# Factorial Sums

Find the sum of all positive integers $m$ such that $2^m$ can be expressed as sums of four factorials (of positive integers).

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, $7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1$.

The factorials do not have to be distinct. For example, $2^4=16$ counts, because it equals $3!+3!+2!+2!$.

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