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: Accepted)

#!/usr/bin/env python3
import sys

def convert(ss):
    if ss == 0:
        return "S"
    else:
        return "W"


def solve(N: int, s: str):
    animals = [0]*N
    ## 0 がひつじ 1が狼を表す
    init = [(0,1),(1,0),(0,0),(1,1)]

    for first,second in init:
        animals[0] = first
        animals[1] = second

        for j in range(1,N):
            ## 最後にたどり着いたとき
            if j == N-1:
                if animals[j] == 0:
                    if s[j] == "o":
                        if animals[j-1] != animals[0]:
                            break
                    else:
                       if animals[j-1] == animals[0]:
                            break
                elif animals[j] == 1:
                    if s[j] == "o":
                        if animals[j-1] == animals[0]:
                            break
                    else:
                       if animals[j-1] != animals[0]:
                            break

                if animals[0] == 0:
                    if s[0] == "o":
                        if animals[N-1] != animals[1]:
                            break
                    else:
                       if animals[N-1] == animals[1]:
                            break
                elif animals[0] == 1:
                    if s[0] == "o":
                        if animals[N-1] == animals[1]:
                            break
                    else:
                       if animals[N-1] != animals[1]:
                            break
                
                print(''.join(list(map(convert,animals))))
                return

            if animals[j] == 0:
                if s[j] == "o":
                    animals[j+1] = animals[j-1]
                else:
                    animals[j+1] = 1^animals[j-1]
            elif animals[j] == 1:
                if s[j] == "o":
                    animals[j+1] = 1^animals[j-1]
                else:
                    animals[j+1] = animals[j-1]    

    print(-1)
    return


def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    s = next(tokens)  # type: str
    solve(N, s)

if __name__ == '__main__':
    main()