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 <bits/stdc++.h>

#define ll long long
#define ld long double
using namespace std;



int main() {
    ll n;
    cin >> n;
    string s;
    cin >> s;
    string answ;
    bool a =true;
    for (ll i = 0; i < n; i++)
        answ.push_back('W');
    if (s[0] == 'x')
    {
        for (ll i = 1; i < n-1; i++)
        {
            if (s[i] == 'x' && answ[i] == 'W')
            {
                answ[i+1] = answ[i-1];
            }
            else if (s[i] == 'o' && answ[i] == 'W')
            {
                answ[i+1] = (answ[i-1] == 'S' ? 'W' : 'S');
            }
            else if (s[i] == 'o' && answ[i] == 'S')
            {
                answ[i+1] = answ[i-1];
            }
            else if (s[i] == 'x' && answ[i] == 'S')
            {
                answ[i+1] = (answ[i-1] == 'S' ? 'W' : 'S');
            }
        }
        if (((s[n-1] == 'o' && answ[n-1] == 'S') && (answ[0] != answ[n-2])) || ((s[n-1] == 'x' && answ[n-1] == 'S') && (answ[0] == answ[n-2])))
        {
            a = false;
//            cout << -1 << endl;
//            return 0;
        }
        else if (((s[n-1] == 'x' && answ[n-1] == 'W') && (answ[0] != answ[n-2])) || ((s[n-1] == 'o' && answ[n-1] == 'W') && (answ[0] == answ[n-2])))
        {
//            cout << -1 << endl;
            a = false;
//            return 0;
        }
        else if (answ[n-1] != answ[1]) {
//            cout << -1 << endl;
            a = false;
//            return 0;
        }
        else {
            cout << answ << endl;
            return 0;
        }
        for (int i = 0; i < n; i++)
            answ[i] = 'W';
        answ[1] = 'S';
        answ[n-1] = 'S';
        for (ll i = 1; i < n-1; i++)
        {
            if (s[i] == 'x' && answ[i] == 'W')
            {
                answ[i+1] = answ[i-1];
            }
            else if (s[i] == 'o' && answ[i] == 'W')
            {
                answ[i+1] = (answ[i-1] == 'S' ? 'W' : 'S');
            }
            else if (s[i] == 'o' && answ[i] == 'S')
            {
                answ[i+1] = answ[i-1];
            }
            else if (s[i] == 'x' && answ[i] == 'S')
            {
                answ[i+1] = (answ[i-1] == 'S' ? 'W' : 'S');
            }
        }
        if (((s[n-1] == 'o' && answ[n-1] == 'S') && (answ[0] != answ[n-2])) || ((s[n-1] == 'x' && answ[n-1] == 'S') && (answ[0] == answ[n-2])))
        {
            a = false;
//            cout << -1 << endl;
//            return 0;
        }
        else if (((s[n-1] == 'x' && answ[n-1] == 'W') && (answ[0] != answ[n-2])) || ((s[n-1] == 'o' && answ[n-1] == 'W') && (answ[0] == answ[n-2])))
        {
//            cout << -1 << endl;
            a = false;
//            return 0;
        }
        else if (answ[n-1] != answ[1]) {
//            cout << -1 << endl;
            a = false;
//            return 0;
        }
        else {
            cout << answ << endl;
            return 0;
        }
    }
    else
    {
        answ[n-1] = 'S';
        for (ll i = 1; i < n-1; i++)
        {
            if (s[i] == 'o' && answ[i] == 'S')
            {
                answ[i+1] = answ[i-1];
            }
            else if (s[i] == 'x' && answ[i] == 'S')
            {
                answ[i+1] = (answ[i-1] == 'S' ? 'W' : 'S');
            }
            else if (s[i] == 'o' && answ[i] == 'W')
            {
                answ[i+1] = (answ[i-1] == 'S' ? 'W' : 'S');
            }
            else if (s[i] == 'x' && answ[i] == 'W')
            {
                answ[i+1] = answ[i-1];
            }
        }
        if (((s[n-1] == 'o' && answ[n-1] == 'S') && (answ[0] != answ[n-2])) || ((s[n-1] == 'x' && answ[n-1] == 'S') && (answ[0] == answ[n-2])))
        {
//            cout << -1 << endl;
//            return 0;
            a = false;
        }
        else if (((s[n-1] == 'x' && answ[n-1] == 'W') && (answ[0] != answ[n-2])) || ((s[n-1] == 'o' && answ[n-1] == 'W') && (answ[0] == answ[n-2])))
        {
//            cout << -1 << endl;
//            return 0;
            a = false;
        }
        else if (answ[n-1] == answ[1]) {
//            cout << -1 << endl;
//            return 0;
            a = false;
        }
        else {
            cout << answ << endl;
            return 0;
        }
        for (int i = 1; i < n; i++)
            answ[i] = 'W';
        answ[1] = 'S';
        for (ll i = 1; i < n-1; i++)
        {
            if (s[i] == 'o' && answ[i] == 'S')
            {
                answ[i+1] = answ[i-1];
            }
            else if (s[i] == 'x' && answ[i] == 'S')
            {
                answ[i+1] = (answ[i-1] == 'S' ? 'W' : 'S');
            }
            else if (s[i] == 'o' && answ[i] == 'W')
            {
                answ[i+1] = (answ[i-1] == 'S' ? 'W' : 'S');
            }
            else if (s[i] == 'x' && answ[i] == 'W')
            {
                answ[i+1] = answ[i-1];
            }
        }
        if (((s[n-1] == 'o' && answ[n-1] == 'S') && (answ[0] != answ[n-2])) || ((s[n-1] == 'x' && answ[n-1] == 'S') && (answ[0] == answ[n-2])))
        {
//            cout << -1 << endl;
//            return 0;
            a = false;
        }
        else if (((s[n-1] == 'x' && answ[n-1] == 'W') && (answ[0] != answ[n-2])) || ((s[n-1] == 'o' && answ[n-1] == 'W') && (answ[0] == answ[n-2])))
        {
//            cout << -1 << endl;
//            return 0;
            a = false;
        }
        else if (answ[n-1] == answ[1]) {
//            cout << -1 << endl;
//            return 0;
            a = false;
        }
        else {
            cout << answ << endl;
            return 0;
        }
    }


    for (ll i = 0; i < n; i++)
        answ[i] = 'S';
    if (s[0] == 'o') {
        for (ll i = 1; i < n-1; i++)
        {
            if (s[i] == 'o' && answ[i] == 'S')
            {
                answ[i+1] = answ[i-1];
            }
            else if (s[i] == 'x' && answ[i] == 'S')
            {
                answ[i+1] = (answ[i-1] == 'S' ? 'W' : 'S');
            }
            else if (s[i] == 'o' && answ[i] == 'W')
            {
                answ[i+1] = (answ[i-1] == 'S' ? 'W' : 'S');
            }
            else if (s[i] == 'x' && answ[i] == 'W')
            {
                answ[i+1] = answ[i-1];
            }
        }
        if (((s[n-1] == 'o' && answ[n-1] == 'S') && (answ[0] != answ[n-2])) || ((s[n-1] == 'x' && answ[n-1] == 'S') && (answ[0] == answ[n-2])))
        {
//            cout << -1 << endl;
//            return 0;
            a = false;
        }
        else if (((s[n-1] == 'x' && answ[n-1] == 'W') && (answ[0] != answ[n-2])) || ((s[n-1] == 'o' && answ[n-1] == 'W') && (answ[0] == answ[n-2])))
        {
//            cout << -1 << endl;
//            return 0;
            a = false;
        }
        else if (answ[n-1] != answ[1]) {
//            cout << -1 << endl;
//            return 0;
            a = false;
        }
        else {
            cout << answ << endl;
            return 0;
        }
        for (int i = 0; i < n; i++)
            answ[i] = 'S';
        answ[n-1] = 'W';
        answ[2] = 'W';
        for (ll i = 1; i < n-1; i++)
        {
            if (s[i] == 'o' && answ[i] == 'S')
            {
                answ[i+1] = answ[i-1];
            }
            else if (s[i] == 'x' && answ[i] == 'S')
            {
                answ[i+1] = (answ[i-1] == 'S' ? 'W' : 'S');
            }
            else if (s[i] == 'o' && answ[i] == 'W')
            {
                answ[i+1] = (answ[i-1] == 'S' ? 'W' : 'S');
            }
            else if (s[i] == 'x' && answ[i] == 'W')
            {
                answ[i+1] = answ[i-1];
            }
        }
        if (((s[n-1] == 'o' && answ[n-1] == 'S') && (answ[0] != answ[n-2])) || ((s[n-1] == 'x' && answ[n-1] == 'S') && (answ[0] == answ[n-2])))
        {
            a = false;
        }
        else if (((s[n-1] == 'x' && answ[n-1] == 'W') && (answ[0] != answ[n-2])) || ((s[n-1] == 'o' && answ[n-1] == 'W') && (answ[0] == answ[n-2])))
        {
            a = false;
        }
        else if (answ[n-1] != answ[1]) {
            a = false;
        }
        else {
            cout << answ << endl;
            return 0;
        }
    }
    else {
        answ[n-1] = 'W';
        for (ll i = 1; i < n-1; i++)
        {
            if (s[i] == 'o' && answ[i] == 'S')
            {
                answ[i+1] = answ[i-1];
            }
            else if (s[i] == 'x' && answ[i] == 'S')
            {
                answ[i+1] = (answ[i-1] == 'S' ? 'W' : 'S');
            }
            else if (s[i] == 'o' && answ[i] == 'W')
            {
                answ[i+1] = (answ[i-1] == 'S' ? 'W' : 'S');
            }
            else if (s[i] == 'x' && answ[i] == 'W')
            {
                answ[i+1] = answ[i-1];
            }
        }
        if (((s[n-1] == 'o' && answ[n-1] == 'S') && (answ[0] != answ[n-2])) || ((s[n-1] == 'x' && answ[n-1] == 'S') && (answ[0] == answ[n-2])))
        {
            a = false;
        }
        if (((s[n-1] == 'x' && answ[n-1] == 'W') && (answ[0] != answ[n-2])) || ((s[n-1] == 'o' && answ[n-1] == 'W') && (answ[0] == answ[n-2])))
        {
            a = false;

        }
        if (answ[n-1] == answ[1]) {
            a = false;

        }
        else {
            cout << answ << endl;
            return 0;
        }
        for (int i = 0; i < n; i++)
            answ[i] = 'S';
        answ[1] = 'W';
        for (ll i = 1; i < n-1; i++)
        {
            if (s[i] == 'o' && answ[i] == 'S')
            {
                answ[i+1] = answ[i-1];
            }
            else if (s[i] == 'x' && answ[i] == 'S')
            {
                answ[i+1] = (answ[i-1] == 'S' ? 'W' : 'S');
            }
            else if (s[i] == 'o' && answ[i] == 'W')
            {
                answ[i+1] = (answ[i-1] == 'S' ? 'W' : 'S');
            }
            else if (s[i] == 'x' && answ[i] == 'W')
            {
                answ[i+1] = answ[i-1];
            }
        }
        if (((s[n-1] == 'o' && answ[n-1] == 'S') && (answ[0] != answ[n-2])) || ((s[n-1] == 'x' && answ[n-1] == 'S') && (answ[0] == answ[n-2])))
        {
            a = false;
        }
        if (((s[n-1] == 'x' && answ[n-1] == 'W') && (answ[0] != answ[n-2])) || ((s[n-1] == 'o' && answ[n-1] == 'W') && (answ[0] == answ[n-2])))
        {
            a = false;
        }
        if (answ[n-1] == answ[1]) {
            a = false;
        }
        else {
            cout << answ << endl;
            return 0;
        }
    }
    cout << -1 << endl;
    return 0;
}