K1o0n gave you an array $a$ of length $n$, consisting of numbers $1, 2, \ldots, n$. Accept it? Of course! But what to do with it? Of course, calculate $\text{MEOW}(a)$.

Let $\text{MEX}(S, k)$ be the $k$-th positive (strictly greater than zero) integer in ascending order that is not present in the set $S$. Denote $\text{MEOW}(a)$ as the sum of $\text{MEX}(b, |b| + 1)$, over all distinct subsets $b$ of the array $a$.

Examples of $\text{MEX}(S, k)$ values for sets:

• $\text{MEX}(\{3,2\}, 1) = 1$, because $1$ is the first positive integer not present in the set;
• $\text{MEX}(\{4,2,1\}, 2) = 5$, because the first two positive integers not present in the set are $3$ and $5$;
• $\text{MEX}(\{\}, 4) = 4$, because there are no numbers in the empty set, so the first $4$ positive integers not present in it are $1, 2, 3, 4$.