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.


-----Input-----

The first line contains three integers HP_{Y}, ATK_{Y}, DEF_{Y}, separated by a space, denoting the initial HP, ATK and DEF of Master Yang.

The second line contains three integers HP_{M}, ATK_{M}, DEF_{M}, 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.


-----Output-----

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


-----Examples-----
Input
1 2 1
1 100 1
1 100 100

Output
99

Input
100 100 100
1 1 1
1 1 1

Output
0



-----Note-----

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.