String Permutation Rank

Function Name: getPermutationRank

Description

Write a function that calculates the rank of a string permutation in lexicographically sorted order without actually generating all permutations. For example, in the sorted list of permutations of 'abc', the rank of 'abc' is 1, 'acb' is 2, and so on. The function should handle duplicates and handle upper and lowercase characters as different. You must not use external libraries or built-in permutation functions. The rank should start at 1.

Requirements

• The function should take a single string parameter.
• All permutations should be considered case-sensitive ('a' is different from 'A').
• The function should return an integer representing the rank of the string's permutation.
• If the string contains non-letter characters, the function should throw an error or return an invalid input message.
• Optimize the function to avoid factorial time complexity if possible.
• Additional functions can be created to help with the main task.

Examples

Given the string 'bac', getPermutationRank('bac') should return 3.Given the string 'Bac', getPermutationRank('Bac') should return 4, since 'Bac', 'Bca', 'aBc' are before it in lexicographic order.Given the string 'aabc', getPermutationRank('aabc') should return 1, as it's the first in sorted order with duplicates.

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