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.io.*;
import java.util.*;
import java.lang.*;

public class Main {
    static class FastScanner {
        private final InputStream in = System.in;
        private final byte[] buffer = new byte[1024];
        private int ptr = 0;
        private int buflen = 0;

        private boolean hasNextByte() {
            if (ptr < buflen) {
                return true;
            } else {
                ptr = 0;
                try {
                    buflen = in.read(buffer);
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (buflen <= 0) {
                    return false;
                }
            }
            return true;
        }

        private int readByte() {
            if (hasNextByte()) return buffer[ptr++];
            else return -1;
        }

        private boolean isPrintableChar(int c) {
            return 33 <= c && c <= 126;
        }

        public boolean hasNext() {
            while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
            return hasNextByte();
        }

        public String next() {
            if (!hasNext()) throw new NoSuchElementException();
            StringBuilder sb = new StringBuilder();
            int b = readByte();
            while (isPrintableChar(b)) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }

        public long nextLong() {
            if (!hasNext()) throw new NoSuchElementException();
            long n = 0;
            boolean minus = false;
            int b = readByte();
            if (b == '-') {
                minus = true;
                b = readByte();
            }
            if (b < '0' || '9' < b) {
                throw new NumberFormatException();
            }
            while (true) {
                if ('0' <= b && b <= '9') {
                    n *= 10;
                    n += b - '0';
                } else if (b == -1 || !isPrintableChar(b)) {
                    return minus ? -n : n;
                } else {
                    throw new NumberFormatException();
                }
                b = readByte();
            }
        }

        public int nextInt() {
            long nl = nextLong();
            if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
            return (int) nl;
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }
    }

    public static void main(String[] args) {
        FastScanner fs = new FastScanner();
        int n = fs.nextInt();
        String s = fs.next();
        char[][] pat = {{'S', 'S'}, {'S', 'W'}, {'W', 'S'}, {'W', 'W'}};
        for (char[] p : pat) {
            String ans = check(s, p[0], p[1]);
            if (!ans.isEmpty()) {
                System.out.println(ans);
                return;
            }
        }
        System.out.println(-1);
    }

    private static String check(String s, char h1, char h2) {
        int n = s.length();
        char[] ans = new char[n];
        ans[0] = h1;
        ans[1] = h2;
        for (int i = 1; i < n - 1; ++i) {
            if (s.charAt(i) == 'o' && ans[i] == 'S') {
                ans[i + 1] = ans[i - 1];
            } else if (s.charAt(i) == 'o' && ans[i] == 'W') {
                if (ans[i - 1] == 'S') {
                    ans[i + 1] = 'W';
                } else {
                    ans[i + 1] = 'S';
                }
            } else if (s.charAt(i) == 'x' && ans[i] == 'S') {
                if (ans[i - 1] == 'S') {
                    ans[i + 1] = 'W';
                } else {
                    ans[i + 1] = 'S';
                }
            } else {
                ans[i + 1] = ans[i - 1];
            }
        }
        if (check(s, ans, n - 2, n - 1, 0) && check(s, ans, n - 1, 0, 1)) {
            return new String(ans);
        } else {
            return "";
        }
    }

    private static boolean check(String s, char[] ans, int i, int j, int k) {
        int n = s.length();
        if (s.charAt(j) == 'o' && ans[j] == 'S') {
            return ans[i] == ans[k];
        } else if (s.charAt(j) == 'o' && ans[j] == 'W') {
            return ans[i] != ans[k];
        } else if (s.charAt(j) == 'x' && ans[j] == 'S') {
            return ans[i] != ans[k];
        }
        return ans[i] == ans[k];
    }
}