3.5 Decoding the Ancient Symmetries
Score: 25pts
Time Limit: 3.20 sec
Gauresh has found delicate ancient texts containing a mysterious language,he needs a tool to count palindromes in ancient texts. Generate an algorithm that counts all posiible palindromes in the texts before the texts decayed.

Constraints
1 <= s.length <= 2000
s consists of lowercase English letters.

Input Format
Single string of lowercase alphabets

Output Format
Single integer(count of all palindromic substrings in the orignal string)

Example 1
Input:
madam

Output:
7

Explanation:
Here are the 7 palindromic substrings in the string "madam":"m","a","d","a","m","ada","madam"

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