How many four-digit positive integers \overline{a_{1} a_{2} a_{3} a_{4}} have only nonzero digits and have the property that \left|a_{i}-a_{j}\right| \neq 1 for all 1 \leq i<j \leq 4?
How many four-digit positive integers \overline{a_{1} a_{2} a_{3} a_{4}} have only nonzero digits and have the property that \left|a_{i}-a_{j}\right| \neq 1 for all 1 \leq i<j \leq 4?