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;
using ll = long long;
#define _overload3(_1,_2,_3,name,...) name
#define _rep(i,n) repi(i,0,n)
#define repi(i,a,b) for(int i=int(a);i<int(b);++i)
#define rep(...) _overload3(__VA_ARGS__,repi,_rep,)(__VA_ARGS__)
#define VIEW(x) do {cerr << #x << ": "; for(auto i : x) cerr << i << " "; cerr << endl;} while(0)
#define ALL(x) (x).begin(),(x).end()
template<class T>bool umax(T &a, const T &b) {if(a<b){a=b;return 1;}return 0;}
template<class T>bool umin(T &a, const T &b) {if(b<a){a=b;return 1;}return 0;}

template<typename A,size_t N,typename T> void FILL(A (&array)[N],const T &val){fill((T*)array,(T*)(array+N),val);}
template<typename T> void FILL(vector<T> &v, const T &x) {fill(v.begin(), v.end(), x);}
template<typename T> void FILL(vector<vector<T>> &v, const T &x) {for(auto &i:v)fill(i.begin(), i.end(), x);}

int n;
string s;
vector<char> r;

void chain() {
  rep(i, 1, n-2) {
    if(s[i] == 'o') {
      if(r[i] == 'S') {
        r[i+1] = r[i-1];
      }
      else {
        r[i+1] = r[i-1]=='S' ? 'W' : 'S';
      }
    }
    else {
      if(r[i] == 'S') {
        r[i+1] = r[i-1]=='S' ? 'W' : 'S';
      }
      else {
        r[i+1] = r[i-1];
      }
    }
  }

  if (r[n-2] == 'S') {
    if(s[n-2] == 'o') {
      if(r[n-3] != r[n-1]) return;
    }
    else {
      if(r[n-3] == r[n-1]) return;
    }
  }
  else {
    if(s[n-2] == 'o') {
      if(r[n-3] == r[n-1]) return;
    }
    else {
      if(r[n-3] != r[n-1]) return;
    }
  }

  if (r[n-1] == 'S') {
    if(s[n-1] == 'o') {
      if(r[n-2] != r[0]) return;
    }
    else {
      if(r[n-2] == r[0]) return;
    }
  }
  else {
    if(s[n-1] == 'o') {
      if(r[n-2] == r[0]) return;
    }
    else {
      if(r[n-2] != r[0]) return;
    }
  }

  rep(i,n) cout << r[i];
  cout << endl;
  exit(0);
}

int main() {
  //https://atcoder.jp/contests/arc069/tasks/arc069_b
  cin >> n >> s;
  r.resize(n);

  char sw[] = {'S' ,'W'};
  for(char z : sw) {
    r[0] = z;
    if(s[0] = 'o') {
      if(z == 'S') {
        r[1] = r[n-1] = 'S';
        chain();
        r[1] = r[n-1] = 'W';
        chain();
      }
      else {
        r[1] = 'S', r[n-1] = 'W';
        chain();
        r[1] = 'W', r[n-1] = 'S';
        chain();
      }
    }
    if(s[0] = 'x') {
      if(z == 'S') {
        r[1] = 'S', r[n-1] = 'W';
        chain();
        r[1] = 'W', r[n-1] = 'S';
        chain();
      }
      else {
        r[1] = r[n-1] = 'S';
        chain();
        r[1] = r[n-1] = 'W';
        chain();
      }
    }
  }
  cout << -1 << endl;
}