human
Write me a the Python code you requested given the following:
I found an interesting problem on https://leetcode.com/problems/palindromic-substrings/:
Given a string, your task is to count how many palindromic substrings in this string.


The substrings with different start indexes or end indexes are counted as different substrings even they consist of same characters. 

Example 1:

Input: "abc"
Output: 3
Explanation: Three palindromic strings: "a", "b", "c".


Example 2:

Input: "aaa"
Output: 6
Explanation: Six palindromic strings: "a", "a", "a", "aa", "aa", "aaa".


Note:

The input string length won't exceed 1000.

I tried it in Python, but could not do it. Can you solve it?
assistant
#Here is the Python code you requested.

class Solution:
     def countSubstrings(self, s):
         """
         :type s: str
         :rtype: int
         """
         
         # manacher, find Z
         s = '^#' + '#'.join(s) + '#$'
         Z = [1] * len(s)
         center, right = 0, 0
         for i in range(len(s)-1): # 注意 i不能取到 $
             if i < right:
                 i_mirror = 2 * center - i
                 Z[i] = min(Z[i_mirror], right - i + 1)
             while s[i+Z[i]] == s[i-Z[i]]:
                 Z[i] += 1
             if i + Z[i] - 1 > right:
                 center, right = i, i + Z[i] - 1
         
         # sum Z
         return sum(z//2 for z in Z)