# 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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