Alice has a sequence of length

, denoted as

.
Now, Alice can perform the following operations an infinite number of times:
1. First operation: Remove a number at a specific position. After removal, the subsequent numbers shift forward. For example, for the sequence {5, 1, 2, 3}, removing 1 will result in {5, 2, 3}.
2. Second operation: Insert a zero before a specific position. After insertion, the number at that position and the subsequent numbers shift backward. For example, for the sequence {5, 1, 2, 3}, inserting zero before 5 will result in {0, 5, 1, 2, 3}.
Now, Alice wants to maximize the number of positions in the sequence where

. Can you help Alice determine the maximum number of such positions?