gerund after "remember"

See that sentence:
I remember crying a lot on my first night away from my parents.
Why couldn’t I write like this:
I remember I cried a lot on my first night away from my parents.

In my opinion, it should be:

I remember that I cried a lot on my first night away from my parents.

Right?

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All three of the following sentences are possible and mean basically the same thing:

  • I remember crying a lot on my first night away from my parents.
  • I remember I cried a lot on my first night away from my parents.
  • I remember that I cried a lot on my first night away from my parents.

The first sentence is perhaps more vivid since it focuses more on the activity (i.e. the actual doing of something) rather than on the fact that something happened.
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