Wash and pick over the cranberries. Drain well. Coarsely chop cranberries in food mill or processor. Stir sugar into berries, cover, and chill for 4 hours. Place cranberries in sieve and allow to drain well (this takes 1 to 2 hours). When cranberries are drained, core and chop apples, but do not peel. Combine apples, celery, grapes, walnuts, and mayonnaise. Gently fold in cranberries.