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 <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <climits>
#include <vector>
#include <string>
#include <queue>
#include <deque>
#include <list>
#include <stack>
#include <set>
#include <map>
#include <algorithm>

#define int long long
#define MOD7 1000000007
#define MOD9 1000000009

#define rep(i, n) for (int i = 0; i < (n); i++)
#define REP(i, a, n) for (int i = (a); i <= (n); i++)
#define all(a) (a).begin(), (a).end()

using namespace std;

int dx[4] = { 1, 0, -1, 0 };
int dy[4] = { 0, -1, 0, 1 };

int nextInt() {int a; cin >> a; return a;}
char nextChar() {char a; cin >> a; return a;}
double nextDouble() {double a; cin >> a; return a;}
string nextString() {string a; cin >> a; return a;}

template<class T> void inputVector(vector<T>& v, int n) {
    v.resize(n);
    for (int i = 0; i < v.size(); i++) cin >> v[i];
}

char f(char a, char b, char c) {
	if (b == 'S') {
		if (c == 'o') return a;
		if (a == 'W') return 'S';
		return 'W';
	}
	if (c == 'x') return a;
	if (a == 'W') return 'S';
	return 'W';
}

int n;
string s;

bool ok(string ret) {
	char a = ret[n - 2];
	char b = ret[n - 1];
	char c = ret[0];
	char d = ret[1];
	if (f(a, b, s[n - 1]) != c) return false;
	if (f(b, c, s[0]) != d) return false;
	return true;
}

signed main() {
	cin >> n;
	cin >> s;

	string ret = "";
	ret += "SS";
	REP(i, 1, n - 2) {
		ret.push_back(f(ret[i - 1], ret[i], s[i]));
	}
	if (ok(ret)) {
		cout << ret << endl;;
		return 0;
	}

	ret = "";
	ret += "SW";
	REP(i, 1, n - 2) {
		ret.push_back(f(ret[i - 1], ret[i], s[i]));
	}
	if (ok(ret)) {
		cout << ret << endl;;
		return 0;
	}

	ret = "";
	ret += "WS";
	REP(i, 1, n - 2) {
		ret.push_back(f(ret[i - 1], ret[i], s[i]));
	}
	if (ok(ret)) {
		cout << ret << endl;;
		return 0;
	}

	ret = "";
	ret += "WW";
	REP(i, 1, n - 2) {
		ret.push_back(f(ret[i - 1], ret[i], s[i]));
	}
	if (ok(ret)) {
		cout << ret << endl;;
		return 0;
	}

	cout << -1 << endl;

    return 0;
}