Define a recursive DP function that takes the current position in the grid, the number of remaining introverts and extroverts, and the compressed state of the last row.
If the current position is beyond the grid or there are no more people to place, return 0.
For each cell, try three possibilities: leave it empty, place an introvert, or place an extrovert.
Update the happiness score based on the current placement and the neighbors (above and to the left).
Recursively call the DP function for the next cell with updated parameters.
Use memoization to store and reuse the results of subproblems.
Start the DP from the first cell with all introverts and extroverts available.
Return the result of the DP function as the maximum grid happiness.