A Sheer Multiplication Of Numbers

Danny wrote the following product:

1!×2!×3!××119!×120!\large 1! \times 2! \times 3! \times \cdots \times 119! \times 120!

He took out one of the following factorials and found that the product had become a perfect square. Find the factorial.

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

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