Poster Mailing

DISASTER! PostNord has raised the postage fee for the $1337$th year in a row, which threatens to break the budget of the Programming Olympiad.

Each year, PO sends out posters to about $450$ high schools. A mailing consists of three items:

• an envelope of C4 size ($229\text { mm} \times 324\text { mm}$)

• two posters of A3 size ($297\text { mm} \times 420\text { mm}$)

• an information sheet of A4 size ($210\text { mm} \times 297\text { mm}$)

It is very important that the letter weighs no more than $50$ grams, as the postage would otherwise be twice as high. To stay within this magical weight limit, PO can choose which type of paper to use for the three items. Each type has a basis weight (weight per area) typically given in $\frac{\text {grams}}{\text {m}^2}$. Note that the envelope consists of two glued sheets of C4 size, while the basis weights and the above dimensions apply to one sheet.

Write a program that calculates the total weight of a letter.

Input

The input consists of three integers between $50$ and $200$, the basis weights in $\frac{\text {grams}}{\text {m}^2}$ for the types used for the envelope, the posters, and the information sheet respectively.

Output

Output a single decimal number: the weight of a complete letter mailing in grams. The answer must be given with at least $3$ decimal places of accuracy (i.e., within $5 \cdot 10^{-4}$ of the correct answer).

Scoring

Your solution will be tested on a set of test groups, each worth a number of points. Each test group contains a set of test cases. To get the points for a test group you need to solve all test cases in the test group.

120 90 70

44.626140

150 200 90

77.768100