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;
class Program{
	static void Main(){
		int n=int.Parse(Console.ReadLine());
		string s=Console.ReadLine();
		string[][] arr=new string[4][];
		arr[0]=new string[n];arr[1]=new string[n];
		arr[2]=new string[n];arr[3]=new string[n];
		string ans="-1";

		arr[0][1]="S";arr[0][n-1]="S";
		arr[1][1]="W";arr[1][n-1]="W";
		arr[2][1]="S";arr[2][n-1]="W";
		arr[3][1]="W";arr[3][n-1]="S";
		if(s[0]=='o'){arr[0][0]="S";arr[1][0]="S";arr[2][0]="W";arr[3][0]="W";}
		else{arr[0][0]="W";arr[1][0]="W";arr[2][0]="S";arr[3][0]="S";}
		for(int i=1;i<n-2;i++){
			for(int j=0;j<4;j++){
				if(s[i]=='o'&&arr[j][i]=="S"){arr[j][i+1]=arr[j][i-1];}
				else if(s[i]=='o'&&arr[j][i]=="W"){arr[j][i+1]=arr[j][i-1]=="S"?"W":"S";}
				else if(s[i]=='x'&&arr[j][i]=="S"){arr[j][i+1]=arr[j][i-1]=="S"?"W":"S";}
				else if(s[i]=='x'&&arr[j][i]=="W"){arr[j][i+1]=arr[j][i-1];}
			}
		}
		for(int j=0;j<4;j++){
			if(fu(arr[j][n-3],arr[j][n-2],arr[j][n-1],s[n-2])&&fu(arr[j][n-2],arr[j][n-1],arr[j][0],s[n-1])){ans=String.Join("",arr[j]);}
		}
	}
	static bool fu(string a,string b,string c,char d){
		if(d=='o'&&b=="S"&&a==c){return true;}
		else if(d=='o'&&b=="W"&&a!=c){return true;}
		else if(d=='x'&&b=="S"&&a!=c){return true;}
		else if(d=='x'&&b=="W"&&a==c){return true;}
		return false;
	}
}