Sorted Permutation Rank with Repeats

Given a string A, 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.

NOTE:

• The answer might not fit in an integer, so return your answer % 1000003 where 1000003 is a prime number.
• String A can consist of both lowercase and uppercase letters. Characters with lesser ASCII values are considered smaller, i.e., 'a' > 'Z'.

1 <= len(A) <= 1000000

First argument is a string A.

Return an integer denoting the rank.

Input 1:

 A = "aba"

Input 2:

 A = "bca"

Output 1:

 2

Output 2:

 4

Explanation 1:

 The order permutations with letters 'a', 'a', and 'b' :
    aab
    aba 
    baa
 So, the rank is 2.

Explanation 2:

 The order permutations with letters 'a', 'b', and 'c' :
    abc
    acb 
    bac
    bca
    cab
    cba
 So, the rank is 4.