Count Palindromic Subsequences

hard
 1. You are given a string str.
2. You are required to print the count of palindromic subsequences in string str.
                               

Input Format

A string str

Output Format

A number representing the count of palindromic subsequences in string str.

Constraints

0 <= str.length <= 10

Notice

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Example

Input
ccbbgd
Output
8
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