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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
 
class Program {
    static int ReadInt() { return int.Parse(Console.ReadLine()); }
    static int[] ReadInts() { return Console.ReadLine().Split().Select(int.Parse).ToArray(); }
    static string[] ReadStrings() { return Console.ReadLine().Split(); }
 
    const int Sheep = 0;
    const int Wolf = 1;
 
    static bool Validate(int p, int[] xs, char reply) {
        int prev = (p - 1 + xs.Length) % xs.Length;
        int next = (p + 1) % xs.Length;
 
        if (xs[p] == Sheep) {
            return reply == 'o' ? xs[prev] == xs[next] : xs[prev] != xs[next];
        }
        else {
            return reply == 'o' ? xs[prev] != xs[next] : xs[prev] == xs[next];
        }
    }
 
    static bool Calc_1(int[] xs, string s) {
 
        Func<int, char, int, int> other = (animal, reply, prev) => {
            if (animal == Sheep) {
                return reply == 'o' ? prev : (prev ^ 1);
            }
            else { // Wolf
                return reply == 'o' ? (prev ^ 1) : prev;
            }
        };
 
        int n = s.Length;
        for (int i = 1; i < n - 1; i++) {
            int prev = xs[i - 1];
            xs[i + 1] = other(xs[i], s[i], prev);
        }
 
        var a = Validate(0, xs, s[0]);
        var b = Validate(n - 1, xs, s[n - 1]);
        var c = Validate(n - 2, xs, s[n - 2]);
        return a && b && c;
    }
 
    static void Calc(string s) {
        int n = s.Length;
 
        bool found = false;
        var xs = new int[n];
        for (int i = 0; i < (1 << 2); i++) {
            // (S, S), (S, W), (W, S), (W, W) の 4 パターン試す
            xs[0] = (i & 2) == 0 ? 0 : 1;
            xs[1] = i & 1;
            if (Calc_1(xs, s)) {
                Console.WriteLine(string.Join("", xs.Select(e => e == Sheep ? "S" : "W")));
                found = true;
                break;
            }
        }
 
        if (!found)
            Console.WriteLine(-1);
    }
 
    static void Main() {
        ReadInt();
        var s = Console.ReadLine();
        Calc(s);
    }
}