How to correctly negate a predicate bounded by some quantifiers?

Question

this is a problem which was asked in GATE CS 2010.

This is question statement:
Q: Suppose the predicate F(x, y, t) is used to represent the statement that person x can fool person y at time t. which one of the statements below expresses best the meaning of the formula ∀x∃y∃t(¬F(x, y, t))?

Options:
A: Everyone can fool some person at some time.
B: No one can fool everyone all the time.
C: Everyone cannot fool some person all the time.
D: No one can fool some person at some time.

According to my solution:
If F(x): person x can fool person y at time t.
Then
$\forall$x $\exists$y $\exists$t ( ¬F( x, y, t ) )
is same as "Not all person x can fool some person y at some time t. which can be rewritten as "No one can fool some person at some time".
Hence Option D must be the correct one.
However I am wrong.

How to approach these type of problems.