\problemname{Removal Game}

Bobby Roberts is totally bored in his algorithms class, so he's
developed a little solitaire game. He writes down a sequence of
positive integers and then begins removing them one at a time. The cost
of each removal is equal to the greatest common divisor (gcd) of the two
surrounding numbers (wrapping around either end if necessary).
For example, if the sequence of numbers was 2, 3, 4, 5 he could remove
the 3 at a cost of 2 (= gcd(2,4)) or he could remove the 4 at a cost of
1 (= gcd(3,5)). The
cost of removing 2 would be 1 and the removal of 5 would cost 2.
Note that if the 4 is removed first, the removal of the 3 afterwards
now has a cost of only 1.

Bobby keeps a running total of each removal cost. When he ends up with
just two numbers remaining he takes their gcd, adds that cost to the running total,
and ends the game by removing them both.
The object of the game is to remove all of the numbers
at the minimum total cost. Unfortunately, he
spent so much time in class on this game, he didn't pay attention to several
important lectures which would lead him to an algorithm to solve this
problem. Since none of you have {\em ever\/} wasted time in your algorithm classes, I'm sure you'll have no
problem finding the minimum cost given any sequence of numbers.

\section*{Input}
Input contains multiple test cases.  Each test case consists of a single line
starting with an integer $n$ which indicates the number of values in the
sequence ($2 \leq n \leq 100$). This is followed by $n$ positive integers
which make up the sequence of values in the game.  All of these integers will
be $\leq 1000$. Input terminates with a line containing a single 0.
There are at most 1000 test cases.

\section*{Output}
For each test case, display the minimum cost of removing all of
the numbers.

