Fewest Stones Left After Merging Equal-Level Pairs

You are carrying a collection of stones, and each stone has a level, which is a positive integer. Two stones with the same level `x` can be merged into one new stone of level `x + 1`. You may perform any number of merges in any order, and a stone created by a merge can itself be merged again. Return the smallest number of stones you can be left with. ### Function Signature ```python def magic(stones: list[int]) -> int: ``` `stones[i]` is the level of the `i`-th stone. ### Rules - A merge always takes exactly two stones of equal level and replaces them with one stone whose level is one higher. Stones of different levels can never be merged. - Merged stones may reach level 10000 or higher; there is no upper limit on the level of a merged stone. - Return the number of stones that remain, not their levels. ### Constraints - `1 <= len(stones) <= 10^5` (the original states only that the list contains at least one stone; the upper bound is assumed for this practice version) - `1 <= stones[i] <= 9999` - The answer is always between `1` and `len(stones)`. ### Examples **Example 1** ```text Input: stones = [1, 2, 1] Output: 1 ``` The two level-1 stones merge into a level-2 stone, and the two level-2 stones then merge into a single level-3 stone. **Example 2** ```text Input: stones = [3, 3, 3] Output: 2 ``` Two of the level-3 stones merge into a level-4 stone. The remaining level-3 stone and the level-4 stone have different levels, so two stones remain. **Example 3** ```text Input: stones = [5, 2, 4, 2, 3] Output: 1 ``` The two level-2 stones merge into level 3, the two level-3 stones into level 4, the two level-4 stones into level 5, and the two level-5 stones into a single level-6 stone.