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)

def solve(votes):
    for start in [(1, 1), (1, 0), (0, 1), (0, 0)]:
        a = animals(start, votes)
        if a[:2] == a[-2:]:
            return a


def animals(start, votes):
    rv = [None] * len(votes)
    rv[:2] = start
    for i in range(1, len(votes) - 1):
        rv[i + 1] = rv[i - 1] ^ rv[i] ^ votes[i]
    return tuple(rv)


def parse(s):
    return tuple(int(v == "o") for v in s + s[:2])


def display(s):
    if not s:
        return "-1"
    return "".join("S" if v else "W" for v in s[:-2])


if __name__ == "__main__":
    import sys
    _n = sys.stdin.readline()
    votes = sys.stdin.readline().strip()
    votes = parse(votes)
    sol = solve(votes)
    print(display(sol))


def test_parse():
    assert parse("ooxoox") == (1, 1, 0, 1, 1, 0, 1, 1)


def test_display():
    assert display((1, 1, 0, 0, 7, 7)) == "SSWW"


def test_animals():
    p = object()  # sentinel or poison
    assert animals((1, 1), (p, 1, p)) == (1, 1, 1)
    assert animals((1, 1), (p, 0, p)) == (1, 1, 0)
    assert animals((0, 1), (p, 1, p)) == (0, 1, 0)
    assert animals((1, 0), (p, 1, p)) == (1, 0, 0)


def test_animals_lex():
    assert animals((1, 1), parse("ooo")) == (1, 1, 1, 1, 1)
    assert animals((1, 1), parse("xxx")) == (1, 1, 0, 1, 1)


def test_solve_atcoder():
    assert display(solve(parse("oox"))) == "-1"
    assert display(solve(parse("ooxoox"))) == "SSSWWS"
    assert display(solve(parse("oxooxoxoox"))) == "SSWWSSSWWS"