Problem Statement  
Taro has prepared delicious kiwi fruit juice. He poured it into N bottles numbered from 0 to N1. Each bottle has a capacity of C liters, and he poured bottles[i] liters of kiwi juice into the ith bottle initially. Taro will sell these bottles after performing an arbitrary number of operations of the following type (possibly zero). In each operation, he chooses two distinct bottles A and B, and pours kiwi juice from bottle A to bottle B until either bottle A becomes empty or bottle B becomes full, whichever happens earlier.
If a bottle contains x liters of kiwi juice at the end (where x is an integer between 0 and C, inclusive), then Taro can sell the bottle for prices[x] dollars. Return the maximum amount of money he can earn.  
Definition  
 
Constraints  
  C will be between 1 and 49, inclusive.  
  bottles will contain between 1 and 15 elements, inclusive.  
  Each element of bottles will be between 0 and C, inclusive.  
  prices will contain exactly C + 1 elements.  
  Each element of prices will be between 0 and 1,000,000, inclusive.  
Examples  
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