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: Wrong Answer)

#include <iostream>

using namespace std;
string str;
bool check(string chk){
    //cout<<str.length()<<endl;
    //cout<<chk<<endl;
    if(str[str.length() - 2] == 'o'){
        if(chk[str.length() - 2] == 'S' and chk[str.length() - 3] != chk[str.length() - 1])
            return false;
        else if(chk[str.length() - 2] == 'W' and chk[str.length() - 3] == chk[str.length() - 1])
            return false;
    }
    if(str[str.length() - 2] == 'x'){
        if(chk[str.length() - 2] == 'S' and chk[str.length() - 3] == chk[str.length() - 1])
            return false;
        else if(chk[str.length() - 2] == 'W' and chk[str.length() - 3] != chk[str.length() - 1])
            return false;
    }
    
    if(str[str.length() - 1] == 'o'){
        if(chk[str.length() - 1] == 'S' and chk[str.length() - 2] != chk[0])
            return false;
        else if(chk[str.length() - 1] == 'W' and chk[str.length() - 2] == chk[0])
            return false;
    }
    if(str[str.length() - 1] == 'x'){
        if(chk[str.length() - 1] == 'S' and chk[str.length() - 2] == chk[0])
            return false;
        else if(chk[str.length() - 1] == 'W' and chk[str.length() - 2] != chk[0])
            return false;
    }
    
    
    
    return true;
}
int main() {
    int n;
    cin>>n;
    cin>>str;
    //cout<<str;
    char ans[4][100005];
    int x = 0,cnt;
    if(str[0] == 'o'){
    // assume first is sheep and given 'o', so sheep on both sides
        cnt = 1;
        ans[x][0]='S';
        ans[x][str.length()-1] = ans[x][1] = 'S';
    for(int i = 1; i < str.length() - 2; i++){
        if(ans[x][i] == 'S' and str[i] == 'o'){
            ans[x][i+1] = ans[x][i-1]; 
        }
        else if(ans[x][i] == 'W' and str[i] == 'x' ){
            ans[x][i+1] = ans[x][i-1];
        }
        else if(ans[x][i] == 'S' and str[i] == 'x' ){
            ans[x][i+1] = (ans[x][i-1] == 'S' ? 'W' : 'S');
        }
        else if(ans[x][i] == 'W' and str[i] == 'o' ){
            ans[x][i+1] = (ans[x][i-1] == 'S' ? 'W' : 'S');
        }
        else
            cnt = 0;
    }
    //cout<<ans[x]<<endl;
    if(check(ans[x]) and cnt){
        cout<<ans[x];
        return 0;
    }
    x++;
    cnt = 1;
    // assume first is sheep and given 'o', so wolf on both sides
        ans[x][0]='S';
        
        ans[x][str.length()-1] = ans[x][1] = 'W';
    for(int i = 1; i < str.length() - 2; i++){
        if(ans[x][i] == 'S' and str[i] == 'o'){
            ans[x][i+1] = ans[x][i-1]; 
        }
        else if(ans[x][i] == 'W' and str[i] == 'x' ){
            ans[x][i+1] = ans[x][i-1];
        }
        else if(ans[x][i] == 'S' and str[i] == 'x' ){
            ans[x][i+1] = (ans[x][i-1] == 'S' ? 'W' : 'S');
        }
        else if(ans[x][i] == 'W' and str[i] == 'o' ){
            ans[x][i+1] = (ans[x][i-1] == 'S' ? 'W' : 'S');
        }
        else
            cnt = 0;
    }
    if(check(ans[x]) and cnt){
        cout<<ans[x];
        return 0;
    }
    x++;
    cnt = 1;
    // assume first is wolf and given 'o', so sheep on L wolf on R
        ans[x][0]='W';
        ans[x][str.length()-1] = 'S';
        ans[x][1] = 'W';
    for(int i = 1; i < str.length() - 2; i++){
        if(ans[x][i] == 'S' and str[i] == 'o'){
            ans[x][i+1] = ans[x][i-1]; 
        }
        else if(ans[x][i] == 'W' and str[i] == 'x' ){
            ans[x][i+1] = ans[x][i-1];
        }
        else if(ans[x][i] == 'S' and str[i] == 'x' ){
            ans[x][i+1] = (ans[x][i-1] == 'S' ? 'W' : 'S');
        }
        else if(ans[x][i] == 'W' and str[i] == 'o' ){
            ans[x][i+1] = (ans[x][i-1] == 'S' ? 'W' : 'S');
        }
        else
            cnt = 0;
    }
    if(check(ans[x]) and cnt){
        cout<<ans[x];
        return 0;
    }
    x++;
    cnt = 1;
    
    // assume first is wolf and given 'o', so sheep R wolf on L
        ans[x][0]='W';
        ans[x][str.length()-1] = 'W';
        ans[x][1] = 'S';
    for(int i = 1; i < str.length() - 2; i++){
        if(ans[x][i] == 'S' and str[i] == 'o'){
            ans[x][i+1] = ans[x][i-1]; 
        }
        else if(ans[x][i] == 'W' and str[i] == 'x' ){
            ans[x][i+1] = ans[x][i-1];
        }
        else if(ans[x][i] == 'S' and str[i] == 'x' ){
            ans[x][i+1] = (ans[x][i-1] == 'S' ? 'W' : 'S');
        }
        else if(ans[x][i] == 'W' and str[i] == 'o' ){
            ans[x][i+1] = (ans[x][i-1] == 'S' ? 'W' : 'S');
        }
        else
            cnt = 0;
    }
    if(check(ans[x]) and cnt){
        cout<<ans[x];
        return 0;
    }
    x++;
    }
    cout<<-1;
    
    
    
}