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>
//#include <ext/pb_ds/assoc_container.hpp>
//#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
//using namespace __gnu_pbds;

#define pb push_back
#define mp make_pair
#define all(x) (x).begin(),(x).end()
#define lb lower_bound
#define ub upper_bound

typedef long long ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
typedef vector<int> vi;
typedef vector<ll> vll;
//template<class T> using oset=tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
const ll mod=1000000007;
ll powmod(ll a,ll b) {ll res=1;a%=mod; assert(b>=0); for(;b;b>>=1){if(b&1)res=res*a%mod;a=a*a%mod;}return res;}
ll gcd(ll a,ll b) { return b?gcd(b,a%b):a;}

//head
int n;
string s;
bool works(int* a1, int e){
	for(int i = 1; i < n -1; i++){
  		if(a1[i] == 0){
  			if(s[i] == 'o'){
  				a1[i+1] = a1[i-1];
  			}
  			else{
  				a1[i+1] = a1[i-1] ^ 1;
  			}
  		}
  		else{
  			if(s[i] == 'o'){
  				a1[i+1] = a1[i-1] ^ 1;
  			}
  			else{
  				a1[i+1] = a1[i-1];
  			}
  		}
  	}
  	if(a1[n-1] == e){
  		return true;
  	}
  	return false;
}
void printans(int* a1){
	for(int i = 0; i < n; i++){
		if(a1[i] == 0){
			cout << 'S';
		}
		else{
			cout << 'W';
		}
	}
	cout << "\n";
}
int main()
{
	ios::sync_with_stdio(false);
  	cin.tie(0);

  	cin >> n;
  	cin >> s;
  	int a1[n];
  	int a2[n];
  	int a3[n];
  	int a4[n];

  	a1[0] = 0;
  	a1[n-1] = 0;
  	if(s[0] == 'o'){
  		a1[1] = 0;
  	}
  	else{
  		a1[1] = 1;
  	}
  	if(s[n-1] == 'o'){
  		a1[n-2] = 0;
  	}
  	else{
  		a1[n-2] = 1;
  	}

  	a2[0] = 0;
  	a2[n-1] = 1;
  	if(s[0] == 'o'){
  		a2[1] = 1;
  	}
  	else{
  		a2[1] = 0;
  	}
  	if(s[n-1] == 'o'){
  		a2[n-2] = 1;
  	}
  	else{
  		a2[n-2] = 0;
  	}

  	a3[0] = 1;
  	a3[n-1] = 0;
  	if(s[0] == 'o'){
  		a3[1] = 0;
  	}
  	else{
  		a3[1] = 1;
  	}
  	if(s[n-1] == 'o'){
  		a3[n-2] = 1;
  	}
  	else{
  		a3[n-2] = 0;
  	}

  	a4[0] = 1;
  	a4[n-1] = 1;
  	if(s[0] == 'o'){
  		a4[1] = 0;
  	}
  	else{
  		a4[1] = 1;
  	}
  	if(s[n-1] == 'o'){
  		a4[n-2] = 0;
  	}
  	else{
  		a4[n-2] = 1;
  	}

  	if(works(a1, 0)){
  		printans(a1);
  		return 0;
  	}
  	else if(works(a2, 1)){
  		printans(a2);
  		return 0;
  	}
  	else if(works(a3, 0)){
  		printans(a3); return 0;
  	}
  	else if(works(a4, 1)){
  		printans(a4); return 0;
  	}
  	cout << -1 << "\n";
	return 0;
}