Sorted Permutation Rank

Given a string, find the rank of the string amongst its permutations sorted lexicographically.
Assume that no characters are repeated.

Example :

Input : 'acb'
Output : 2

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

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