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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;

public class Main{
    static int N;
    static String s;
    static char[] c;
    public static void main(String args[]){
        Scanner sc = new Scanner(System.in);
        
        N =sc.nextInt();
        s = sc.next();
        c = s.toCharArray();
        sc.close();
        char[] ans = new char[N];

        ans[0] = 'S'; ans[1] = 'S';
        for(int i = 0; i < N; i++){
            if(i == 0){
                if(ans[i] == 'S' && c[i] == 'o'){
                    ans[N-1] = ans[i+1];
                } else if(ans[i] == 'S' && c[i] == 'x'){
                    if(ans[i+1] == 'S')
                        ans[N-1] = 'W';
                    else
                        ans[N-1] = 'S';
                } else if(ans[i] == 'W' && c[i] == 'o'){
                    if(ans[i+1] == 'S')
                        ans[N-1] = 'W';
                    else
                        ans[N-1] = 'S';
                } else if(ans[i] == 'W' && c[i] == 'x'){
                    ans[N-1] = ans[i+1];
                }
            }
            if(i!=0 && i < N-1){
                if(ans[i] == 'S' && c[i] == 'o'){
                    ans[i+1] = ans[i-1];
                } else if(ans[i] == 'S' && c[i] == 'x'){
                    if(ans[i-1] == 'S')
                        ans[i+1] = 'W';
                    else
                        ans[i+1] = 'S';
                } else if(ans[i] == 'W' && c[i] == 'o'){
                    if(ans[i-1] == 'S')
                        ans[i+1] = 'W';
                    else
                        ans[i+1] = 'S';
                } else if(ans[i] == 'W' && c[i] == 'x'){
                    ans[i+1] = ans[i-1];
                }
            }
            if(i == N-2){
                if(ans[i] == 'S' && c[i] == 'o'){
                    if(ans[i+1] != ans[i-1]){
                        break;
                    } else
                        continue;
                } else if(ans[i] == 'S' && c[i] == 'x'){
                    if(ans[i-1] == 'S')
                        if(ans[i+1] != 'W'){
                            break;
                        } else
                            continue;
                    else
                        if(ans[i+1] != 'S'){
                            break;
                        } else {
                            continue;
                        }
                } else if(ans[i] == 'W' && c[i] == 'o'){
                    if(ans[i-1] == 'S')
                        if(ans[i+1] != 'W')
                            break;
                        else
                            continue;
                    else
                        if(ans[i+1] != 'S')
                            break;
                        else
                            continue;
                } else if(ans[i] == 'W' && c[i] == 'x'){
                    if(ans[i+1] != ans[i-1])
                        break;
                    else
                        continue;
                }
            }
            if(i == N-1){
                if(ans[i] == 'S' && c[i] == 'o'){
                    if(ans[0] != ans[i-1]){
                    } else {
                        for(int j = 0; j < N; j++){
                            System.out.print(ans[j]);
                        }
                        return;
                    }
                } else if(ans[i] == 'S' && c[i] == 'x'){
                    if(ans[i-1] == 'S')
                        if(ans[0] != 'W'){
                        } else{
                            for(int j = 0; j < N; j++){
                                System.out.print(ans[j]);
                            }
                            return;
                        }
                    else
                        if(ans[0] != 'S'){
                        } else {
                            for(int j = 0; j < N; j++){
                                System.out.print(ans[j]);
                            }
                            return;
                        }
                } else if(ans[i] == 'W' && c[i] == 'o'){
                    if(ans[i-1] == 'S')
                        if(ans[0] != 'W')
                            break;
                        else{
                            for(int j = 0; j < N; j++){
                                System.out.print(ans[j]);
                            }
                            return;
                        }
                    else
                        if(ans[0] != 'S')
                            break;
                        else{
                            for(int j = 0; j < N; j++){
                                System.out.print(ans[j]);
                            }
                            return;
                        }
                } else if(ans[i] == 'W' && c[i] == 'x'){
                    if(ans[0] != ans[i-1])
                        break;
                    else{
                        for(int j = 0; j < N; j++){
                            System.out.print(ans[j]);
                        }
                        return;
                    }
                }
            }
        }
        ans[0] = 'S'; ans[1] = 'W';
        for(int i = 0; i < N; i++){
            if(i == 0){
                if(ans[i] == 'S' && c[i] == 'o'){
                    ans[N-1] = ans[i+1];
                } else if(ans[i] == 'S' && c[i] == 'x'){
                    if(ans[i+1] == 'S')
                        ans[N-1] = 'W';
                    else
                        ans[N-1] = 'S';
                } else if(ans[i] == 'W' && c[i] == 'o'){
                    if(ans[i+1] == 'S')
                        ans[N-1] = 'W';
                    else
                        ans[N-1] = 'S';
                } else if(ans[i] == 'W' && c[i] == 'x'){
                    ans[N-1] = ans[i+1];
                }
            }
            if(i!=0 && i < N-1){
                if(ans[i] == 'S' && c[i] == 'o'){
                    ans[i+1] = ans[i-1];
                } else if(ans[i] == 'S' && c[i] == 'x'){
                    if(ans[i-1] == 'S')
                        ans[i+1] = 'W';
                    else
                        ans[i+1] = 'S';
                } else if(ans[i] == 'W' && c[i] == 'o'){
                    if(ans[i-1] == 'S')
                        ans[i+1] = 'W';
                    else
                        ans[i+1] = 'S';
                } else if(ans[i] == 'W' && c[i] == 'x'){
                    ans[i+1] = ans[i-1];
                }
            }
            if(i == N-2){
                if(ans[i] == 'S' && c[i] == 'o'){
                    if(ans[i+1] != ans[i-1]){
                        break;
                    } else
                        continue;
                } else if(ans[i] == 'S' && c[i] == 'x'){
                    if(ans[i-1] == 'S')
                        if(ans[i+1] != 'W'){
                            break;
                        } else
                            continue;
                    else
                        if(ans[i+1] != 'S'){
                            break;
                        } else {
                            continue;
                        }
                } else if(ans[i] == 'W' && c[i] == 'o'){
                    if(ans[i-1] == 'S')
                        if(ans[i+1] != 'W')
                            break;
                        else
                            continue;
                    else
                        if(ans[i+1] != 'S')
                            break;
                        else
                            continue;
                } else if(ans[i] == 'W' && c[i] == 'x'){
                    if(ans[i+1] != ans[i-1])
                        break;
                    else
                        continue;
                }
            }
            if(i == N-1){
                if(ans[i] == 'S' && c[i] == 'o'){
                    if(ans[0] != ans[i-1]){
                    } else {
                        for(int j = 0; j < N; j++){
                            System.out.print(ans[j]);
                        }
                        return;
                    }
                } else if(ans[i] == 'S' && c[i] == 'x'){
                    if(ans[i-1] == 'S')
                        if(ans[0] != 'W'){
                        } else{
                            for(int j = 0; j < N; j++){
                                System.out.print(ans[j]);
                            }
                            return;
                        }
                    else
                        if(ans[0] != 'S'){
                        } else {
                            for(int j = 0; j < N; j++){
                                System.out.print(ans[j]);
                            }
                            return;
                        }
                } else if(ans[i] == 'W' && c[i] == 'o'){
                    if(ans[i-1] == 'S')
                        if(ans[0] != 'W')
                            break;
                        else{
                            for(int j = 0; j < N; j++){
                                System.out.print(ans[j]);
                            }
                            return;
                        }
                    else
                        if(ans[0] != 'S')
                            break;
                        else{
                            for(int j = 0; j < N; j++){
                                System.out.print(ans[j]);
                            }
                            return;
                        }
                } else if(ans[i] == 'W' && c[i] == 'x'){
                    if(ans[0] != ans[i-1])
                        break;
                    else{
                        for(int j = 0; j < N; j++){
                            System.out.print(ans[j]);
                        }
                        return;
                    }
                }
            }
        }
        ans[0] = 'W'; ans[1] = 'S';
        for(int i = 0; i < N; i++){
            if(i == 0){
                if(ans[i] == 'S' && c[i] == 'o'){
                    ans[N-1] = ans[i+1];
                } else if(ans[i] == 'S' && c[i] == 'x'){
                    if(ans[i+1] == 'S')
                        ans[N-1] = 'W';
                    else
                        ans[N-1] = 'S';
                } else if(ans[i] == 'W' && c[i] == 'o'){
                    if(ans[i+1] == 'S')
                        ans[N-1] = 'W';
                    else
                        ans[N-1] = 'S';
                } else if(ans[i] == 'W' && c[i] == 'x'){
                    ans[N-1] = ans[i+1];
                }
            }
            if(i!=0 && i < N-1){
                if(ans[i] == 'S' && c[i] == 'o'){
                    ans[i+1] = ans[i-1];
                } else if(ans[i] == 'S' && c[i] == 'x'){
                    if(ans[i-1] == 'S')
                        ans[i+1] = 'W';
                    else
                        ans[i+1] = 'S';
                } else if(ans[i] == 'W' && c[i] == 'o'){
                    if(ans[i-1] == 'S')
                        ans[i+1] = 'W';
                    else
                        ans[i+1] = 'S';
                } else if(ans[i] == 'W' && c[i] == 'x'){
                    ans[i+1] = ans[i-1];
                }
            }
            if(i == N-2){
                if(ans[i] == 'S' && c[i] == 'o'){
                    if(ans[i+1] != ans[i-1]){
                        break;
                    } else
                        continue;
                } else if(ans[i] == 'S' && c[i] == 'x'){
                    if(ans[i-1] == 'S')
                        if(ans[i+1] != 'W'){
                            break;
                        } else
                            continue;
                    else
                        if(ans[i+1] != 'S'){
                            break;
                        } else {
                            continue;
                        }
                } else if(ans[i] == 'W' && c[i] == 'o'){
                    if(ans[i-1] == 'S')
                        if(ans[i+1] != 'W')
                            break;
                        else
                            continue;
                    else
                        if(ans[i+1] != 'S')
                            break;
                        else
                            continue;
                } else if(ans[i] == 'W' && c[i] == 'x'){
                    if(ans[i+1] != ans[i-1])
                        break;
                    else
                        continue;
                }
            }
            if(i == N-1){
                if(ans[i] == 'S' && c[i] == 'o'){
                    if(ans[0] != ans[i-1]){
                    } else {
                        for(int j = 0; j < N; j++){
                            System.out.print(ans[j]);
                        }
                        return;
                    }
                } else if(ans[i] == 'S' && c[i] == 'x'){
                    if(ans[i-1] == 'S')
                        if(ans[0] != 'W'){
                        } else{
                            for(int j = 0; j < N; j++){
                                System.out.print(ans[j]);
                            }
                            return;
                        }
                    else
                        if(ans[0] != 'S'){
                        } else {
                            for(int j = 0; j < N; j++){
                                System.out.print(ans[j]);
                            }
                            return;
                        }
                } else if(ans[i] == 'W' && c[i] == 'o'){
                    if(ans[i-1] == 'S')
                        if(ans[0] != 'W')
                            break;
                        else{
                            for(int j = 0; j < N; j++){
                                System.out.print(ans[j]);
                            }
                            return;
                        }
                    else
                        if(ans[0] != 'S')
                            break;
                        else{
                            for(int j = 0; j < N; j++){
                                System.out.print(ans[j]);
                            }
                            return;
                        }
                } else if(ans[i] == 'W' && c[i] == 'x'){
                    if(ans[0] != ans[i-1])
                        break;
                    else{
                        for(int j = 0; j < N; j++){
                            System.out.print(ans[j]);
                        }
                        return;
                    }
                }
            }
        }
        ans[0] = 'W'; ans[1] = 'W';
        for(int i = 0; i < N; i++){
            if(i == 0){
                if(ans[i] == 'S' && c[i] == 'o'){
                    ans[N-1] = ans[i+1];
                } else if(ans[i] == 'S' && c[i] == 'x'){
                    if(ans[i+1] == 'S')
                        ans[N-1] = 'W';
                    else
                        ans[N-1] = 'S';
                } else if(ans[i] == 'W' && c[i] == 'o'){
                    if(ans[i+1] == 'S')
                        ans[N-1] = 'W';
                    else
                        ans[N-1] = 'S';
                } else if(ans[i] == 'W' && c[i] == 'x'){
                    ans[N-1] = ans[i+1];
                }
            }
            if(i!=0 && i < N-1){
                if(ans[i] == 'S' && c[i] == 'o'){
                    ans[i+1] = ans[i-1];
                } else if(ans[i] == 'S' && c[i] == 'x'){
                    if(ans[i-1] == 'S')
                        ans[i+1] = 'W';
                    else
                        ans[i+1] = 'S';
                } else if(ans[i] == 'W' && c[i] == 'o'){
                    if(ans[i-1] == 'S')
                        ans[i+1] = 'W';
                    else
                        ans[i+1] = 'S';
                } else if(ans[i] == 'W' && c[i] == 'x'){
                    ans[i+1] = ans[i-1];
                }
            }
            if(i == N-2){
                if(ans[i] == 'S' && c[i] == 'o'){
                    if(ans[i+1] != ans[i-1]){
                        break;
                    } else
                        continue;
                } else if(ans[i] == 'S' && c[i] == 'x'){
                    if(ans[i-1] == 'S')
                        if(ans[i+1] != 'W'){
                            break;
                        } else
                            continue;
                    else
                        if(ans[i+1] != 'S'){
                            break;
                        } else {
                            continue;
                        }
                } else if(ans[i] == 'W' && c[i] == 'o'){
                    if(ans[i-1] == 'S')
                        if(ans[i+1] != 'W')
                            break;
                        else
                            continue;
                    else
                        if(ans[i+1] != 'S')
                            break;
                        else
                            continue;
                } else if(ans[i] == 'W' && c[i] == 'x'){
                    if(ans[i+1] != ans[i-1])
                        break;
                    else
                        continue;
                }
            }
            if(i == N-1){
                if(ans[i] == 'S' && c[i] == 'o'){
                    if(ans[0] != ans[i-1]){
                    } else {
                        for(int j = 0; j < N; j++){
                            System.out.print(ans[j]);
                        }
                        return;
                    }
                } else if(ans[i] == 'S' && c[i] == 'x'){
                    if(ans[i-1] == 'S')
                        if(ans[0] != 'W'){
                        } else{
                            for(int j = 0; j < N; j++){
                                System.out.print(ans[j]);
                            }
                            return;
                        }
                    else
                        if(ans[0] != 'S'){
                        } else {
                            for(int j = 0; j < N; j++){
                                System.out.print(ans[j]);
                            }
                            return;
                        }
                } else if(ans[i] == 'W' && c[i] == 'o'){
                    if(ans[i-1] == 'S')
                        if(ans[0] != 'W')
                            break;
                        else{
                            for(int j = 0; j < N; j++){
                                System.out.print(ans[j]);
                            }
                            return;
                        }
                    else
                        if(ans[0] != 'S')
                            break;
                        else{
                            for(int j = 0; j < N; j++){
                                System.out.print(ans[j]);
                            }
                            return;
                        }
                } else if(ans[i] == 'W' && c[i] == 'x'){
                    if(ans[0] != ans[i-1])
                        break;
                    else{
                        for(int j = 0; j < N; j++){
                            System.out.print(ans[j]);
                        }
                        return;
                    }
                }
            }
        }
        System.out.println(-1);

    }
}