RU-SPB 2008 Problem 114

There are $100$ numbers on circle, and no one number is divided by other. In same time for all numbers we make next operation: If $(a,b)$ are two neighbors ( $a$ is left neighbor) , then we write between $a,b$ number $\frac{a}{(a,b)}$ and erase $a,b$ This operation was repeated some times. What maximum number of $1$ we can receive ?

Example: If we have circle with $3$ numbers $4,5,6$ then after operation we receive circle with numbers $\frac{4}{(4,5)}=4,\frac{5}{(5,6)}=5, \frac{6}{(6,4)}=3$ .