A9746 | Fight the Monster

A monster is attacking the Cyberland!

Master Yang, a braver, is going to beat the monster. Yang and the monster each have 3 attributes: hitpoints ( $HP$ ), offensive power ( $ATK$ ) and defensive power ( $DEF$ ).

During the battle, every second the monster's HP decrease by $max(0,ATK_{Y}-DEF_{M})$ , while Yang's HP decreases by $max(0,ATK_{M}-DEF_{Y})$ , where index $Y$ denotes Master Yang and index $M$ denotes monster. Both decreases happen simultaneously Once monster's $HP<=0$ and the same time Master Yang's $HP>0$ , Master Yang wins.

Master Yang can buy attributes from the magic shop of Cyberland: $h$ bitcoins per $HP$ , $a$ bitcoins per $ATK$ , and $d$ bitcoins per $DEF$ .

Now Master Yang wants to know the minimum number of bitcoins he can spend in order to win.

A monster is attacking the Cyberland!

Master Yang, a braver, is going to beat the monster. Yang and the monster each have 3 attributes: hitpoints ( $HP$ ), offensive power ( $ATK$ ) and defensive power ( $DEF$ ).

During the battle, every second the monster's HP decrease by $max(0,ATK_{Y}-DEF_{M})$ , while Yang's HP decreases by $max(0,ATK_{M}-DEF_{Y})$ , where index $Y$ denotes Master Yang and index $M$ denotes monster. Both decreases happen simultaneously Once monster's $HP<=0$ and the same time Master Yang's $HP>0$ , Master Yang wins.

Master Yang can buy attributes from the magic shop of Cyberland: $h$ bitcoins per $HP$ , $a$ bitcoins per $ATK$ , and $d$ bitcoins per $DEF$ .

Now Master Yang wants to know the minimum number of bitcoins he can spend in order to win.

The only output line should contain an integer, denoting the minimum bitcoins Master Yang should spend in order to win.