Problem Statement  
A decomposition of a nonnegative integer n is a list of nonnegative integers that sum to exactly n. The product of a decomposition is the product of all its members. For example, if n = 4, the following decompositions are possible:
4 = 1+1+1+1, product is 1*1*1*1 = 1. Given an int n, determine the decomposition of n with the maximal product, and return that product modulo 10007. In the example above, the maximal product is 4 (the product of the decomposition 2 + 2).  
Definition  
 
Constraints  
  n will be between 0 and 10000, inclusive.  
Examples  
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