Problem 125 of Project Euler deals with a property we have worked with before, palindromic numbers. The problem reads

The palindromic number 595 is interesting because it can be written as the sum of consecutive squares: 6^{2}+ 7^{2}+ 8^{2}+ 9^{2}+ 10^{2}+ 11^{2}+ 12^{2}.

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 = 0^{2}+ 1^{2}has not been included as this problem is concerned with the squares of positive integers.

Find the sum of all the numbers less than 10^{8}that are both palindromic and can be written as the sum of consecutive squares.