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 Python (3.4.3) (judge verdict: Wrong Answer)

N = int(input())
s = input()

s_flag = [1 if s[i]=='o' else -1 for i in range(N)]

def find_pattern(init_t_flag):
    for i in range(2, len(s_flag)):
        init_t_flag.append(init_t_flag[i-2]*init_t_flag[i-1]*s_flag[i-1])
    last_t_flag = init_t_flag[0] * init_t_flag[1] * s_flag[0]
    if init_t_flag[-1] == last_t_flag:
        return init_t_flag
    else:
        return -1

def output_result():
    res_SS = find_pattern([1,1])
    if res_SS != -1:
        res = ['S' if res_SS[i]==1 else 'W' for i in range(N)]
        return("".join(res))

    res_SW = find_pattern([1, -1])
    if res_SW != -1:
        res = ['S' if res_SW[i]==1 else 'W' for i in range(N)]
        return("".join(res))

    res_WS = find_pattern([-1,1])
    if res_WS != -1:
        res = ['S' if res_WS[i]==1 else 'W' for i in range(N)]
        return("".join(res))

    res_WW = find_pattern([-1, -1])
    if res_WW != -1:
        res = ['S' if res_WW[i]==1 else 'W' for i in range(N)]
        return("".join(res))

    return("-1")

print(output_result())