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.

输入描述:

The first line contains three integers HPY, ATKY, DEFY, separated by a space, denoting the initial HP, ATK and DEF of Master Yang.The second line contains three integers HPM, ATKM, DEFM, separated by a space, denoting the HP, ATK and DEF of the monster.The third line contains three integers h, a, d, separated by a space, denoting the price of 1 HP, 1 ATK and 1 DEF.All numbers in input are integer and lie between 1 and 100 inclusively.

输出描述:

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

备注:

For the first sample, prices for ATK and DEF are extremely high. Master Yang can buy 99 HP, then he can beat the monster with 1 HP left.For the second sample, Master Yang is strong enough to beat the monster, so he doesn't need to buy anything.