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.Linq;
using System.Collections.Generic;
class P
{
    static void Main()
    {
        //[マルバツ][自分][一つ前]
        int[][][] q =
        {
            //◯
            new int[][]
            {
                //羊
                new int[]{0,1},
                //狼
                new int[]{1,0}
            },
            //×
            new int[][]
            {
                //羊
                new int[]{1,0},
                //狼
                new int[]{0,1}
            }
        };
        int n = int.Parse(Console.ReadLine());
        int[] s = Console.ReadLine().Select(x => x == 'o' ? 0 : 1).ToArray();
        for (int i = 0; i <= 1; i++)
        {
            for (int j = 0; j <= 1; j++)
            {
                int[] a = new int[n];
                a[0] = i;
                a[1] = j;
                for (int k = 2; k < n; k++)
                {
                    a[k] = q[s[k - 1]][a[k - 1]][a[k - 2]];
                }
                if (q[s[n - 1]][a[n - 1]][a[n - 2]] == a[0] && q[s[0]][a[0]][a[n - 1]] == a[1])
                {
                    Console.WriteLine(string.Join("", a.Select(x => x == 0 ? "S" : "W").ToArray()));
                    return;
                }
            }
        }
        Console.WriteLine(-1);
    }
}