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# Sorted Permutation Rank with Repeats

Problem Description

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'.

Problem Constraints

1 <= len(A) <= 1000000

Input Format

First argument is a string A.

Output Format

Return an integer denoting the rank.

Example Input

Input 1:

` A = "aba"`

Input 2:

` A = "bca"`

Example Output

Output 1:

` 2`

Output 2:

` 4`

Example Explanation

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.```

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 question? Checkout Sample Codes for more details.
Hints
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## Discussion

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