Problem:
Score : 500 points

Problem Statement

Snuke, who loves animals, built a zoo.

There are N animals in this zoo. They are conveniently numbered 1 through N, and arranged in a circle.
The animal numbered i (2≤i≤N-1) is adjacent to the animals numbered i-1 and i+1. Also, the animal numbered 1 is adjacent to the animals numbered 2 and N, and the animal numbered N is adjacent to the animals numbered N-1 and 1.

There are two kinds of animals in this zoo: honest sheep that only speak the truth, and lying wolves that only tell lies.

Snuke cannot tell the difference between these two species, and asked each animal the following question: "Are your neighbors of the same species?" The animal numbered i answered s_i. Here, if s_i is o, the animal said that the two neighboring animals are of the same species, and if s_i is x, the animal said that the two neighboring animals are of different species.

More formally, a sheep answered o if the two neighboring animals are both sheep or both wolves, and answered x otherwise.
Similarly, a wolf answered x if the two neighboring animals are both sheep or both wolves, and answered o otherwise.

Snuke is wondering whether there is a valid assignment of species to the animals that is consistent with these responses. If there is such an assignment, show one such assignment. Otherwise, print -1.

Constraints

3 ≤ N ≤ 10^{5}

s is a string of length N consisting of o and x.

Input

The input is given from Standard Input in the following format:

N
s

Output

If there does not exist an valid assignment that is consistent with s, print -1.
Otherwise, print an string t in the following format. The output is considered correct if the assignment described by t is consistent with s.

t is a string of length N consisting of S and W.

If t_i is S, it indicates that the animal numbered i is a sheep. If t_i is W, it indicates that the animal numbered i is a wolf.

Sample Input 1

6
ooxoox

Sample Output 1

SSSWWS

For example, if the animals numbered 1, 2, 3, 4, 5 and 6 are respectively a sheep, sheep, sheep, wolf, wolf, and sheep, it is consistent with their responses. Besides, there is another valid assignment of species: a wolf, sheep, wolf, sheep, wolf and wolf.

Let us remind you: if the neiboring animals are of the same species, a sheep answers o and a wolf answers x. If the neiboring animals are of different species, a sheep answers x and a wolf answers o.

Sample Input 2

3
oox

Sample Output 2

-1

Print -1 if there is no valid assignment of species.

Sample Input 3

10
oxooxoxoox

Sample Output 3

SSWWSSSWWS

Solution in OCaml (4.02.3) (judge verdict: Accepted)

let first_some f =
  List.fold_left (fun v e -> match v with None -> f e | _ -> v) None

let nb a b r =
  let f b = if b then 1 else 0 in
  [|'W';'S'|].((f (b = 'S') + f (r = 'o') + f (a = 'S')) mod 2)

let () =
  Scanf.scanf "%d %s" @@ fun n s ->
  [('S','S'); ('S','W'); ('W','S'); ('W','W')]
  |> first_some (fun (h0, h1) ->
      let h = Array.make n '0' in
      h.(0) <- h0; h.(1) <- h1;

      let t = String.init n (fun i ->
        if i < 2 then h.(i)
        else
          let v = nb h.(i-2) h.(i-1) s.[i-1] in
          h.(i) <- v; v)
      in

      if nb h.(n-2) h.(n-1) s.[n-1] = h.(0) && nb h.(n-1) h.(0) s.[0] = h.(1) then
        Some t
      else None)
  |> (function Some x -> x | _ -> "-1") |> print_endline