Excel: Array Formula Sum lookup of one list to another

I'm trying to find the total cost of a strategy by looking up the elements that make up that strategy from a table of unique item id's matched to development cost. If an item is in the strategy twice I only want to count the cost once. So strategy 1 would be the cost of Name 1, Name 5, Name 12 and Name 14.

I've played around with this for ages trying various combinations of index match, lookup, and sumif but haven't quite cracked it.