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<bits/stdc++.h>
using namespace std;
#define rep(i,a,b) for(int i=a;i<b;i++)
#define rrep(i,a,b) for(int i=a;i>=b;i--)
#define erep(i,a,n) for(int i = a;i<=n;i++)
typedef long long ll;
#define int long long
#define vint vector<int>
#define vvint vector<vector<int>>
#define vstring vector<string>
#define vdouble vector<double>
#define vll vector<ll>:
#define vbool vector<bool>
#define INF 1101010101010101010
#define MOD 1000000007
#define P = pair<int,int>;
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a = b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a = b; return 1; } return 0; }

signed main(){
  int n;
  cin >> n;
  string s;
  cin >> s;
  vector<char> ans(n);
  bool flag1 = false;
  bool flag2 = false;
  ans[0] = 'S';
  ans[1] = 'S';
  rep(i,1,n-1){
    if(s[i] == 'o'){
      if((ans[i-1] == 'S' && ans[i] == 'W') || (ans[i-1] == 'W' && ans[i] == 'S')){
        ans[i+1] = 'W';
      }
      else if((ans[i-1] == 'W' && ans[i] == 'W') || (ans[i-1] == 'S' && ans[i] == 'S')){
        ans[i+1] = 'S';
      }
    }
    else if(s[i] == 'x'){
      if((ans[i-1] == 'S' && ans[i] == 'W') || (ans[i-1] == 'W' && ans[i] == 'S')){
        ans[i+1] = 'S';
      }
      else if((ans[i-1] == 'W' && ans[i] == 'W') || (ans[i-1] == 'S' && ans[i] == 'S')){
        ans[i+1] = 'W';
      }
    }
  }
  if(s[n-1] == 'o' && ans[n-1] == 'S') if(ans[n-2] == ans[0]) flag1 = true;
  if(s[n-1] == 'o' && ans[n-1] == 'W') if(ans[n-2] != ans[0]) flag1 = true;
  if(s[n-1] == 'x' && ans[n-1] == 'S') if(ans[n-2] != ans[0]) flag1 = true;
  if(s[n-1] == 'x' && ans[n-1] == 'W') if(ans[n-2] == ans[0]) flag1 = true;
  if(s[0] == 'o' && ans[0] == 'S') if(ans[n-1] == ans[1]) flag2 = true;
  if(s[0] == 'o' && ans[0] == 'W') if(ans[n-1] != ans[1]) flag2 = true;
  if(s[0] == 'x' && ans[0] == 'S') if(ans[n-1] != ans[1]) flag2 = true;
  if(s[0] == 'x' && ans[0] == 'W') if(ans[n-1] == ans[1]) flag2 = true;
  if(flag1 && flag2){
    rep(i,0,n) cout << ans[i];
    return 0;
  }
  flag1 = false;
  flag2 = false;
  ans[0] = 'S';
  ans[1] = 'W';
  rep(i,1,n-1){
    if(s[i] == 'o'){
      if((ans[i-1] == 'S' && ans[i] == 'W') || (ans[i-1] == 'W' && ans[i] == 'S')){
        ans[i+1] = 'W';
      }
      else if((ans[i-1] == 'W' && ans[i] == 'W') || (ans[i-1] == 'S' && ans[i] == 'S')){
        ans[i+1] = 'S';
      }
    }
    else if(s[i] == 'x'){
      if((ans[i-1] == 'S' && ans[i] == 'W') || (ans[i-1] == 'W' && ans[i] == 'S')){
        ans[i+1] = 'S';
      }
      else if((ans[i-1] == 'W' && ans[i] == 'W') || (ans[i-1] == 'S' && ans[i] == 'S')){
        ans[i+1] = 'W';
      }
    }
  }
  if(s[n-1] == 'o' && ans[n-1] == 'S') if(ans[n-2] == ans[0]) flag1 = true;
  if(s[n-1] == 'o' && ans[n-1] == 'W') if(ans[n-2] != ans[0]) flag1 = true;
  if(s[n-1] == 'x' && ans[n-1] == 'S') if(ans[n-2] != ans[0]) flag1 = true;
  if(s[n-1] == 'x' && ans[n-1] == 'W') if(ans[n-2] == ans[0]) flag1 = true;
  if(s[0] == 'o' && ans[0] == 'S') if(ans[n-1] == ans[1]) flag2 = true;
  if(s[0] == 'o' && ans[0] == 'W') if(ans[n-1] != ans[1]) flag2 = true;
  if(s[0] == 'x' && ans[0] == 'S') if(ans[n-1] != ans[1]) flag2 = true;
  if(s[0] == 'x' && ans[0] == 'W') if(ans[n-1] == ans[1]) flag2 = true;
  if(flag1 && flag2){
    rep(i,0,n) cout << ans[i];
    return 0;
  }
  flag1 = false;
  flag2 = false;
  ans[0] = 'W';
  ans[1] = 'S';
  rep(i,1,n-1){
    if(s[i] == 'o'){
      if((ans[i-1] == 'S' && ans[i] == 'W') || (ans[i-1] == 'W' && ans[i] == 'S')){
        ans[i+1] = 'W';
      }
      else if((ans[i-1] == 'W' && ans[i] == 'W') || (ans[i-1] == 'S' && ans[i] == 'S')){
        ans[i+1] = 'S';
      }
    }
    else if(s[i] == 'x'){
      if((ans[i-1] == 'S' && ans[i] == 'W') || (ans[i-1] == 'W' && ans[i] == 'S')){
        ans[i+1] = 'S';
      }
      else if((ans[i-1] == 'W' && ans[i] == 'W') || (ans[i-1] == 'S' && ans[i] == 'S')){
        ans[i+1] = 'W';
      }
    }
  }
  if(s[n-1] == 'o' && ans[n-1] == 'S') if(ans[n-2] == ans[0]) flag1 = true;
  if(s[n-1] == 'o' && ans[n-1] == 'W') if(ans[n-2] != ans[0]) flag1 = true;
  if(s[n-1] == 'x' && ans[n-1] == 'S') if(ans[n-2] != ans[0]) flag1 = true;
  if(s[n-1] == 'x' && ans[n-1] == 'W') if(ans[n-2] == ans[0]) flag1 = true;
  if(s[0] == 'o' && ans[0] == 'S') if(ans[n-1] == ans[1]) flag2 = true;
  if(s[0] == 'o' && ans[0] == 'W') if(ans[n-1] != ans[1]) flag2 = true;
  if(s[0] == 'x' && ans[0] == 'S') if(ans[n-1] != ans[1]) flag2 = true;
  if(s[0] == 'x' && ans[0] == 'W') if(ans[n-1] == ans[1]) flag2 = true;
  if(flag1 && flag2){
    rep(i,0,n) cout << ans[i];
    return 0;
  }
  flag1 = false;
  flag2 = false;
  ans[0] = 'W';
  ans[1] = 'W';
  rep(i,1,n-1){
    if(s[i] == 'o'){
      if((ans[i-1] == 'S' && ans[i] == 'W') || (ans[i-1] == 'W' && ans[i] == 'S')){
        ans[i+1] = 'W';
      }
      else if((ans[i-1] == 'W' && ans[i] == 'W') || (ans[i-1] == 'S' && ans[i] == 'S')){
        ans[i+1] = 'S';
      }
    }
    else if(s[i] == 'x'){
      if((ans[i-1] == 'S' && ans[i] == 'W') || (ans[i-1] == 'W' && ans[i] == 'S')){
        ans[i+1] = 'S';
      }
      else if((ans[i-1] == 'W' && ans[i] == 'W') || (ans[i-1] == 'S' && ans[i] == 'S')){
        ans[i+1] = 'W';
      }
    }
  }
  if(s[n-1] == 'o' && ans[n-1] == 'S') if(ans[n-2] == ans[0]) flag1 = true;
  if(s[n-1] == 'o' && ans[n-1] == 'W') if(ans[n-2] != ans[0]) flag1 = true;
  if(s[n-1] == 'x' && ans[n-1] == 'S') if(ans[n-2] != ans[0]) flag1 = true;
  if(s[n-1] == 'x' && ans[n-1] == 'W') if(ans[n-2] == ans[0]) flag1 = true;
  if(s[0] == 'o' && ans[0] == 'S') if(ans[n-1] == ans[1]) flag2 = true;
  if(s[0] == 'o' && ans[0] == 'W') if(ans[n-1] != ans[1]) flag2 = true;
  if(s[0] == 'x' && ans[0] == 'S') if(ans[n-1] != ans[1]) flag2 = true;
  if(s[0] == 'x' && ans[0] == 'W') if(ans[n-1] == ans[1]) flag2 = true;
  if(flag1 && flag2){
    rep(i,0,n) cout << ans[i];
    return 0;
  }
  cout << -1 << endl;
  return 0;
}