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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define agewari(a, b) ((ll)a + ((ll)b - 1)) / b
const int MOD = 1000000007;
const long long INF = 1LL << 60;
using Graph = vector<vector<ll>>;

int main()
{
    ll n;
    string s;
    cin >> n >> s;

    vector<char> t(n+1);
    //SSから始まる可能性
    t[0] = 'S';
    t[1] = 'S';
    for (int i = 2; i < n+1; i++)
    {
        if (s[i - 1] == 'o')
        {
            if (t[i - 1] == 'S')
                t[i] = t[i - 2];
            else if (t[i - 2] == 'S')
                t[i] = 'W';
            else
                t[i] = 'S';
        }
        else
        {
            if (t[i - 1] == 'S')
            {
                if (t[i - 2] == 'S')
                    t[i] = 'W';
                else
                    t[i] = 'S';
            }
            else
            {
                t[i] = t[i - 2];
            }
        }
    }
    //答え合わせ
    char ans;
    if (s[0] == 'o')
        ans = 'S';
    else
        ans = 'W';
    if (ans == t[n - 1]&&t[0]==t[n])
    {
        rep(i, n) cout << t[i];
        cout << endl;
        return 0;
    }

    //SWから始まる可能性
    t[0] = 'S';
    t[1] = 'W';
    for (int i = 2; i < n+1; i++)
    {
        if (s[i - 1] == 'o')
        {
            if (t[i - 1] == 'S')
                t[i] = t[i - 2];
            else if (t[i - 2] == 'S')
                t[i] = 'W';
            else
                t[i] = 'S';
        }
        else
        {
            if (t[i - 1] == 'S')
            {
                if (t[i - 2] == 'S')
                    t[i] = 'W';
                else
                    t[i] = 'S';
            }
            else
            {
                t[i] = t[i - 2];
            }
        }
    }
    //答え合わせ
    if (s[0] == 'o')
        ans = 'W';
    else
        ans = 'S';
    if (ans == t[n - 1] && t[0] == t[n])
    {
        rep(i, n) cout << t[i];
        cout << endl;
        return 0;
    }

    //WSから始まる可能性
    t[0] = 'W';
    t[1] = 'S';
    for (int i = 2; i < n+1; i++)
    {
        if (s[i - 1] == 'o')
        {
            if (t[i - 1] == 'S')
                t[i] = t[i - 2];
            else if (t[i - 2] == 'S')
                t[i] = 'W';
            else
                t[i] = 'S';
        }
        else
        {
            if (t[i - 1] == 'S')
            {
                if (t[i - 2] == 'S')
                    t[i] = 'W';
                else
                    t[i] = 'S';
            }
            else
            {
                t[i] = t[i - 2];
            }
        }
    }
    //答え合わせ
    if (s[0] == 'o' && t[0] == t[n])
        ans = 'W';
    else
        ans = 'S';
    if (ans == t[n - 1])
    {
        rep(i, n) cout << t[i];
        cout << endl;
        return 0;
    }

    //SSから始まる可能性
    t[0] = 'S';
    t[1] = 'S';
    for (int i = 2; i < n+1; i++)
    {
        if (s[i - 1] == 'o')
        {
            if (t[i - 1] == 'S')
                t[i] = t[i - 2];
            else if (t[i - 2] == 'S')
                t[i] = 'W';
            else
                t[i] = 'S';
        }
        else
        {
            if (t[i - 1] == 'S')
            {
                if (t[i - 2] == 'S')
                    t[i] = 'W';
                else
                    t[i] = 'S';
            }
            else
            {
                t[i] = t[i - 2];
            }
        }
    }
    //答え合わせ
    if (s[0] == 'o' && t[0] == t[n])
        ans = 'W';
    else
        ans = 'S';
    if (ans == t[n - 1])
    {
        rep(i, n) cout << t[i];
        cout << endl;
        return 0;
    }

    cout << -1 << endl;
}
//方針ok
//実装力