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 Java (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;
import java.util.stream.Collectors;
import java.io.*;
import java.math.BigDecimal;
import java.nio.charset.StandardCharsets;

public class Main {

	public static void main(String[] args) throws IOException {
		InputStreamReader reader = new InputStreamReader(System.in, StandardCharsets.UTF_8);
		BufferedReader in = new BufferedReader(reader);
		Main ins = new Main(in);
		ins.calc();
		ins.showResult();
	}

	int N;
	char[] s;
	char[] result;
	boolean enable = false;

	Main(BufferedReader in) throws IOException {
		N = Integer.parseInt(in.readLine());
		s = in.readLine().toCharArray();
	}

	boolean enable(char first, char second) {
		char[] pat = new char[N];
		pat[0] = first;
		pat[1] = second;
		for (int i = 2; i < N; ++i) {
			if (s[i - 1] == 'o') {
				if (pat[i - 1] == 'S') {
					pat[i] = pat[i - 2];
				} else {
					pat[i] = pat[i - 2] == 'S' ? 'W' : 'S';
				}
			} else {
				if (pat[i - 1] == 'S') {
					pat[i] = pat[i - 2] == 'S' ? 'W' : 'S';
				} else {
					pat[i] = pat[i - 2];
				}
			}
		}
		// 矛盾がないかチェック
		if (s[N - 1] == 'o') {
			if (pat[N - 1] == 'S') {
				if (pat[0] == pat[N - 2]) {
					result = Arrays.copyOf(pat, N);
					return true;
				} else {
					return false;
				}
			} else {
				if (pat[0] != pat[N - 2]) {
					result = Arrays.copyOf(pat, N);
					return true;
				} else {
					return false;
				}
			}
		} else {
			if (pat[N - 1] == 'S') {
				if (pat[0] != pat[N - 2]) {
					result = Arrays.copyOf(pat, N);
					return true;
				} else {
					return false;
				}
			} else {
				if (pat[0] == pat[N - 2]) {
					result = Arrays.copyOf(pat, N);
					return true;
				} else {
					return false;
				}
			}
		}
	}

	void calc() {
		if (enable('S', 'S')) {
			enable = true;
			return;
		} else if (enable('S', 'W')) {
			enable = true;
			return;
		} else if (enable('W', 'S')) {
			enable = true;
			return;
		} else {
			enable = enable('W', 'W');
		}
	}

	void showResult() {
		if (!enable) {
			System.out.println("-1");
		} else {
			for (int i = 0; i < N; ++i) {
				System.out.print(result[i]);
			}
			System.out.println("");
		}
	}
}