A. Fight the Monstertime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputA 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, ATKY - DEFM), while Yang's HP decreases by max(0, ATKM - DEFY), 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.InputThe 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.OutputThe only output line should contain an integer, denoting the minimum bitcoins Master Yang should spend in order to win.ExamplesInput1 2 11 100 11 100 100Output99Input100 100 1001 1 11 1 1Output0NoteFor 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.
Input1 2 11 100 11 100 100
Output99
['binary search', 'brute force', 'implementation', '*1800']