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: Wrong Answer)

#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <stdint.h> // int64_t

#define max(a,b) ((a) > (b) ? (a) : (b))
#define min(a,b) ((a) > (b) ? (b) : (a))

int get_int(void) {
  int num;
  scanf("%d", &num);
  return num;
}

int get_str(char *str, int size)
{
    char format[100];
    if (size == 0)
        return 0;
    snprintf(format, sizeof(format), "%%%ds", size);
    scanf(format, str);
    return 0;
}

#define NUM_MAX 100000

enum type {
    TYPE_WOLF,
    TYPE_SHEEP
};

enum reply {
    REPLY_X,
    REPLY_O,
};

static char type_table[2] = {
    [TYPE_WOLF] = 'W',
    [TYPE_SHEEP] = 'S'
};

static char reply_table[256] = {
    ['o'] = REPLY_O,
    ['x'] = REPLY_X
};

// right = [cur][reply][left]
static char next[2][2][2] = {
    // I'm wolf
    {
        // says 'x'
        {
            // When left is TYPE_WOLF
            TYPE_WOLF,
            // left is TYPE_SHEEP
            TYPE_SHEEP
        },
        // says 'o'
        {
            // When left is TYPE_WOLF
            TYPE_SHEEP,
            TYPE_WOLF,
        },
    },
    // I'm sheep
    {
        // says 'x'
        {
            TYPE_SHEEP,
            TYPE_WOLF,
        },
        // says 'o'
        {
            TYPE_WOLF,
            TYPE_SHEEP,
        },
    },
};

int main(void) {
    int num = get_int();
    static char str[NUM_MAX];
    get_str(str, num);

    int t, i;
    int ok = 0;
    static char types[NUM_MAX];
    for(t = 0; t < 4; t++) {
        memset(types, 0, NUM_MAX);
        // 0: wolf 1: sheep
        types[0] = t&1;
        types[1] = t&3;
        int flag = 1;
        for(i = 1; i <= num; i++) {
            int cur = i%num;
            int left = (i+num-1)%num;
            int right = (i+num+1)%num;
            int cur_type = types[cur];
            int reply = reply_table[str[cur]];
            int next_type = next[cur_type][reply][types[left]];
            if(i >= num-1) {
                if(next_type != types[right]) {
                    flag = 0;
                    break;
                }
            }
            types[right] = next_type;
        }
        if(flag) { ok=1; break; }
    }

    if(ok) {
        for(i = 0; i < num; i++) {
            putchar(type_table[types[i]]);
        }
    } else {
        printf("%d", -1);
    }
    putchar('\n');
    return 0;
}