Phigros is a music game in which players are required to touch the screen following the rhythm of songs and try to get the highest scores.

The total score of a song is the sum of the following two parts rounded to the nearest integer (assume that the song has $$$n$$$ notes in total):

• Accuracy. The accuracy score for each note is added up independently according to the judgment:
  • Perfect: $$$900\,000\cdot n^{-1}$$$;
  • Good: $$$585\,000\cdot n^{-1}$$$;
  • Bad or miss: $$$0$$$.

• Combo. The Max Combo of a song is the maximum number of continuous notes with perfect or good judgements. The combo score for a song with Max Combo $$$m$$$ is $$$100\,000 \,m\cdot n^{-1}$$$.

Recall that $$$$$$ \text{round}(x)=\begin{cases} \lfloor x\rfloor, & x \lt \lfloor x\rfloor+0.5 \\ \lfloor x\rfloor + 1, & x\ge\lfloor x\rfloor+0.5 \end{cases} $$$$$$

Now Walk Alone is playing a song with $$$n$$$ notes. He has already got the judgement of the first $$$k$$$ notes, and he wants to know the maximum score he could get if he played the rest of the song perfectly.