Minimum Number of Operations to Make String Sorted

Compute how many distinct permutations of the multiset of characters in s are lexicographically smaller than s (equivalently the number of previous-permutation steps to reach the sorted string), returning the count modulo 10^9+7. The core challenge is efficient combinatorial counting of permutations with duplicates (multinomial coefficients/factorials with modular inverses) for n up to 3000.