always stay at least as long as he did the previous day. That is to say, Bergur intends to show up for Hot Yoga every day for the next $N$ days. You are given for each day, how long he can be in Hot Yoga class, defined as $a_i$ for the $i$-th day. He is welcome to leave earlier than that.

Bergur wants to spend the maximum amount of time possible in Hot Yoga classes over these $N$ days but still satisfy the requirement of staying at least as long as the previous day every time.

That is to say, the amount of time Bergur spends on Hot Yoga over the days is non-decreasing.

Input

The first line of the input contains one integer $N$ ($1\le N\le 3\cdot {10}^5$), the number of days.

The next line contains $N$ integers $1\le a_i\le {10}^4$ where the $i$-th number denotes the maximum amount of time Bergur can stay in class that day.

Output

Print a single integer, the maximum amount of time Bergur can spend in Hot Yoga classes in total while still satisfying the requirements described above.

Scoring

10
5 6 7 8 9 3 2 7 8 9

38

3
3 2 1

3