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)

//
//  main.c
//  Main
//
//  Created by xiangwei wang on 2017/02/20.
//  Copyright © 2017年 xiangwei wang. All rights reserved.
//

#include <stdio.h>

#define MAX 100000
#define SHEEP 1
#define WOLF 2

int check(int n, int ans[MAX], const char s[MAX]) {
    for(int i = 1; i < n; i++) {
        if(ans[i] == SHEEP) {
            if(*(s + i) == 'o') {
                if(ans[(i + 1)%n] != 0 && ans[(i + 1)%n] != ans[i - 1]) {
                    return 1;
                }
                ans[i + 1] = ans[i - 1];
            } else {
                if(ans[(i + 1)%n] != 0 && ans[(i + 1)%n] != (ans[i - 1] == SHEEP ? WOLF : SHEEP)) {
                    return 1;
                }
                ans[i + 1] = ans[i - 1] == SHEEP ? WOLF : SHEEP;
            }
        } else {
            if(*(s + i) == 'o') {
                if(ans[(i + 1)%n] != 0 && ans[(i + 1)%n] != (ans[i - 1] == SHEEP ? WOLF : SHEEP)) {
                    return 1;
                }
                ans[i + 1] = ans[i - 1] == SHEEP ? WOLF : SHEEP;
            } else {
                if(ans[(i + 1)%n] != 0 && ans[(i + 1)%n] != ans[i - 1]) {
                    return 1;
                }
                ans[i + 1] = ans[i - 1];
            }
        }
    }
    
    return 0;
}
int main(int argc, const char * argv[]) {
    int n = 0;
    char s[MAX];
    int ans[MAX + 1];
    scanf("%d", &n);
    scanf("%s", s);
    
    for(int i = 0; i < n; i++) {
        ans[i] = 0;
    }
    
    ans[0] = SHEEP;

    if(*(s) == 'o') {
        ans[1] = SHEEP;
        ans[n-1] = SHEEP;
    } else {
        ans[1] = WOLF;
        ans[n-1] = WOLF;
    }
    
    int result = check(n, ans, s);
    
    if(result == 1) {
        ans[0] = WOLF;
        if(*(s) == 'o') {
            ans[1] = WOLF;
            ans[n-1] = SHEEP;
            
            result = check(n, ans, s);
            if(result == 1) {
                ans[1] = SHEEP;
                ans[n-1] = WOLF;
                
                result = check(n, ans, s);
            }
            
        } else {
            ans[1] = WOLF;
            ans[n-1] = WOLF;
            result = check(n, ans, s);
            if(result == 1) {
                ans[1] = SHEEP;
                ans[n-1] = SHEEP;
                
                result = check(n, ans, s);
            }
            
        }
    }
    
    
    if(result == 1) {
        printf("-1");
    } else {
        for(int i = 0; i < n; i++) {
            printf("%s", ans[i] == 1 ? "S" : "W");
        }
    }
    printf("\n");
    return 0;
}