3001.Fight the Monster

Time Limit: 1s Memory Limit: 256MB

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,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 \le 0 and the same time Master Yang's HP \gt 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.

Input Format(From the terminal/stdin)

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 1HP, 1ATK and 1DEF.

All numbers in input are integer and lie between 1 and 100 inclusively.

Output Format(To the terminal/stdout)

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

Sample Input 1

Copy 
1 2 1
1 100 1
1 100 100
 · · \n
 ·   · \n
 ·   ·   \n

Sample Output 1

Copy 
99
  \n

Sample Input 2

Copy 
100 100 100
1 1 1
1 1 1
   ·   ·   \n
 · · \n
 · · \n

Sample Output 2

Copy 
0
 \n

Hints

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.

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