A11760 | Feed the cat

After waking up at $hh$ : $mm$ , Andrew realised that he had forgotten to feed his only cat for yet another time (guess why there's only one cat). The cat's current hunger level is $H$ points, moreover each minute without food increases his hunger by $D$ points.

At any time Andrew can visit the store where tasty buns are sold (you can assume that is doesn't take time to get to the store and back). One such bun costs $C$ roubles and decreases hunger by $N$ points. Since the demand for bakery drops heavily in the evening, there is a special $20%$ discount for buns starting from $20$ : $00$ (note that the cost might become rational). Of course, buns cannot be sold by parts.

Determine the minimum amount of money Andrew has to spend in order to feed his cat. The cat is considered fed if its hunger level is less than or equal to zero.

The first line contains two integers $hh$ and $mm$ $(00<=hh<=23,00<=mm<=59)$ — the time of Andrew's awakening.

The second line contains four integers $H$ , $D$ , $C$ and $N$ $(1<=H<=10^{5},1<=D,C,N<=10^{2})$ .

Output the minimum amount of money to within three decimal digits. You answer is considered correct, if its absolute or relative error does not exceed $10^{-4}$ .

Formally, let your answer be $a$ , and the jury's answer be $b$ . Your answer is considered correct if .