To solve this problem, we can use a queue data structure to represent the line of clients waiting to collect their packages. We can also use a set to keep track of the packages on the shelf.

Here is the Python code to solve the problem:

def solution(client): N = len(client) line = [] shelf = set() max_packages = 0

for i in range(N):
    if client[i] == 1:
        max_packages = max(max_packages, len(shelf))
        shelf.discard(1)
    else:
        line.append(client[i])
        shelf.add(client[i]-1)
    
    while line and line[0] == max(shelf) + 1:
        max_packages = max(max_packages, len(shelf))
        shelf.discard(line.pop(0))
        
return max_packages

test cases

print(solution([3, 2, 4, 5, 1])) # output: 2 print(solution([1, 2, 3, 4, 5])) # output: 0 print(solution([3, 2, 7, 5, 4, 1, 6])) # output: