Problem link: https://mirror.codeforces.com/problemset/problem/2181/B

I'm specifically not able to make sense of this claim

In each pair of moves, at least the maximum is subtracted from the sum of all N numbers. Therefore, the total sum is multiplied by at most $$$1 − \frac{1}{N}$$$ in each step.

I've tried getting AI to explain it to me but it keeps getting confused as well :((