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 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;
string str;
bool fun(int* fp,int x)
{
    int i;bool flg=0;
    for(i=2;i<x;i++)
    {
        if(str[i-1]=='x'&&fp[i-1]==1)fp[i]=!fp[i-2];
        else if(str[i-1]=='x'&&fp[i-1]==0)fp[i]=fp[i-2];
        
        if(str[i-1]=='o'&&fp[i-1]==1)fp[i]=fp[i-2];
        else if(str[i-1]=='o'&&fp[i-1]==0)fp[i]=!fp[i-2];
    }
    if(str[x-1]=='x')
    {
        if(fp[0]==fp[x-2]&&fp[x-1]==1)flg=1;
        if(fp[0]!=fp[x-2]&&fp[x-1]==0)flg=1;
    }
    else{
        if(fp[0]!=fp[x-2]&&fp[x-1]==1)flg=1;
        if(fp[0]==fp[x-2]&&fp[x-1]==0)flg=1;
    }
    
    if(str[0]=='x')
    {
        if(fp[x-1]==fp[1]&&fp[0]==1)flg=1;
        if(fp[x-1]!=fp[1]&&fp[0]==0)flg=1;
    }
    else{
        if(fp[1]!=fp[x-1]&&fp[0]==1)flg=1;
        if(fp[x-1]==fp[1]&&fp[0]==0)flg=1;
    }
    return flg;
}

void print(int *fp,int x)
{
    for(int i=0;i<x;i++)
    {
        if(fp[i]==1)cout<<"S";
        else cout<<"W";
    }
}
int main()
{
    int n;
    
    int fp[100000];
    cin>>n;
    cin>>str;
    int i;
    int x= str.length();
    int cnt1=0,cnt2=0;
    
    fp[0]=fp[1]=1;
    bool FF=0;
    if(!fun(fp,x))
    {
        print(fp,x);FF=1;
    }
    fp[0]=fp[1]=0;
    if(!fun(fp,x)&&FF==0)
    {
        print(fp,x);FF=1;
    }
    fp[0]=1;fp[1]=0;
    if(!fun(fp,x)&&FF==0)
    {
        print(fp,x);FF=1;
    }
    fp[0]=0,fp[1]=1;
    if(!fun(fp,x)&&FF==0)
    {
        print(fp,x);FF=1;
    }
    if(!FF)cout<<"-1";
    cout<<endl;
    
    return 0;
}