Please solve in typescript. Thank you.

There is an array A of N integers sorted in non$-$decreasing order. In one move, you can either remove an integer from A or insert an integer before or after any element of A $.$ The goal is to achieve an array in which all values

X that are present in the array occur exactly X times.

For example, given $A=[1,1,3,4,4,4],$ value $1$ occurs twice, value $3$ occurs once and value $4$ occurs three times. You can remove one occurrence each of both $1$ and $3,$ and insert one occurrence $4,$ resulting in the array $,$

$4,4,4].$ In this array, every element X occurs exactly X times.

What is the minimum number of moves after which every value X in the array occurs exactly X times?

Write a function:

function solution$($A$)$;

that, given an array A$,$ returns the minimum number of moves after which every value X in the array occurs exactly X times. Note that it is permissible to remove some values entirely, if appropriate.

Examples:

Given $A=[1,1,3,4,4,4],$ your function should return $3,$ as described above.

Given $A=[1,2,2,2,5,5,5,8],$ your function should return $4.$ You can delete the $8$ and one occurrence of $2,$ and insert $5$ twice, resulting in $1,2,2,5,5,5,5,5$ after four moves. Notice that after the removals, there is no

occurrence of $8$ in the array anymore.

Given $A=[1,1,1,1,3,3,4,4,4,4,4],$ your function should return $5.$

Given $A=[10,10,10],$ your function should return $3.$ You can remove all elements, resulting in an empty array.

Write an efficient algorithm for the following assumptions:

N is an integer within the range $[1..\mathrm{.}100,000]$;

each element of array A is an integer within the range $[1.\mathrm{.}100,000,000]$;

elements of array A are sorted in non$-$decreasing order.