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 <iostream>
#include <vector>
#include <string>
#include <sstream>
#include <utility>
#include <set>
#include <map>
#include <queue>
#include <stack>
#include <algorithm>
#include <istream>
#include <ostream>

#include <cstdlib>
#include <cmath>
#include <cstdio>

using namespace std;

#define fi first
#define se second
#define mkp make_pair
#define all(x) (x).begin(), (x).end()
#define pb push_back
#define rep(i,n) for(ll i=0; i < (n); ++i)
#define rrep(i,n) for(ll i=((n)-1); i >= 0; --i)

#define OPLT(T) bool operator<(const T & lop_, const T & rop_)
#define OPEQ(T) bool operator==(const T & lop_, const T & rop_)

typedef long long ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;

istream& operator>>(istream& istr, __float128& obj) { double d; istr >> d; obj = d; return istr; };
ostream& operator<<(ostream& ostr, __float128& obj) { ostr << static_cast<double>(obj); return ostr; };

int main() {
	int N;
	string s;
	cin >> N >> s;
	for(int i = 0; i < 4; i++) {
		string t = "";
		for(int j = 0; j < 2; j++) t += (i&(1<<j))?"S":"W";
		for(int j = 1; j < s.size(); j++) {
			string tmp = string(t.end()-2,t.end());
			char add = (s[j]=='o') ? tmp[0] : ('S' + 'W' - tmp[0]);
			if(tmp[1] == 'W') add = 'S' + 'W' - add;
			t += add;
		}
		if(t[0] == t[t.size()-1] && ((s[0]=='o'&&t[1]==t[N-1]) || (s[1]=='x'&&t[1]!=t[N-1]))^(t[0]=='W')) {
			cout << string(t.begin(), t.end()-1) << endl;
			return 0;
		}
	}
	cout << -1 << endl;
	return 0;
}