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C. Fight the Monster

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard 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, *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.

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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