p03617 AtCoder Grand Contest 019 - 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
```python
Q, H, S, D = map(int, input().split())
N = int(input())

H = min(H, 2 * Q)
S = min(S, 2 * H)
D = min(D, 2 * S)
print((N // 2) * D + (N % 2) * S)

```