Add largest value and half the others (some cells blank)

I would think this would be simple using the max function or large function but I keep getting #value or #NUM errors
I have a row of 9 cells (some are blank). I want to add several together and then add the largest in a subset of 6 cells and add half sum of the other 5 cells in the same subset.

My general formula looks like this =ROUND(SUM(F13,G13,M13,N13)+(SUM(H13,I13,J13,K13,L13)/2),0) And that will work if G13 is the highest of cells in G13:L13. But I would like it to choose the highest from G13:L13 (and some or all will be blank)

Thank you,
Stuart

I am having trouble following your example. Please post a workbook with several examples that show what you might have and what you expect.

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