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.util.stream.Collectors;
import java.util.stream.IntStream;

import static java.lang.Math.*;
import static java.lang.String.format;

public class Main {
    public static void main(String[] args) {
        solve();
    }
    final static int INF = Integer.MAX_VALUE>>1;
    final static int MOD = 1_000_000_007;
    final static int[] dx4 = { 0, 1, 0, -1 };
    final static int[] dy4 = { 1, 0, -1, 0 };
    final static int[] dx8 = {0, 1, 1,  1,  0, -1, -1, -1};
    final static int[] dy8 = {1, 1, 0, -1, -1, -1, 0, 1};
    final static Runnable me=()->{};
    public static void solve(){
        //TODO:Solve problem like ***
        Scanner sc=new Scanner();
        int n = sc.nextInt();
        String s = sc.next();
        //s[0]==sheep
        {
            boolean[][] isSheep = new boolean[2][n];
            isSheep[0][0]=true;
            if(s.charAt(0)=='o'){
                isSheep[0][n-1]=true;
                isSheep[0][1]=true;
            }else{
                isSheep[0][n-1]=true;
                isSheep[0][1]=false;
            }

            isSheep[1][0]=true;
            if(s.charAt(0)=='o'){
                isSheep[1][n-1]=false;
                isSheep[1][1]=false;
            }else{
                isSheep[1][n-1]=false;
                isSheep[1][1]=true;
            }
            for (boolean[] isS : isSheep) {
                for (int i = 1; i < n-2; i++) {
                    if(s.charAt(i)=='o'){
                        isS[i+1]=isS[i]?isS[i-1]:!isS[i-1];
                    }else{
                        isS[i+1]=isS[i]?!isS[i-1]:isS[i-1];
                    }
                }
            }
//            put("isSheep[0]",Arrays.toString(isSheep[0]));
//            put("isSheep[1]",Arrays.toString(isSheep[1]));
            //i==n-2,n-1
            for (boolean[] isS : isSheep) {
                boolean expectedLastSheep=false;
                if(s.charAt(n-2)=='o'){
                    expectedLastSheep=isS[n-2]?isS[n-3]:!isS[n-3];
                }else{
                    expectedLastSheep=isS[n-2]?!isS[n-3]:isS[n-3];
                }
                if(isS[n-1]!=expectedLastSheep)continue;
                boolean expectedFisrtSheep=false;
                if(s.charAt(n-1)=='o'){
                    expectedFisrtSheep=isS[n-1]?isS[n-2]:!isS[n-2];
                }else{
                    expectedFisrtSheep=isS[n-1]?!isS[n-2]:isS[n-2];
                }
                if(isS[0]!=expectedFisrtSheep)continue;
                StringBuilder sb = new StringBuilder();
                for (boolean b : isS) {
                    if(b){
                        sb.append('S');
                    }else{
                        sb.append('W');
                    }
                }
                put(sb);
                return;
            }
        }

        //s[0]==wolf
        {
            boolean[][] isSheep = new boolean[2][n];
            isSheep[0][0]=false;
            if(s.charAt(0)=='o'){
                isSheep[0][n-1]=true;
                isSheep[0][1]=false;
            }else{
                isSheep[0][n-1]=true;
                isSheep[0][1]=true;
            }

            isSheep[1][0]=false;
            if(s.charAt(0)=='o'){
                isSheep[1][n-1]=false;
                isSheep[1][1]=true;
            }else{
                isSheep[1][n-1]=false;
                isSheep[1][1]=false;
            }
            for (boolean[] isS : isSheep) {
                for (int i = 1; i < n-2; i++) {
                    if(s.charAt(i)=='o'){
                        isS[i+1]=isS[i]?isS[i-1]:!isS[i-1];
                    }else{
                        isS[i+1]=isS[i]?!isS[i-1]:isS[i-1];
                    }
                }
            }
            //i==n-2,n-1
            for (boolean[] isS : isSheep) {
                boolean expectedLastSheep=false;
                if(s.charAt(n-2)=='o'){
                    expectedLastSheep=isS[n-2]?isS[n-3]:!isS[n-3];
                }else{
                    expectedLastSheep=isS[n-2]?!isS[n-3]:isS[n-3];
                }
                if(isS[n-1]!=expectedLastSheep)continue;
                boolean expectedFisrtSheep=false;
                if(s.charAt(n-1)=='o'){
                    expectedFisrtSheep=isS[n-1]?isS[n-2]:!isS[n-2];
                }else{
                    expectedFisrtSheep=isS[n-1]?!isS[n-2]:isS[n-2];
                }
                if(isS[0]!=expectedFisrtSheep)continue;
                StringBuilder sb = new StringBuilder();
                for (boolean b : isS) {
                    if(b){
                        sb.append('S');
                    }else{
                        sb.append('W');
                    }
                }
                put(sb);
                return;
            }
        }
        put(-1);
    }
    //runWhenEAで使う
    private static Runnable func(Object... objects){
        try{
            assert false;
            return me;
        }catch(AssertionError e){
            return ()->{put(objects);};
        }
    }
    private static void print(Object... objects){
        if(objects.length==1){
            System.out.print(objects[0]);
        }else{
            System.out.print(Arrays.toString(objects));
        }
    }
    private static void put(Object... objects) {
        print(objects);
        put();
    }
    private static void put(){
        System.out.println();
    }


    private static void runWhenEA(Runnable runnable){
        try{
            assert false;
        }catch(AssertionError e){
            PrintStream ps=System.out;
            PrintStream pse=System.err;
            System.setOut(pse);
            runnable.run();
            System.setOut(ps);
        }
    }
    private static void putM(String name,char[][] mat){
        put("---------------------"+name+"-----------------");
        for (int i = 0; i < mat.length; i++) {
            put(Arrays.toString(mat[i]));
        }
    }
    private static void putM(String name,int[][] mat){
        put("---------------------"+name+"-----------------");
        for (int i = 0; i < mat.length; i++) {
            put(Arrays.toString(mat[i]));
        }
    }
    private static void putM(String name,long[][] mat){
        put("---------------------"+name+"-----------------");
        for (int i = 0; i < mat.length; i++) {
            put(Arrays.toString(mat[i]));
        }
    }
    private static void putM(String name,boolean[][] mat){
        put("---------------------"+name+"-----------------");
        for (int i = 0; i < mat.length; i++) {
            put(Arrays.toString(mat[i]));
        }
    }
    final static private class Scanner {
        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());
        }
    }
    final static private class FixedIntPair {
        final public int x, y;
        final static public FixedIntPair ZEROS=new FixedIntPair(0,0);
        FixedIntPair(int x, int y) {
            this.x = x;
            this.y = y;
        }
        public static double distance(FixedIntPair fip1,FixedIntPair fip2){
            double x = (double) fip1.x - fip2.x;
            double y = (double) fip1.y - fip2.y;
            return Math.sqrt(x*x+y*y);
        }

        @Override
        public int hashCode() {
            return x*100000+y;
        }

        @Override
        public boolean equals(Object obj) {
            if(obj==null)return false;
            if(!(obj instanceof FixedIntPair)) return false;
            FixedIntPair pair=(FixedIntPair) obj;
            return this.x==pair.x&&this.y==pair.y;
        }

        @Override
        public String toString() {
            return format(FixedIntPair.class.getSimpleName()+":(%d,%d)", x, y);
        }
    }
    final static private class FixedLongPair {
        final public long x, y;
        final static public FixedLongPair ZEROS=new FixedLongPair(0,0);
        FixedLongPair(long x, long y) {
            this.x = x;
            this.y = y;
        }
        public static double distance(FixedLongPair flp1,FixedLongPair flp2){
            double x = (double) flp1.x - flp2.x;
            double y = (double) flp1.y - flp2.y;
            return Math.sqrt(x*x+y*y);
        }

        @Override
        public int hashCode() {
            return (int)x+(int)y;
        }

        @Override
        public boolean equals(Object obj) {
            if(obj==null)return false;
            if(!(obj instanceof FixedLongPair)) return false;
            FixedLongPair pair=(FixedLongPair)obj;
            return this.x==pair.x&&this.y==pair.y;
        }

        @Override
        public String toString() {
            return format(FixedLongPair.class.getSimpleName()+":(%d,%d)", x, y);
        }
    }
    final static private class Binary{
        public static String toZeroPadding(int i){
            return format("%"+Integer.toBinaryString(-1).length()+"s",Integer.toBinaryString(i)).replace(' ','0');
        }
        public static String toZeroPadding(long i){
            return format("%"+Long.toBinaryString(-1).length()+"s",Long.toBinaryString(i)).replace(' ','0');
        }
    }

    final static private class Util {
        static long gcd(long a,long b){
            a= abs(a);
            b= abs(b);
            if(a<b){
                long tmp=a;
                a=b;
                b=tmp;
            }
            while(b!=0){
                long r=a%b;
                a=b;
                b=r;
            }
            return a;
        }
        static int gcd(int a,int b){
            a= abs(a);
            b= abs(b);
            if(a<b){
                int tmp=a;
                a=b;
                b=tmp;
            }
            while(b!=0){
                int r=a%b;
                a=b;
                b=r;
            }
            return a;
        }
        static long lcm(long a,long b){
            long gcd=gcd(a,b);
            long result=b/gcd;
            return a*result;
        }
        static boolean isValidCell(int i,int j,int h,int w){
            return i>=0&&i<h&&j>=0&&j<w;
        }
    }
}































































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