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 11.0.6) (judge verdict: Wrong Answer)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;
import java.util.function.BinaryOperator;
import java.util.function.Function;

 
public class Main {
	static final long MOD1=1000000007;
	static final long MOD2=998244353;
	public static void main(String[] args) {
		PrintWriter out = new PrintWriter(System.out);
		InputReader sc=new InputReader(System.in);
		int N=sc.nextInt();
		char[] cs=sc.next().toCharArray();
		char[] csW=new char[N];
		csW[N-1]='S';
		csW[0]='S';
		for (int i = 0; i < cs.length-2; i++) {
			if (csW[i]=='S') {
				if (cs[i]=='o') {
					csW[i+1]=csW[(i-1+N)%N];
				}else {
					if (csW[(i-1+N)%N]=='S') {
						csW[i+1]='W';
					}else {
						csW[i+1]='S';
					}
				}
			}else {
				if (cs[i]=='o') {
					if (csW[(i-1+N)%N]=='S') {
						csW[i+1]='W';
					}else {
						csW[i+1]='S';
					}
				}else {
					csW[i+1]=csW[(i-1+N)%N];
				}
			}
		}
		boolean[] flag=new boolean[2];
		for (int i = 0; i <= 1; i++) {
			if (csW[N-2+i]=='S') {
				if (cs[N-2+i]=='o') {
					if (csW[N-3+i]==csW[(N-1+i)%N]) {
						flag[i]=true;
					}
				}else {
					if (csW[N-3+i]!=csW[(N-1+i)%N]) {
						flag[i]=true;
					}
				}
			}else {
				if (cs[N-2+i]!='o') {
					if (csW[N-3+i]==csW[(N-1+i)%N]) {
						flag[i]=true;
					}
				}else {
					if (csW[N-3]!=csW[(N-1+i)%N]) {
						flag[i]=true;
					}
				}
			}
		}
		if (flag[0]&&flag[1]) {
			System.out.println(String.valueOf(csW));
			return;
		}
		csW[N-1]='W';
		csW[0]='S';
		for (int i = 0; i < cs.length-2; i++) {
			if (csW[i]=='S') {
				if (cs[i]=='o') {
					csW[i+1]=csW[(i-1+N)%N];
				}else {
					if (csW[(i-1+N)%N]=='S') {
						csW[i+1]='W';
					}else {
						csW[i+1]='S';
					}
				}
			}else {
				if (cs[i]=='o') {
					if (csW[(i-1+N)%N]=='S') {
						csW[i+1]='W';
					}else {
						csW[i+1]='S';
					}
				}else {
					csW[i+1]=csW[(i-1+N)%N];
				}
			}
		}
		Arrays.fill(flag, false);
		for (int i = 0; i <= 1; i++) {
			if (csW[N-2+i]=='S') {
				if (cs[N-2+i]=='o') {
					if (csW[N-3+i]==csW[(N-1+i)%N]) {
						flag[i]=true;
					}
				}else {
					if (csW[N-3+i]!=csW[(N-1+i)%N]) {
						flag[i]=true;
					}
				}
			}else {
				if (cs[N-2+i]!='o') {
					if (csW[N-3+i]==csW[(N-1+i)%N]) {
						flag[i]=true;
					}
				}else {
					if (csW[N-3]!=csW[(N-1+i)%N]) {
						flag[i]=true;
					}
				}
			}
		}
		if (flag[0]&&flag[1]) {
			System.out.println(String.valueOf(csW));
			return;
		}
		csW[N-1]='S';
		csW[0]='W';
		for (int i = 0; i < cs.length-2; i++) {
			if (csW[i]=='S') {
				if (cs[i]=='o') {
					csW[i+1]=csW[(i-1+N)%N];
				}else {
					if (csW[(i-1+N)%N]=='S') {
						csW[i+1]='W';
					}else {
						csW[i+1]='S';
					}
				}
			}else {
				if (cs[i]=='o') {
					if (csW[(i-1+N)%N]=='S') {
						csW[i+1]='W';
					}else {
						csW[i+1]='S';
					}
				}else {
					csW[i+1]=csW[(i-1+N)%N];
				}
			}
		}
		Arrays.fill(flag, false);
		for (int i = 0; i <= 1; i++) {
			if (csW[N-2+i]=='S') {
				if (cs[N-2+i]=='o') {
					if (csW[N-3+i]==csW[(N-1+i)%N]) {
						flag[i]=true;
					}
				}else {
					if (csW[N-3+i]!=csW[(N-1+i)%N]) {
						flag[i]=true;
					}
				}
			}else {
				if (cs[N-2+i]!='o') {
					if (csW[N-3+i]==csW[(N-1+i)%N]) {
						flag[i]=true;
					}
				}else {
					if (csW[N-3]!=csW[(N-1+i)%N]) {
						flag[i]=true;
					}
				}
			}
		}
		if (flag[0]&&flag[1]) {
			System.out.println(String.valueOf(csW));
			return;
		}
		csW[N-1]='W';
		csW[0]='W';
		for (int i = 0; i < cs.length-2; i++) {
			if (csW[i]=='S') {
				if (cs[i]=='o') {
					csW[i+1]=csW[(i-1+N)%N];
				}else {
					if (csW[(i-1+N)%N]=='S') {
						csW[i+1]='W';
					}else {
						csW[i+1]='S';
					}
				}
			}else {
				if (cs[i]=='o') {
					if (csW[(i-1+N)%N]=='S') {
						csW[i+1]='W';
					}else {
						csW[i+1]='S';
					}
				}else {
					csW[i+1]=csW[(i-1+N)%N];
				}
			}
		}
		Arrays.fill(flag, false);
		for (int i = 0; i <= 1; i++) {
			if (csW[N-2+i]=='S') {
				if (cs[N-2+i]=='o') {
					if (csW[N-3+i]==csW[(N-1+i)%N]) {
						flag[i]=true;
					}
				}else {
					if (csW[N-3+i]!=csW[(N-1+i)%N]) {
						flag[i]=true;
					}
				}
			}else {
				if (cs[N-2+i]!='o') {
					if (csW[N-3+i]==csW[(N-1+i)%N]) {
						flag[i]=true;
					}
				}else {
					if (csW[N-3]!=csW[(N-1+i)%N]) {
						flag[i]=true;
					}
				}
			}
		}
		if (flag[0]&&flag[1]) {
			System.out.println(String.valueOf(csW));
			return;
		}
		System.out.println(-1);
	}
		static class InputReader { 
		private InputStream in;
		private byte[] buffer = new byte[1024];
		private int curbuf;
		private int lenbuf;
		public InputReader(InputStream in) {
			this.in = in;
			this.curbuf = this.lenbuf = 0;
		}
 
		public boolean hasNextByte() {
			if (curbuf >= lenbuf) {
				curbuf = 0;
				try {
					lenbuf = in.read(buffer);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (lenbuf <= 0)
					return false;
			}
			return true;
		}
 
		private int readByte() {
			if (hasNextByte())
				return buffer[curbuf++];
			else
				return -1;
		}
 
		private boolean isSpaceChar(int c) {
			return !(c >= 33 && c <= 126);
		}
 
		private void skip() {
			while (hasNextByte() && isSpaceChar(buffer[curbuf]))
				curbuf++;
		}
 
		public boolean hasNext() {
			skip();
			return hasNextByte();
		}
 
		public String next() {
			if (!hasNext())
				throw new NoSuchElementException();
			StringBuilder sb = new StringBuilder();
			int b = readByte();
			while (!isSpaceChar(b)) {
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}
 
		public int nextInt() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}
 
		public long nextLong() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}
 
		public double nextDouble() {
			return Double.parseDouble(next());
		}
 
		public int[] nextIntArray(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}
 
		public long[] nextLongArray(int n) {
			long[] a = new long[n];
			for (int i = 0; i < n; i++)
				a[i] = nextLong();
			return a;
		}
 
		public char[][] nextCharMap(int n, int m) {
			char[][] map = new char[n][m];
			for (int i = 0; i < n; i++)
				map[i] = next().toCharArray();
			return map;
		}
	}
}