Problem O
Kitten Zero
Your kitten, Zero, has contracted the sniffles. Zero is a very sociable kitten so you suspect that it may have spread the disease. You wonder how many kittens are likely to become ill.
You check on Wikipedia and see that the common cold has a basic reproduction number $R_0$ between 2 and 3.
You grab a napkin and do the math. Suppose that $R_0$ is 2.
Then Kitten Zero infects two kittens, who each then infect two other kittens and so on and so forth. After 3 rounds of transmissions the total number of cases is: $1 + 2 + (2*2) + (2*2*2) = 15$
But what if $R_0$ is 2.5...or 2.7...or 2.67?
Input
Input consists of one line with one floating point number $R_0$, the reproduction rate for the infection, where $2 \leq R_0 \leq 3$. It is guaranteed that the number is given with at most two digits after the decimal point.
Output
Output consists of one line with one integer, the total amount of cases, rounded to the nearest kitten.
| Sample Input 1 | Sample Output 1 |
|---|---|
2 |
15 |
| Sample Input 2 | Sample Output 2 |
|---|---|
2.5 |
25 |
| Sample Input 3 | Sample Output 3 |
|---|---|
2.67 |
30 |
