Software Licenses

You are launching a security company that must obtain licenses for $n$ different pieces of cryptographic software. Regulations let you obtain at most one license per month.

License $i$ currently sells for $P_i$ dollars, but every license appreciates along an exponential growth curve: the price of license $i$ grows by a factor of $R_i > 1$ each month. Concretely, if you wait $t$ months before buying license $i$ (so $t = 0$ means buying it in the first month at its current price), it costs $P_i \cdot R_i^{t}$ dollars.

Because you may buy at most one license per month, obtaining all $n$ licenses takes exactly $n$ months: you buy exactly one license in each of the months $t = 0, 1, \dots, n - 1$. Decide which license to buy in each month so that the total amount paid is as small as possible, and report that minimum total cost.

The first line contains a positive integer $n$ ($1 \le n \le 100$), the number of licenses you must obtain.

Each of the next $n$ lines contains two numbers $P_i$ and $R_i$ ($R_i > 1$): the current price of license $i$ and its monthly growth factor.

Print a single line containing the minimum total cost, rounded to two decimal places.