Poster mailing

VE OCH FASA! For the $1337$th year in a row, PostNord has raised the postage, and the budget of the Programming Olympiad (Programmeringsolympiaden, PO) is at risk of breaking.

Every year PO sends posters to about $450$ upper secondary schools. One mailing consists of three things:

• an envelope of C4 size ($229\text{ mm} \times 324\text{ mm}$)
• two posters of A3 size ($297\text{ mm} \times 420\text{ mm}$)
• one information sheet of A4 size ($210\text{ mm} \times 297\text{ mm}$)

The letter must weigh at most $50$ grams, since otherwise the postage is twice as high. To meet this magic weight limit, PO can choose which kind of paper is used for the three things. Each kind has a basis weight (weight per area), usually given in $\frac{\text{gram}}{\text{m}^2}$. Note that the envelope is made of two sheets glued together of C4 size, while the basis weights and the dimensions above apply to one sheet.

Write a program that computes the total weight of one letter.

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

Print a single real number: the weight of one complete mailing in grams. The answer must be given with an accuracy of at least $3$ decimals, that is, within $5 \cdot 10^{-4}$ of the correct answer.