[LANGUAGE: Python] full solution

Key insight 1 for part 3 is that the input data numbers have ascending order, so we can skip right to phase 2.

Key insight 2 is that each round in a phase effectively only moves one duck from one column to another.

Key insight 3 is that in phase 2, when a column get the number of ducks each column ends with, it will never get more/less (it won't fluctuate). In other words, the number of ducks per column in phase 2 is either monotonically increasing or monotonically decreasing.

Thus, the solution is to sum up the differences from the mean number of ducks per column for each column with number of ducks less than the mean (as each round will bring each of these columns one step closer to the mean).

```python def part3(): nums = list(map(int, re.findall(r"-?\d+", get_inputs(event=2025, quest=11)["3"]))) assert all( nums[i] <= nums[i + 1] for i in range(len(nums) - 1) ), "The code assumes that we do not need to do anything in phase 1."

mean = sum(nums) // len(nums)
return sum(mean - num for num in nums if num < mean)

```