In Alfred Hitchcock's movie "To Catch a Thief", the retired infamous jewel thief John Robie has to crack a safe with a complicated $4\times4$ pattern of keys. Each of the 16 keys is either turned around ($+$) or not turned around ($-$):
- - + - + - - + - + - - + - - +
To open the safe, John Robie must make all keys turned around. The catch is that whenever Robie turns one key (from $+$ to $-$ or from $-$ to $+$), then all the keys in the same row and all the keys in the same column simultaneously turn (from $+$ to $-$ or from $-$ to $+$ respectively). John Robie may turn any key as often as he likes.
Question: What is the minimum number of keys that John Robie has to turn to open the safe?