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.

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.