GAIC Math 2024 Problem 115

A six-digit number $N=\overline{a_1a_2...a_{6}}$ composed of non-repeating digits from 1 to 6 satisfies the condition $|a_{k+1}-a_{k}| \neq 1, (k\in \{1,2, \cdots, 5\})$. Then the number of such six-digit numbers is _____.