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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

Given a string, return the length of the longest palindromic subsequence in the string.

For example, given the following string:

MAPTPTMTPA

Return 7, since the longest palindromic subsequence in the string is APTMTPA. Recall that a subsequence of a string does not have to be contiguous!

Your algorithm should run in O(n^2) time and space.