You are given a string, tiles, consisting of uppercase English letters. You can arrange the tiles into sequences of any length (from 1 to the length of tiles), and each sequence must include at most one tile, tiles[i], from tiles.

Your task is to return the number of possible non-empty unique sequences you can make using the letters represented on tiles[i].

Constraints:

• $1 \leq$ tiles.length $\leq 7$

• The tiles string consists of uppercase English letters.

This problem would have been straightforward if the tiles had no duplicates and we only needed to find sequences of the same length as the given tiles. In that case, we could simply calculate the total unique sequences using $n!$ (where $n$ is the length of the tiles).