A positive integer x can represent as $(a_1a_2 \ldots a_ka_k \ldots a_2a_1)_{10}$ or $(a_1a_2 \ldots a_{k-1}a_ka_{k-1} \ldots a_2a_1)_{10}$ of a 10-based notational system, we always call x is a Palindrome Number. If it satisfies $0<a_1<a_2< \ldots<a_k \leq 9$, we call x is a Beautiful Palindrome Number.
Now, we want to know how many Beautiful Palindrome Numbers are between 1 and $10^N$.