# Too many ceilings

Algebra Level 3

$\large \left (\lceil(\lceil(\{\lceil x \rceil\}+\lceil \{x\} \rceil +\{x\})\rceil + \{x\})\rceil \right)!$

Find the value of the expression above, where $x$ is an irrational real number.

If you believe there are multiple values, submit your answer as 12345.

Notations:

• $\lceil \cdot \rceil$ denotes the ceiling function.

• $\{ \cdot \}$ denotes the fractional part function.

• $!$ denotes the factorial notation. For example, $8! = 1\times2\times3\times\cdots\times8$.

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