Olympics

The weightlifting event is next, and it is time to impress the crowd. Your strength $S$ stays the same all evening, but your energy $E$ drops with every attempt. On each attempt you pick any positive weight $W$, which need not be an integer. If $S \ge W$ the lift succeeds and your energy drops by $E_{succ}$. If $S < W$ the lift fails and your energy drops by $E_{fail}$. You may keep attempting lifts while your energy stays above $0$, and once it reaches $0$ or less you cannot attempt anything more. Your score is the heaviest weight you lifted successfully, or $0$ if every attempt failed.

The best score comes from lifting exactly at your strength limit, but you do not know that limit. You know only two things. The 25 kg bar always goes up. And 225 kg, the bar plus 100 kg on each side, is the heaviest lift anyone can imagine. So $25 \le S \le 225$, and $S$ can be any value in that range.

How close to the optimal score can you guarantee? That is, find the smallest $d$ such that you can guarantee a score of at least $S - d$ whatever $S$ turns out to be.

The first line contains three space-separated integers $E$, $E_{succ}$ and $E_{fail}$ ($1 \le E, E_{succ}, E_{fail} \le 10^7$).

Print the minimum $d$ on one line, rounded at the seventh decimal place and padded to exactly six decimal places.