How many schools did Holden get kicked out of in The Catcher in the Rye?

Three schools that Holden has left are mentioned in The Catcher in the Rye.
The first school that Holden mentions is Pencey Prep. He starts his story on the day he left the school which is apparently well-known since he tells the reader confidently that they've probably heard of it or seen ads for it. Holden was the manager of the fencing team at Pencey. He says he was being kicked out because he was flunking four classes and not applying himself.
Holden later explains that he also left Whooton School and Elkton Hills. However, he says that he wasn't kicked out of Elkton Hills. He says he left because he was surrounded by phonies and that he hated the school. He says during the story that he drank a pint of scotch at Whooton School. He often reflects back on life at Whooton, things he learned there, and people he met there. He also looks back at Elkton Hills, though less frequently.

Holden has been kicked out of at least three schools, but it's not clear whether he was kicked out of the others. He has been kicked out of Pencey Prep at the beginning of the novel for flunking his classes, and his teacher Spencer says, "If I’m not mistaken, I believe you also had some difficulty at the Whooton School and at Elkton Hills."
However, Holden clarifies Spencer's remarks and says that he wasn't kicked out of Elkton Hills but instead quit the school. Holden found the headmaster at Elkton Hills, Mr. Haas, a phony, as he cozied up with stylish parents and wasn't as friendly with parents he considered gauche or not up to snuff. Holden tells Spencer that being at Elkton Hills depressed him so much that he had to quit the school. Therefore, Holden has attended at least three schools, but it's not clear if he was kicked out of the others or simply chose to leave them.

We learn of at least three schools that Holden Caulfield has attended (and been kicked out of). As the story opens, Holden is at Pencey Prep, though not for much longer. He has flunked all of his classes except one, so he is going to be expelled. We discover that Holden previously attended The Whooton School and Elkton Hills. All of these schools are undoubtedly expensive, elite institutions, in keeping with the Caulfields' upper-middle-class status. However, Holden just cannot seem to fit in anywhere. He stubbornly resists the expectations of his family to be someone in life. They have already mapped out his future for him—he is to go to school, followed by an Ivy League college, and then onward to a respectable profession befitting someone of a privileged background. However, Holden does not want that; to him, that is all so incredibly phony, to use one of his favorite words. The elite schools he has attended and the values they promote epitomize everything he hates about the big, bad adult world—in which he does not want to live and in which he does not truly belong.