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 <iostream>
#include <iomanip>
#include <fstream>
#include <string>
#include <array>
#include <vector>
#include <deque>
#include <list>
#include <set>
#include <map>
#include <unordered_map>
#include <unordered_set>
#include <stack>
#include <queue>
#include <bitset>
#include <tuple>
#include <cmath>
#include <complex>
#include <algorithm>
#include <utility>
#include <regex>
#include <cstdint>
#include <numeric>
#include <functional>
#include <cassert>

using namespace std;
using ll = long long;
using ull = unsigned long long;

constexpr ll INF = 1'000'000'000'000'000'000;
namespace utils{
#define ALL(x) begin(x), end(x)
#define RALL(x) rbegin(x), rend(x)
    template<class T, class Compare> using p_queue = priority_queue<T, vector<T>, Compare>;
    template<class T> using min_queue = p_queue<T, greater<T>>;
    template<class T> using max_queue = p_queue<T, less<T>>;

    template<class T> bool up_min(T& X, const T& A){ if(X > A) {X = A; return true;} return false; }
    template<class T> bool up_max(T& X, const T& A){ if(X < A) {X = A; return true;} return false; }

    ll operator"" _64(unsigned long long x){ return ll(x); }
    ull operator"" _64u(unsigned long long x){ return ull(x); }

    template<class T>
    vector<T> make_mdvector(int n, T t){
        return vector<T>(n, t);
    }
    template<class ...Ts>
    auto make_mdvector(int n, Ts ... ts){
        return vector<decltype(make_mdvector(ts...))>(n, make_mdvector(ts...));
    }

    inline ll bit(int x){
        return 1ll << x;
    }

    template<class T>
    istream& operator>>(istream& is, vector<T>& v){
        for (auto &&x : v) { is >> x; } return is;
    }

    template<class T>
    ostream& operator<<(ostream& os, const vector<T>& v){
        for (auto &&x : v) { os << x << ' '; } cout << endl; return os ;
    }
}
using namespace utils;

class solver{
    istream& is;
    ostream& os;

public:
    solver(istream& I, ostream& O) :is(I), os(O) {}
    ll N;
    string S;
    vector<int> V;
    void run();

    bool check(){
        for (int i = 1; i < N-1; ++i) {
            assert(V[i] != -1);
            int pre = i-1;
            int next = i+1;
            V[next] = V[pre] ^ (S[i] == 'o') ^ !V[i];
        } // end i

        for (int i = 0; i < N; ++i) {
            int pre = i-1; if(pre < 0) pre += N;
            int next = i+1; if(next >= N) next -= N;
            if(V[next] == V[pre] xor S[i] == 'o' xor V[i]){
                return false;
            }
        } // end i
        return true;

    }

};

int main(int argc, char *argv[]) {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << setprecision(16) << scientific;
#ifdef XELMH
    string test_cases = "test_D.txt";
    cerr << test_cases << " -->" << endl;
    auto fs = fstream(test_cases, fstream::in);
    int loop = 0;
    while(fs) {
        loop++;
        cout << '#' << loop << "#------\n";
        solver(fs, cout).run();
    }
    if(loop <= 1) {
        cout << "===" << endl;
        while(cin) solver(cin, cout).run();
    }
#else
    solver(cin, cout).run();
#endif
    return 0;
}


void solver::run(){
    is >> N;
    if(!is) return;
    is >> S;
    for (int i = 0; i < 4; ++i) {
        V = make_mdvector(N, -1);
        V[0] = (i & 1) >= 1;
        V[1] = (i & 2) >= 1;
        if(check()) {
            for (auto &&v : V) {
                os << (v ? 'W' : 'S');
            } // end v
            os << endl;
            return;
        }
    } // end i
    os << -1 << endl;


}