Ice Tea Store

You've come to your favorite store Infinitesco to buy some ice tea.

The store sells ice tea in bottles of different volumes at different costs. Specifically, a 0.25-liter bottle costs Q yen, a 0.5-liter bottle costs H yen, a 1-liter bottle costs S yen, and a 2-liter bottle costs D yen. The store has an infinite supply of bottles of each type.

You want to buy exactly N liters of ice tea. How many yen do you have to spend?

Constraints

• 1 \leq Q, H, S, D \leq 10^8
• 1 \leq N \leq 10^9
• All input values are integers.

Input

Input is given from Standard Input in the following format:

Q H S D N

Output

Print the smallest number of yen you have to spend to buy exactly N liters of ice tea.

Examples

Input

20 30 70 90 3

Output

150

Input

10000 1000 100 10 1

Output

100

Input

10 100 1000 10000 1

Output

40

Input

12345678 87654321 12345678 87654321 123456789

Output

1524157763907942

inputFormat

input values are integers.

Input

Input is given from Standard Input in the following format:

Q H S D N

outputFormat

Output

Print the smallest number of yen you have to spend to buy exactly N liters of ice tea.

Examples

Input

20 30 70 90 3

Output

150

Input

10000 1000 100 10 1

Output

100

Input

10 100 1000 10000 1

Output

40

Input

12345678 87654321 12345678 87654321 123456789

Output

1524157763907942

样例

10 100 1000 10000
1

40