Description

On this planet, there are two different kinds of minerals. One is called “ice mineral”, a blue high-energy mineral that is a solid similar to $\text{H}_{2}\text{O}$. The other is called “gas mineral”, an allotrope form of carbon tetrachloride.

Humans refine these two minerals to obtain energy for survival. $\text{SCV}$ is the only intelligent robot that can collect both kinds of minerals. Each time it collects an ice mineral, it takes $t_{1}$ time; each time it collects a gas mineral, it takes $t_{2}$ time. After a collection is finished, it yields $8$ units of ice mineral or $8$ units of gas mineral. Each time, an $\text{SCV}$ can only collect one of the two types: ice mineral or gas mineral.

$\text{SCV}$ can be produced by the main base. For each $\text{SCV}$ produced, the main base will spend $50$ units of ice mineral. Due to limited manufacturing capacity, the main base can only produce one $\text{SCV}$ at the same time. Producing one $\text{SCV}$ takes $t_{3}$ time.

At the beginning, humans have $50$ units of ice mineral and $4$ $\text{SCV}$s. They need to collect $p_{1}$ units of ice mineral and $p_{2}$ units of gas mineral. Please compute the minimum time they need.

Input Format

The input file contains only one line, in order: $t_{1}$, $t_{2}$, $t_{3}$, $p_{1}$, $p_{2}$, with one space between every two numbers.

Output Format

The output file contains only one number, which is the minimum time needed to reach the goal.

10 9 18 150 0

40

Hint

$1 \leq t_{1}, t_{2}, t_{3} \leq 18$, $0 \leq p_{1}, p_{2} \leq 150$. The data is chosen randomly and uniformly from valid data.

Constraints

Translated by ChatGPT 5