Light ray polygon

Chang-yeon drew a picture with light rays by placing $n$ mirrors and a very small laser pointer on a plane.

An example of a picture drawn with light rays

The finished drawing forms a convex polygon $A\_0A\_1\cdots A\_n$. $A\_0$ is the point where the laser pointer is located. The ray reflects off the mirrors at $A\_1,A\_2,\ldots ,A\_n$ in order and returns to $A\_0$, where the laser pointer blocks it so it goes no further.

A ray reflecting off mirrors as it travels

The ray moves as follows. For convenience, let $A\_{n+1}=A\_0$.

• The ray travels in a straight line from $A\_{i-1}$ toward $A\_i$, reflects at $A\_i$, and then travels in a straight line toward $A\_{i+1}$.
• The angle of incidence $\theta\_i$ at $A\_i$ is $\displaystyle \frac{\angle A\_{i-1}A\_iA\_{i+1}}{2}$, as shown in the figure.

Given the angles of incidence $\theta\_1,\theta\_2,\ldots ,\theta\_n$ measured at the moment of reflection at each point $A\_1,A\_2,\ldots ,A\_n$, find $\angle A\_nA\_0A\_1$ in the figure. All angles in the problem use degrees, where a full turn is $360^\circ$.

The first line contains an integer $n$.

The second line contains $n$ integers $\theta\_1,\theta\_2,\ldots ,\theta\_n$ separated by spaces.

Print an integer equal to the size of $\angle A\_nA\_0A\_1$.

• $2\le n\le 50$.
• $1\le\theta\_i\le 89$.
• All interior angles of the convex polygon drawn on the plane are integers, and each is guaranteed to be at least $1^\circ$ and at most $179^\circ$.