Integer number $\displaystyle n\geqslant 1$ is given. For every subset (not empty) $\displaystyle A$ of set $\displaystyle \lbrace 1, 2, 3, 4,...n \rbrace$ we assing number $\displaystyle w(A)$ in such a way: if numbers $\displaystyle a_{1}>a_{2}>a_{3}>...>a_{k}$ are all elements of set $\displaystyle A$, therefore:

$\displaystyle w(A)=a_{1}-a_{2}+a_{3}-...+(-1)^{k+1}a_{k}$

Count the sum of all$\displaystyle 2^{n}-1$numbers$\displaystyle w(A)$