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.

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