Sad Splits

You are given a positive integer $N$. You have to split **each digit** of $N$ into either of two **non-empty** subsequences $A$ or $B$. For example, if $N = 104$, some possible values of $(A, B)$ can be $(10, 4), (14, 0)$ and $(1, 4)$. Note that, after separating the digits into $A$ and $B$, these subsequences are considered as **positive integers** and thus leading zeros can be omitted. Let u