Sorted Permutation Rank

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

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

1 <= |A| <= 1000

First argument is a string A.

Return an integer denoting the rank of the given string.

Input 1:

A = "acb"

Input 2:

A = "a"

Output 1:

2

Output 2:

1

Explanation 1:

Given A = "acb".
The order permutations with letters 'a', 'c', and 'b' : 
abc
acb
bac
bca
cab
cba
So, the rank of A is 2.

Explanation 2:

Given A = "a".
Rank is clearly 1.