Freaky Factorials

Find the sum of all integers \(m\) that are less than \(1000\) and equal to \(\sqrt{n!+1}\) for some positive integer \(n\).

Details and assumptions

The number \( n!\), read as n factorial, is equal to the product of all positive integers less than or equal to \(n\). For example, \( 7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1\).

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