Given an integer array banned and two integers n and max_sum, determine the maximum number of integers you can choose while adhering to the following rules:

1. The selected integers must fall within the range $[1, n]$.

2. Each integer can be chosen at most once.

3. No selected integer can be present in the banned array.

4. The sum of the selected integers must not exceed max_sum.

Your goal is to return the maximum count of integers that can be chosen while satisfying all the above constraints.

Constraints:

• $1 \leq$ banned.length $\leq 10^3$

• $1 \leq$ banned[i], n $\leq 10^3$

• $1 \leq$ max_sum $\leq 10^6$