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: Wrong Answer)

using System;
using System.Linq;
using System.IO;
using System.Text;
using System.Collections;
using System.Collections.Generic;
using System.Text.RegularExpressions;
 
class Program
{
    static void Main()
    {
        const int Kind = 4;
        int n = int.Parse(Console.ReadLine());
        string s = Console.ReadLine();
        char[,] pattern = new char[Kind, n];
        pattern[0, 0] = 'S'; pattern[0, 1] = 'S';
        pattern[1, 0] = 'S'; pattern[1, 1] = 'W';
        pattern[2, 0] = 'W'; pattern[2, 1] = 'S';
        pattern[3, 0] = 'W'; pattern[3, 1] = 'W';
        bool[] possible = new bool[Kind];
        for(int i = 0; i < Kind; i++) possible[i] = true;
        for (int i = 1; i < n + 1; i++)
        {
            for (int j = 0; j < Kind; j++)
            {
                if(i == n)
                {
                    if(pattern[j, 0] == 'S')
                    {
                        if(!(s[0] == 'o' && pattern[j, n - 1] == pattern[j, 1]
                          || s[0] == 'x' && pattern[j, n - 1] != pattern[j, 1])) possible[j] = false;
                    }
                    else
                    {
                        if(!(s[0] == 'o' && pattern[j, n - 1] != pattern[j, 1]
                          || s[0] == 'x' && pattern[j, n - 1] == pattern[j, 1])) possible[j] = false;
                    }
                    break;
                }
                else if(i == n - 1)
                {
                    if(pattern[j, i] == 'S')
                    {
                        if(!(s[i] == 'o' && pattern[j, i - 1] == pattern[j, 0]
                          || s[i] == 'x' && pattern[j, i - 1] != pattern[j, 0])) possible[j] = false;
                    }
                    else
                    {
                        if(!(s[i] == 'o' && pattern[j, i - 1] != pattern[j, 0]
                          || s[i] == 'x' && pattern[j, i - 1] == pattern[j, 0])) possible[j] = false;
                    }
                    continue;
                }
                else if(pattern[j, i] == 'S' && s[i] == 'o' || pattern[j, i] == 'W' && s[i] == 'x') pattern[j, i + 1] = pattern[j, i - 1];
                else pattern[j, i + 1] = pattern[j, i - 1] == 'S' ? 'W' : 'S';
            }
        }
        int idx = Array.IndexOf(possible, true);
        if(idx == -1) Console.WriteLine(-1);
        else
        {
            for(int i = 0; i < n; i++) Console.Write(pattern[idx, i]);
            Console.WriteLine();
        }
    }
}