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.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Runtime.InteropServices;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using static System.Math;
using static Math2;
using static io;
using static Utils;

public class CompetitiveProgramming {
  public void Solve () {
    var N = Int1;
    var s = Str;

    //animal[k]==0 sheep
    //animal[k]==1 wolf
    for (int i = 0; i < 2; ++i) {
      for (int j = 0; j < 2; ++j) {
        var animal = Enumerable.Repeat (-1, N).ToArray ();
        animal[0] = i;
        animal[1] = j;

        for (int k = 2; k < N; ++k) {
          if (animal[k - 1] == 0) {
            if (s[k - 1] == 'o') {
              animal[k] = animal[k - 2];
            } else {
              animal[k] = animal[k - 2] == 1 ? 0 : 1;
            }
          } else {
            if (s[k - 1] == 'x') {
              animal[k] = animal[k - 2];
            } else {
              animal[k] = animal[k - 2] == 1 ? 0 : 1;
            }
          }
        }
        Put (animal);
        var flg = false;
        var flg2 = false;
        if (animal[N - 1] == 0 && s[N - 1] == 'o' && animal[N - 2] == animal[0]) flg = true;
        if (animal[N - 1] == 0 && s[N - 1] == 'x' && animal[N - 2] != animal[0]) flg = true;
        if (animal[N - 1] == 1 && s[N - 1] == 'o' && animal[N - 2] != animal[0]) flg = true;
        if (animal[N - 1] == 1 && s[N - 1] == 'x' && animal[N - 2] == animal[0]) flg = true;
        if (animal[0] == 0 && s[0] == 'o' && animal[N - 1] == animal[1]) flg2 = true;
        if (animal[0] == 0 && s[0] == 'x' && animal[N - 1] != animal[1]) flg2 = true;
        if (animal[0] == 1 && s[0] == 'o' && animal[N - 1] != animal[1]) flg2 = true;
        if (animal[0] == 1 && s[0] == 'x' && animal[N - 1] == animal[1]) flg2 = true;
        if (flg && flg2) {
          var ans = new StringBuilder ();

          for (int k = 0; k < N; ++k) {
            if (animal[k] == 0) ans.Append ('S');
            else ans.Append ('W');
          }
          Put (ans);
          return;
        }
      }
    }
    Put ("-1");
  }
}

public static class Math2 {
  public const int INF = 1 << 29;
  public const long INFL = 1L << 60;
  public const long MOD = 1000000007;
  public const int MOD2 = 998244353;

  public static long Power (long a, long b, long MOD = 1000000007) //i^N
  {
    long res = 1;
    while (b > 0) {
      if ((b & 1) != 0) res = res * a % MOD;
      a = a * a % MOD;
      b >>= 1;
    }
    return res;
  }
  public static long Power2 (long a, long b) //i^N
  {
    long res = 1;
    while (b > 0) {
      if ((b & 1) != 0) res = res * a;
      a = a * a;
      b >>= 1;
    }
    return res;
  }
  public static long GCD (long a, long b) {
    while (b > 0) {
      var r = a % b;
      a = b;
      b = r;
    }
    return a;
  }
  public static long LCM (long a, long b) => (b / GCD (a, b)) * a;
  public static long Comb (long n, long r, int MOD = 1000000007) {
    if (r > n - r) r = n - r;
    long Nume = 1;
    long Deno = 1;

    if (r > n - r) r = n - r;
    for (long i = 1; i <= r; ++i) {
      Deno = (Deno * i) % MOD;
      Nume = Nume * (n - i + 1) % MOD;
    }
    return (Nume * inv (Deno)) % MOD;
  }
  public static long Comb2 (long n, long r) {
    long Nume = 1;
    long Deno = 1;

    if (r > n - r) r = n - r;
    for (long i = 1; i <= r; ++i) {
      Deno *= i;
      Nume *= n - i + 1;
    }
    return Nume / Deno;
  }
  public static long inv (long x, int MOD = 1000000007) {
    return Power (x, MOD - 2, MOD);
  }
}
public static class Utils {
  public static void Swap<T> (ref T A, ref T B) {
    T x = A;
    A = B;
    B = x;
  }
  public static int DigitSum (int N) {
    string s = N.ToString ();
    int ret = 0;
    for (int i = 0; i < s.Length; ++i) ret += s[i] - '0';
    return ret;
  }
  public static string ConvertBase (long N, int K) {
    StringBuilder ret = new StringBuilder ();
    while (N > 0) {
      var r = N % K;
      N /= K;
      ret.Append (r);
    }
    return new string (ret.ToString ().ToCharArray ().Reverse ().ToArray ());
  }
}
class Program {
  static void Main (string[] args) {
    var CompetitiveProgramming = new CompetitiveProgramming ();
    CompetitiveProgramming.Solve ();
  }
}
public static class io {
  public static string Str => Console.ReadLine ();
  public static string[] Strs => Str.Split (' ');
  public static long[] Longs => Strs.Select (long.Parse).ToArray ();
  public static int[] Ints => Strs.Select (int.Parse).ToArray ();
  public static char[] Chars => Str.ToArray ();
  public static double[] Doubles => Strs.Select (double.Parse).ToArray ();
  public static long Long1 => Longs[0];
  public static int Int1 => Ints[0];
  public static char Char1 => Chars[0];
  public static double Double1 => Doubles[0];
  public static long[] VerticalRead (int N) { long[] A = new long[N]; for (int i = 0; i < N; ++i) A[i] = Long1; return A; }
  public static void Put (string a) => Console.WriteLine (a);
  public static void Put (params object[] i) => Put (string.Join (" ", i));
  public static void Put<T> (IEnumerable<T> a) => Put (string.Join (" ", a));
  public static void VerticalPut<T> (IEnumerable<T> a) { foreach (var z in a) Put (z); }
  public static void YN (bool i) {
    if (i) Put ("Yes");
    else Put ("No");
  }
}