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++14 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include<iostream>
#include<cstring>
using namespace std;
int  an[4][2]={{2, 2},{2,1},{1,1},{1,2}};//WW WS SS SW
int i,j,kind[100005],n;
char ans[100005];
int main()
{
    while(cin>>n&&(n>=3))
    {
        int flag=0;
        memset(kind,0,sizeof(kind));
        for(i=1;i<=n;i++)
        {
            cin>>ans[i];
        }

        for(j=0;j<4;j++)
        {
            kind[1]=an[j][0];
            kind[2]=an[j][1];
            for(i=2;i<=n;i++)
            {
             if(kind[i]==2)//is wolf
             {
                 if(ans[i]=='o')
                 kind[i+1]=kind[i-1]%2+1;
                 else kind[i+1]=kind[i];
             }
             else
                if(ans[i]=='x')
                 kind[i+1]=kind[i-1]%2+1;
                 else kind[i+1]=kind[i];
            }


if(kind[n+1]==kind[1])
            if(kind[n+1]==1)
            {
                if(ans[1]=='o')
                {
                    kind[2]==kind[n];
                    flag++;
                    break;
                }
                if(ans[1]=='x')
                {
                    kind[2]!=kind[n];
                    flag++;
                    break;
                }

            }
            else
            {

              if(ans[1]=='x')
                {
                    kind[2]==kind[n];
                    flag++;
                    break;
                }
                if(ans[1]=='0')
                {
                    kind[2]!=kind[n];
                    flag++;
                    break;
                }
            }


        }


        if(flag==0)cout<<"-1"<<endl;
        else
        {


        for(i=1;i<=n;i++)
        {
            if(kind[i]==1)cout<<'S';
            else cout<<'W';
        }
            cout<<endl;
           // cout<<kind[n+1]<<endl;

        }
    }

}