You are given five integers: cost1, cost2, costBoth, need1, and need2.

There are three types of items available for purchase:

• An item of type $1$ costs cost1 and provides $1$ unit of type $1$.

• An item of type $2$ costs cost2 and provides $1$ unit of type $2$.

• An item of type $3$ costs costBoth and provides $1$ unit of type $1$ and $1$ unit of type $2$.

Return the minimum total cost needed to acquire at least need1 units of type $1$ and at least need2 units of type $2$.

Constraints:

• $1 \leq$ cost1, cost2, costBoth $\leq 10^6$

• $0 \leq$ need1, need2 $\leq 10^9$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.