In each of the cases below, there exists only one solution whereby the sum of $n$ **positive** integers equals the product.

- For $n=2$, we have $2+2=2\times 2$.
- For $n=3$, we have $1+2+3=1\times2\times3$.
- For $n=4$, we have $1+1+2+4=1\times 1\times2\times4$.

If solution(s) exist for $n=5,$ find the **sum** of all possible sums (or equivalently, products).

If such a solution does not exist, submit your answer as 0.

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