Problem Statement  
You are testing several algorithms and you want to find the fastest one for your task. Computational complexities of these algorithms will be given to you in three int[]s  constant, power and logPower. The i^{th} algorithm needs on average constant[i]*N^{power[i]}*ln^{logPower[i]}(N) operations to solve your task.
Given an int N, the size of your task, return the 0based index of the fastest algorithm. In case of a tie, return the smallest index.  
Definition  
 
Notes  
  ln(x) in the formula means natural logarithm of x. It can be computed as:  Math.log(x) in java  log(x) in C++  Math.Log(x) in C# and VB.  
Constraints  
  constant, power and logPower will have the same number of elements.  
  constant, power and logPower will each have between 1 and 50 elements, inclusive.  
  N will be between 1 and 1000, inclusive.  
  All elements of power and logPower will be between 0 and 5, inclusive.  
  All elements of constant will be between 1 and 100, inclusive.  
Examples  
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