Too many ceilings

Algebra Level 3

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

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

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


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

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

  • !! denotes the factorial notation. For example, 8!=1×2×3××88! = 1\times2\times3\times\cdots\times8 .


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