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Sorted Permutation Rank with Repeats

Given a string, find the rank of the string amongst its permutations sorted lexicographically.
Note that the characters might be repeated. If the characters are repeated, we need to look at the rank in unique permutations.
Look at the example for more details.

Example :

Input : 'aba'
Output : 2

The order permutations with letters 'a', 'a', and 'b' : 

The answer might not fit in an integer, so return your answer % 1000003

NOTE: 1000003 is a prime number
NOTE: Assume the number of characters in string < 1000003

NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a doubt? Checkout Sample Codes for more details.
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