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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Scanner;
import java.util.stream.IntStream;

/**
 * 解説どおりに作成したソースコード
 */
public class Main {

	/** 羊の定義 */
	private static final char SHEEP = 'S';
	/** 狼の定義 */
	private static final char WOLF = 'W';

	public static void main(String[] args) {
		try (Scanner scanner = new Scanner(System.in)) {
			int n = scanner.nextInt();
			char[] s = scanner.next().toCharArray();
			boolean[] b = new boolean[n];
			IntStream.range(0, n).forEach(i -> b[i] = (s[i] == 'o'));
			char[] result = new char[n];
			result[0] = SHEEP;
			result[1] = SHEEP;
			if (checkResult(n, b, result)) {
				System.out.println(result);
				return;
			}
			result[0] = SHEEP;
			result[1] = WOLF;
			if (checkResult(n, b, result)) {
				System.out.println(result);
				return;
			}
			result[0] = WOLF;
			result[1] = WOLF;
			if (checkResult(n, b, result)) {
				System.out.println(result);
				return;
			}
			result[0] = WOLF;
			result[1] = SHEEP;
			if (checkResult(n, b, result)) {
				System.out.println(result);
				return;
			}
			System.out.println(-1);
		}
	}

	/**
	 * @param n
	 * @param b
	 * @param result
	 * @return このまま矛盾することなく計算できるかどうか
	 */
	private static boolean checkResult(int n, boolean[] b, char[] result) {
		// 2〜n-1まで動物を計算
		IntStream.range(2, n).forEach(i -> {
			if (WOLF == result[i - 1]) {
				result[i] = (b[i - 1]) ? reverse(result[i - 2]) : result[i - 2];
			} else {
				result[i] = (b[i - 1]) ? result[i - 2] : reverse(result[i - 2]);
			}
		});
		boolean lastOk = false, firstOk = false;
		if (WOLF == result[n - 1]) {
			lastOk = (b[n - 1]) ? (result[0] != result[n - 2]) : (result[0] == result[n - 2]);
		} else {
			lastOk = (b[n - 1]) ? (result[0] == result[n - 2]) : (result[0] != result[n - 2]);
		}
		if (WOLF == result[0]) {
			firstOk = (b[0]) ? (result[1] != result[n - 1]) : (result[1] == result[n - 1]);
		} else {
			firstOk = (b[0]) ? (result[1] == result[n - 1]) : (result[1] != result[n - 1]);
		}
		return lastOk && firstOk;
	}

	/**
	 * @param c
	 * @return cの反対の動物
	 */
	private static char reverse(char c) {
		return (c == SHEEP) ? WOLF : SHEEP;
	}
}