Problem Statement  
A common task for math students is to solve 'word math' questions, where each distinct letter represents a distinct digit. Given a list of word math numbers to add, your task is to calculate the greatest possible sum of those numbers. For example, given the expression: TOP + CODERthe maximum sum possible by substituting numbers is: 783 + 98654  99437with C = 9, D = 6, E = 5, O = 8, P = 3, R = 4 and T = 7. Please note that, for this question, word math numbers are allowed to start with a zero.  
Definition  
 
Notes  
  Different letters must represent different digits, identical letters must represent identical digits.  
  Not all digits in the result must appear in the summands.  
Constraints  
  summands will contain between 1 and 10 elements, inclusive.  
  Each element of summands will contain between 1 and 8 characters, inclusive.  
  Each element of summands will contain only uppercase letters ('A''Z').  
  summands will contain at most 10 distinct letters.  
Examples  
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