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 (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#define MAXNUM 100001

int main(void)
{
    int N = 0;
    int i;
    char judge[MAXNUM] = {'\0'};
    int animal[MAXNUM] = {-1};

    scanf("%d", &N);
    scanf("%s", judge);

    animal[0] = 0; //S:0, W:1
    animal[N - 1] = 1;
    for (i = 0; i < N; i++)
    {
        if (judge[i] == 'o')
        {
            if (i == 0)
            {
                if (animal[i])
                    animal[i + 1] = !animal[N - 1];
                else
                    animal[i + 1] = animal[N - 1];
            }
            else if (i == N-1)
            {
                if (animal[i])
                    animal[0] = !animal[N - 2];
                else
                    animal[0] = animal[N - 2];
            }
            else
            {
                if (animal[i])
                    animal[i + 1] = !animal[i - 1];
                else
                    animal[i + 1] = animal[i - 1];
            }
        }
        else
        {
            if (i == 0)
            {
                if (animal[i])
                    animal[i + 1] = animal[N - 1];
                else
                    animal[i + 1] = !animal[N - 1];
            }
            else if (i == N-1)
            {
                if (animal[i])
                    animal[0] = animal[N - 2];
                else
                    animal[0] = !animal[N - 2];
            }
            else
            {
                if (animal[i])
                    animal[i + 1] = animal[i - 1];
                else
                    animal[i + 1] = !animal[i - 1];
            }
        }
    }

    if (animal[0] == 0 && animal[N-1] == 1)
    {
        for (i = 0; i < N; i++)
        {
            if (animal[i])
                printf("W");
            else
                printf("S");
        }
        return 0;
    }

    animal[0] = 0; //S:0, W:1
    animal[N - 1] = 0;
    for (i = 0; i < N; i++)
    {
        if (judge[i] == 'o')
        {
            if (i == 0)
            {
                if (animal[i])
                    animal[i + 1] = !animal[N - 1];
                else
                    animal[i + 1] = animal[N - 1];
            }
            else if (i == N-1)
            {
                if (animal[i])
                    animal[0] = !animal[N - 2];
                else
                    animal[0] = animal[N - 2];
            }
            else
            {
                if (animal[i])
                    animal[i + 1] = !animal[i - 1];
                else
                    animal[i + 1] = animal[i - 1];
            }
        }
        else
        {
            if (i == 0)
            {
                if (animal[i])
                    animal[i + 1] = animal[N - 1];
                else
                    animal[i + 1] = !animal[N - 1];
            }
            else if (i == N-1)
            {
                if (animal[i])
                    animal[0] = animal[N - 2];
                else
                    animal[0] = !animal[N - 2];
            }
            else
            {
                if (animal[i])
                    animal[i + 1] = animal[i - 1];
                else
                    animal[i + 1] = !animal[i - 1];
            }
        }
    }

    if (animal[0] == 0 && animal[N-1] == 0)
    {
        for (i = 0; i < N; i++)
        {
            if (animal[i])
                printf("W");
            else
                printf("S");
        }
        return 0;
    }

    animal[0] = 1; //S:0, W:1
    animal[N - 1] = 0;
    for (i = 0; i < N; i++)
    {
        if (judge[i] == 'o')
        {
            if (i == 0)
            {
                if (animal[i])
                    animal[i + 1] = !animal[N - 1];
                else
                    animal[i + 1] = animal[N - 1];
            }
            else if (i == N-1)
            {
                if (animal[i])
                    animal[0] = !animal[N - 2];
                else
                    animal[0] = animal[N - 2];
            }
            else
            {
                if (animal[i])
                    animal[i + 1] = !animal[i - 1];
                else
                    animal[i + 1] = animal[i - 1];
            }
        }
        else
        {
            if (i == 0)
            {
                if (animal[i])
                    animal[i + 1] = animal[N - 1];
                else
                    animal[i + 1] = !animal[N - 1];
            }
            else if (i == N-1)
            {
                if (animal[i])
                    animal[0] = animal[N - 2];
                else
                    animal[0] = !animal[N - 2];
            }
            else
            {
                if (animal[i])
                    animal[i + 1] = animal[i - 1];
                else
                    animal[i + 1] = !animal[i - 1];
            }
        }
    }

    if (animal[0] == 1 && animal[N-1] == 0)
    {
        for (i = 0; i < N; i++)
        {
            if (animal[i])
                printf("W");
            else
                printf("S");
        }
        return 0;
    }

    animal[0] = 1; //S:0, W:1
    animal[N - 1] = 1;
    for (i = 0; i < N; i++)
    {
        if (judge[i] == 'o')
        {
            if (i == 0)
            {
                if (animal[i])
                    animal[i + 1] = !animal[N - 1];
                else
                    animal[i + 1] = animal[N - 1];
            }
            else if (i == N-1)
            {
                if (animal[i])
                    animal[0] = !animal[N - 2];
                else
                    animal[0] = animal[N - 2];
            }
            else
            {
                if (animal[i])
                    animal[i + 1] = !animal[i - 1];
                else
                    animal[i + 1] = animal[i - 1];
            }
        }
        else
        {
            if (i == 0)
            {
                if (animal[i])
                    animal[i + 1] = animal[N - 1];
                else
                    animal[i + 1] = !animal[N - 1];
            }
            else if (i == N-1)
            {
                if (animal[i])
                    animal[0] = animal[N - 2];
                else
                    animal[0] = !animal[N - 2];
            }
            else
            {
                if (animal[i])
                    animal[i + 1] = animal[i - 1];
                else
                    animal[i + 1] = !animal[i - 1];
            }
        }
    }

    if (animal[0] == 1 && animal[N-1] == 1)
    {
        for (i = 0; i < N; i++)
        {
            if (animal[i])
                printf("W");
            else
                printf("S");
        }
        return 0;
    }

    printf("-1");

    return 0;
}