Longest Palindromic Subsequences

medium
1. You are given a string str.
2. You are required to print the length of longest palindromic subsequence of string str.

Input Format

A string str

Output Format

A number representing the length of longest palindromic subsequence of string str.

Constraints

0 <= str.length <= 10

Notice

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Example

Input
abcgackbc
Output
5
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