A microwave has a keypad with digits from $0$ to $9$ and a $4$ digit display showing time in the format mm:ss, representing minutes and seconds. The displayed time can be set by typing a sequence of $1$ to $4$ digits.

When a sequence of digits is entered:

• The entered sequence represents the number of minutes and seconds, where the last $2$ digits correspond to the seconds and any preceding digits correspond to the minutes.

• Entering fewer than $4$ digits is valid. For instance, entering $3$ digits d1, d2, d3 is interpreted as 0d1:d2d3 ($d_1$ minutes and $d_2d_3$ seconds).

• The total cooking time in seconds is calculated as $ ext{minutes} imes 60 + ext{seconds}$.

• Both minutes and seconds can range from $0$ to $99$.

You are given four integers: startAt, moveCost, pushCost, and targetSeconds.

Initially, your finger is positioned over the digit startAt.

• Moving your finger from the current digit to a different digit costs moveCost. Moving to the same digit costs $0$.

• Pressing the button under your finger costs pushCost.

Return the minimum cost to set the microwave to cook for exactly targetSeconds seconds.

Constraints:

• $0 \leq$ startAt $\leq 9$

• $1 \leq$ moveCost, pushCost $\leq 10^5$

• $1 \leq$ targetSeconds $\leq 6039$

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.