Problem Statement  
Bunnies like programming and they often practice for contests.
There is a special computer named BComputer, which all bunnies are eager to use. All bunnies want to solve a difficult problem using BComputer. Because they type very fast, each of them wants to solve the problem according to the following process that consists of 3 stages (no delay is allowed between subsequent stages):
A day is divided into a number of equal time units, and each time unit has an associated positive integer value called preference. You are given a int[] preference, which contains the preference values for a day. The number of elements in preference is the number of time units in the day, and the ith element of preference is the preference of the ith time unit. Bunnies want to design a BComputer schedule for a single day so that the sum of preferences of time units in which one of them uses BComputer is maximized. The schedule must be such that each bunny uses Bcomputer exactly as described above and both time units at which the same bunny uses Bcomputer are in the same day. Return the maximum possible sum of preferences. You can assume that there are infinitely many bunnies.  
Definition  
 
Constraints  
  preference will contain between 1 and 50 elements, inclusive.  
  Each element of preference will be between 1 and 1,000,000, inclusive.  
  k will be between 1 and 50, inclusive.  
Examples  
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