A computer game to ascend a building with a specified number of floors. You have three different facilities for each floor to reach the top: the elevator $(1),$ the escalator $(2),$ and walking up the stairs $(3).$

Each facility has its own scoring rule. Assume the initial score is zero.

$$ Elevator $(1)$: Score increments to the next even number.

$$ Escalator $(2)$: Score increments to the next odd number.

$$ Walk $(3)$: Score increments to the next prime number.

Write an algorithm and python code to display the score to ascend a building. $[$Difficult$]$

Example: If number of floors $4$ and person chosen $3$ for first floor, $2$ for second floor, $3$ for third floor and $2$ for fourth floor. The score is $2($first prime number$)+1($first odd number$)+3($next prime number$)+3($next odd number$)=9.$

Inputs:

Number of floors $($n$)$

Enter facility number $(1$ or $2$ or $3$ n$-$times$)$

Output:

Score

Test cases:

Test $1$: $1$

$---$ Input $---$

$5$

$1$

$2$

$3$

$1$

$2$

$---$ Expected output $($numbers$)---$

$12$

Test $2$: $2$

$---$ Input $---$

$10$

$1$

$2$

$3$

$3$

$2$

$1$

$1$

$2$

$3$

$3$

$---$ Expected output $($numbers$)---$

$38$

Test $3$: $3$

$---$ Input $---$

$7$

$3$

$3$

$3$

$3$

$3$

$3$

$3$

$---$ Expected output $($numbers$)---$

$58$

Test $4$: $4$

$---$ Input $---$

$6$

$3$

$2$

$3$

$2$

$3$

$2$

$---$ Expected output $($numbers$)---$

$19$