Let's fix the middle chosen item.

For a fixed item with an index <code>j</code>, iterate over items with an index <code>k > j</code> such that <code>prices[k] > prices[j]</code>.

Find the maximum <code>profit[k]</code> with the above condition. Let's call this maximum value <code>max_right</code>.

Do the same for items with an index <code>i < j</code> such that <code>prices[i] < prices[j]</code> and find the maximum <code>profit[i]</code> among them. Let's call this maximum value <code>max_left</code>.

Now the profit when an item with the index <code>j</code> is the middle one would be <code>profit[j] + max_right + max_left</code>.

Finally, do the above procedure for all <code>j</code>'s and find the maximum profit among them. That would be the final answer.