The palindromic number 595 is interesting because it can be written as the sum of consecutive squares: 6² + 7² + 8² + 9² + 10² + 11² + 12².

There are exactly eleven palindromes below one-thousand that can be written as consecutive square sums, and the sum of these palindromes is 4164. Note that 1 = 0² + 1² has not been included as this problem is concerned with the squares of positive integers.

Find the sum of all the numbers less than 10⁸ that are both palindromic and can be written as the sum of consecutive squares.