Let \(n > 3\) be a positive integer. Suppose that \(n\) children are arranged in a circle, and \(n\) coins are distributed between them (some children may have no coins). At every step, a child with at least \(2\) coins may give \(1\) coin to each of their immediate neighbors on the right and left. Determine all initial distributions of the coins from which it is possible that, after a finite number of steps, each child has exactly one coin.