Which U.S. Presidents smoked (or didn’t, depending on the default)?

Is this even something we can document? It was a random thought that occurred to me when I saw a picture of Warren G. Harding with a cigarette as he spoke to Thomas Edison.

Which Presidents smoked?

As I consider it, though, I wonder if we should just start with the presumption that smoking was typical through most of history, and so I should ask the opposite:

Which of our Presidents didn’t smoke?

I know, in modern times, that Obama did occasionally, and that Reagan cited his jelly bean habit as his method for quitting. Gerald Ford notably smoked a pipe, and JFK ordered a bunch of Cuban Cigars right before enacting an embargo on the island. FDR had his cigarette holder. What about honest Abe, or any of the founders (especially guys who grew tobacco)?

Any other notable smokers in the White House?