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.Text;

class Menagerie
{
	static int N;
	static string s;

	static public void Main(string[] args)
	{

		N = int.Parse(Console.ReadLine());
		s = Console.ReadLine();

		StringBuilder sb = new StringBuilder(N);
		sb.Append('S', N);

		sb[0] = 'S';
		sb[1] = 'S';
		if(check(sb, 2))
		{
			Console.WriteLine(sb);
			return;
		}
		sb[0] = 'S';
		sb[1] = 'W';
		if(check(sb, 2))
		{
			Console.WriteLine(sb);
			return;
		}
		sb[0] = 'W';
		sb[1] = 'W';
		if(check(sb, 2))
		{
			Console.WriteLine(sb);
			return;
		}
		sb[0] = 'W';
		sb[1] = 'S';
		if(check(sb, 2))
		{
			Console.WriteLine(sb);
			return;
		}
		Console.WriteLine(-1);
	}


	static private bool check(StringBuilder sb, int i)
	{
		if(i < N)
		{
			if(sb[i-1] == 'S')
			{
				if(s[i-1] == 'o')
				{
					sb[i] = sb[i-2];
				}
				else
				{
					if(sb[i-2] == 'S')
						sb[i] = 'W';
					else
						sb[i] = 'S';
				}
			}
			else
			{
				if(s[i-1] == 'o')
				{
					if(sb[i-2] == 'S')
						sb[i] = 'W';
					else
						sb[i] = 'S';
				}
				else
				{
					sb[i] = sb[i-2];
				}
			}
			return check(sb, i+1);
		}
		else if(i == N)
		{
			if(sb[N-1] == 'S')
			{
				if(s[N-1] == 'o')
				{
					if(sb[N-2] != sb[0])
					{
						return false;
					}
				}
				else
				{
					if(sb[N-2] == sb[0])
					{
						return false;
					}
				}
			}
			else
			{
				if(s[N-1] == 'o')
				{
					if(sb[N-2] == sb[0])
					{
						return false;
					}
				}
				else
				{
					if(sb[N-2] != sb[0])
					{
						return false;
					}
				}
			}
			return check(sb, i+1);
		}
		else
		{
			if(sb[0] == 'S')
			{
				if(s[0] == 'o')
				{
					return (sb[1] == sb[N-1]);
				}
				else
				{
					return (sb[1] != sb[N-1]);
				}
			}
			else
			{
				if(s[0] == 'o')
				{
					return (sb[1] != sb[N-1]);
				}
				else
				{
					return (sb[1] == sb[N-1]);
				}
			}
		}

	}
}