Total sum is invariant. Final sorted array must have all elements = average S/n. Twice the average (2S/n) must be integer for pairwise averaging to work.

Greedy scan: if element equals S/n skip; otherwise pair it with next neighbor and check they sum to 2S/n. If pairing covers whole array, answer Yes.

If pairing fails, check if any split i exists where prefix average < suffix average (strict). That gap lets you sort. No such split = No.