As the chefs await the dishes to be finalized, they sit around a circular table. Let the chefs be $1, 2, \dots, n$, where $n$ ($1\leq n \leq 10^5$) represents the number of chefs — yes, being the international chef's day, we may have many chefs join us, and we say chef $i$ has tastebud index $C_i$ ($1 \leq C_i \leq 10^9$).

As the judging process begins, a waiter stands behind chef $k$ ($1\leq k \leq n$), and pass the dish to the chef, so that the chef may taste and judge the dish. Once that is completed, the waiter moves on to chef $k+1$; if $k=n$, then the waiter would move on to chef $1$. This process (of passing the dish, recording the chef's rating, and moving to the next chef) continues until every chef has had the chance to taste the dish, and each time, the chef's tastebud index would be added up.

The chefs are impatient and that impacts their tastebuds' sensitivity: if they are the $i$th chef to be given the dish, their tastebud index is multiplied by $i$. As the contest organizer, you desire the maximum sum of tastebud index so that the judged dish is under the most rigorous scrutiny from the chefs' tastebuds: so it is your job to determine the optimal total tastebud index obtainable from the $n$ chefs given their tastebud indexes over all the possible chefs that the waiter may start with.