Problem Statement  
In Chemistry, there's a different meaning to the word 'solution' than in programming. When we mix x liters of some substance with (100x) liters of water, we get 100 liters of x% solution of that substance. You are given several bottles containing solutions of the same substance. The ith bottle contains amount[i] liters of percent[i]% solution. Return the maximal number of liters of need% solution we can get by pouring together some of these bottles (possibly partially, see example 0).  
Definition  
 
Notes  
  The returned value must have an absolute or relative error less than 1e9.  
Constraints  
  percent will contain between 1 and 50 elements, inclusive.  
  Each element of percent will be between 0 and 100, inclusive.  
  amount will contain the same number of elements as percent.  
  Each element of amount will be between 1 and 1000, inclusive.  
  need will be between 0 and 100, inclusive.  
Examples  
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