[Python] Longest palindrome substring algorithm not working properly for even palindromes

The algorithm I wrote in Python seems to be working fine when it comes to extracting longest palindromes that have even number of characters but not for their odd counterparts:

some_input_2 = "abdbaabeeba"
size_of_some_input_2 = len(some_input_2)
max = 0
final_max = 0
idx_center_letter = 0
final_idx_center_letter = 0
for j in range(2):
for idx, letter in enumerate(some_input_2):
i = 0
while i <= int(size_of_some_input_2 / 2) + 1 and not idx - i < 0 and not idx + i+j >= size_of_some_input_2:
upper_idx = idx + i +j
bottom_idx = idx - i
if some_input_2[bottom_idx] == some_input_2[upper_idx]:
i = i + 1
else:
break
if max < i :
max = i #-j
idx_center_letter = idx + 1

if final_max <= max:
final_max = max
final_idx_center_letter = idx_center_letter
print(max)
print(idx_center_letter)
print(some_input_2[final_idx_center_letter - final_max:final_idx_center_letter + final_max])


here the even palindrome abdbaa is the output which is wrong. If the input was some_input_2 = "abbaabeeba" then the output would be abeeba which is correct. Any idea what is wrong here?

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