Both of them are correct.
Some words like this are confusing in English.For example:
American history teacher
It has two meanings:
1- That teacher is from America and he teaches history.
2- That teacher is teaching America's history.
The meaning of these kinds of phrases depend on the sentence.
The country's ongoing widely discussed problems are hopeless.
The country's ongoing widely-discussed problems are hopeless.
It is an expensive well-designed program.
It is a well-designed expensive program.
We need a hyphen after widely to form the adjective widely-discussed.
The terms ongoing and widely-discussed are coordinate adjectives, and we should ...
It doesn't really work to string adjectives together with hyphens like that. You would have to say that he is a well-educated Oxford-educated politician, but the repetition is awkward. I would use a well-educated politician who attended Oxford.