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 string_to_list str =
  let rec loop i limit =
    if i = limit then []
    else (String.get str i) :: (loop (i + 1) limit)
  in
  loop 0 (String.length str)


let fwd arr_length n = if n = (arr_length - 1) then 0 else n+1
let prev arr_length n = if n = 0 then arr_length - 1 else n-1
let flip c = if c = 'S' then 'W' else 'S'
let print_chars arr = Array.iter (fun x -> Printf.printf "%c" x) arr; Printf.printf "\n"
           
let fill arr arr_length n by =
  if (arr.(n) == 'S' && by = 'o') || (arr.(n) == 'W' && by = 'x') then
    begin
      arr.(fwd arr_length n) <- arr.(prev arr_length n);
    end
  else
    begin
      arr.(fwd arr_length n) <- flip arr.(prev arr_length n);
    end    

let rec extend answers ans_length cursor ret = match answers with
  | [] -> ret
  | 'o'::rest ->
     fill ret ans_length cursor 'o';
     extend rest ans_length (cursor+1) ret
  | 'x'::rest ->
     fill ret ans_length cursor 'x';
     extend rest ans_length (cursor+1) ret
  | _ -> ret

let check arr arr_length by n =
  if (arr.(n) == 'S' && by = 'o') || (arr.(n) == 'W' && by = 'x') then
    arr.(fwd arr_length n) = arr.(prev arr_length n)
  else
    arr.(fwd arr_length n) <> arr.(prev arr_length n)

let make_list f t step =
  let rec make_list_inner c t lst =
    if c >= t then lst else make_list_inner (c+step) t (c::lst)
  in
  List.rev (make_list_inner f t [])

let check_all pos_ans length pairs =
  let checks = List.map (fun (x,y) -> check pos_ans length y x) pairs in
  List.fold_left (fun x y -> x && y) true checks

let array_make length a b =
  let ret = (Array.make length a) in
  ret.(length - 1) <- b;
  ret

let solve str =
  let str_list = (string_to_list str) in
  let length = List.length str_list in
  let pairs = List.combine (make_list 0 length 1) str_list in
  let pos_ans = extend str_list length 0 (array_make length 'S' 'S') in
  if check_all pos_ans length pairs then pos_ans else
    let pos_ans = extend str_list length 0 (array_make length 'S' 'W') in
    if check_all pos_ans length pairs then pos_ans else
      let pos_ans = extend str_list length 0 (array_make length 'W' 'W') in
      if check_all pos_ans length pairs then pos_ans else
        let pos_ans = extend str_list length 0 (array_make length 'W' 'S') in
        if check_all pos_ans length pairs then pos_ans else
          [||]
  
let () =
  let _ = read_int() in
  let str = read_line () in
  let ans = solve str in
  if ans = [||] then
    Printf.printf ("-1")
  else
    Array.iter (fun x -> Printf.printf "%c" x) ans;
  Printf.printf "\n"
;;