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 C (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <limits.h>

typedef unsigned long long ULL;

enum{SHEEP, WOLF};



int ans(ULL N, char *s, int first, int second, int *animals) {
    //int *animals = malloc(sizeof(int) * N);
    memset(animals, 0, sizeof(int) * N);
    int result = 0;
    
    *animals = first;
    *(animals + 1) = second;

    for(ULL i = 1; i < N - 1; i++) {
        char ans = *(s + i);
        if(ans == 'o') {
            if(*(animals + i) == SHEEP) {
                *(animals + i + 1) = *(animals + i - 1);
            } else {
                *(animals + i + 1) = *(animals + i - 1) == SHEEP ? WOLF : SHEEP;
            }
        } else {
            if(*(animals + i) == SHEEP) {
                *(animals + i + 1) = *(animals + i - 1) == SHEEP ? WOLF : SHEEP;
            } else {
                *(animals + i + 1) = *(animals + i - 1);
            }
        }
    }
    
    //check first, last and last - 1
    if(*(animals + N - 1) == SHEEP) {
        if(strncmp(s+ N - 1, "o", 1) == 0) {
            result = *(animals + 0) == *(animals + N - 2);
        } else {
            result = *(animals + 0) != *(animals + N - 2);
        }
    } else {
        if(strncmp(s+ N - 1, "o", 1) == 0) {
            result = *(animals + 0) != *(animals + N - 2);
        } else {
            result = *(animals + 0) == *(animals + N - 2);
        }
    }
    if(result) {
        if(*(animals) == SHEEP) {
            if(strncmp(s, "o", 1) == 0) {
                result = *(animals + 1) == *(animals + N - 1);
            } else {
                result = *(animals + 1) != *(animals + N - 1);
            }
        } else {
            if(strncmp(s, "o", 1) == 0) {
                result = *(animals + 1) != *(animals + N - 1);
            } else {
                result = *(animals + 1) == *(animals + N - 1);
            }
        }
    }
    
    return result;
}

void menagerie(ULL N, char *s) {
    int *animals = malloc(sizeof(int) * (N+1));
    memset(animals, 0, sizeof(int) * (N+1));
    
    int result = ans(N, s, SHEEP, SHEEP, animals);
    if(!result) {
        result = ans(N, s, SHEEP, WOLF, animals);
    }
    if(!result) {
        result = ans(N, s, WOLF, WOLF, animals);
    }
    if(!result) {
        result = ans(N, s, WOLF, SHEEP, animals);
    }
    
    if(result) {
        for(ULL i = 0; i < N; i++) {
            printf("%s", *(animals + i) == SHEEP ? "S" : "W");
        }
    }else {
        printf("-1");
    }
    printf("\n");
    free(animals);
}


int main(int argc, const char * argv[]) {
    ULL N;
    char s[100000];
    scanf("%llu\n%s", &N, s);
    if(N < 3 || N > 100000) {
        return 1;
    }
    
    menagerie(N, s);
    printf("\n");
    return 0;
}