Bun Lover

Tema loves cinnabon rolls — buns with cinnabon and chocolate in the shape of a "snail".

Cinnabon rolls come in different sizes and are square when viewed from above. The most delicious part of a roll is the chocolate, which is poured in a thin layer over the cinnabon roll in the form of a spiral and around the bun, as in the following picture:

Cinnabon rolls of sizes 4, 5, 6

For a cinnabon roll of size $$$n$$$, the length of the outer side of the square is $$$n$$$, and the length of the shortest vertical chocolate segment in the central part is one.

Formally, the bun consists of two dough spirals separated by chocolate. A cinnabon roll of size $$$n + 1$$$ is obtained from a cinnabon roll of size $$$n$$$ by wrapping each of the dough spirals around the cinnabon roll for another layer.

It is important that a cinnabon roll of size $$$n$$$ is defined in a unique way.

Tema is interested in how much chocolate is in his cinnabon roll of size $$$n$$$. Since Tema has long stopped buying small cinnabon rolls, it is guaranteed that $$$n \ge 4$$$.

Answer this non-obvious question by calculating the total length of the chocolate layer.