A palindrome is a word, phrase, or positive integer that reads the same forwards and backwards. For example, "kayak" is a palindrome. The integers \(292\), \(11\), and \(6\,357\,536\) are also palindromes.
Determine the number of nine-digit palindromic integers that satisfy the following:
The first five digits in the integer are distinct.
The integer is divisible by 4 and/or the integer ends with an 8.