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)

open Printf
let input_int_array n =
	Array.init n (fun _ -> Scanf.scanf " %d" (fun v -> v))

let get_int () = Scanf.scanf " %d" (fun v -> v)
let get_2_ints () = Scanf.scanf " %d %d" (fun u v -> u,v)
let get_3_ints () = Scanf.scanf " %d %d %d" (fun u v w -> u,v,w)
let get_4_ints () = Scanf.scanf " %d %d %d %d" (fun u v w x -> u,v,w,x)
let get_5_ints () = Scanf.scanf " %d %d %d %d %d" (fun u v w x y -> u,v,w,x,y)

let () =
	let n = get_int ()
	in let a = 
		Array.init n (fun _ -> Scanf.scanf " %c" (fun v -> v))
	in let b = Array.make n 0
	in
	let f,i,e = ref true,ref 0,[|0,0;0,1;1,1;1,0|] in
	while !f && !i<4 do
		let e0,e1 = e.(!i) in
		b.(0) <- e0; b.(1) <- e1;
		for j=2 to n-1 do
			b.(j) <- match b.(j-1),a.(j-1) with
				| 0,'o' | 1,'x' -> b.(j-2)
				| 0,'x' | 1,'o' -> 1-b.(j-2)
				| _ -> failwith ""
		done;
		f := not (
			b.(0) = (
				match b.(n-1),a.(n-1) with
				| 0,'o' | 1,'x' -> b.(n-2)
				| 0,'x' | 1,'o' -> 1-b.(n-2)
				| _ -> failwith ""
			)
			&&
			b.(1) = match b.(0),a.(0) with
			| 0,'o' | 1,'x' -> b.(n-1)
			| 0,'x' | 1,'o' -> 1-b.(n-1)
			| _ -> failwith ""
		);
;		i := !i+1;
	done;
	if not !f then (
		Array.iter (fun v -> print_string @@ if v=0 then "S" else "W") b; print_newline ()
	) else printf "-1\n"