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 Ruby (2.3.3) (judge verdict: Wrong Answer)

N = gets.to_i
S = gets.chomp

WOLF = 0
SHEEP = 1

def check(list, idx)
  N.times do |j|
    i = (idx + j) % N
    left = i - 1
    right = (i + 1) % N

    if list[i] == SHEEP
      if S[i] == 'o'
        return [false, list] if list[left] == WOLF && list[right] == SHEEP
        return [false, list] if list[left] == SHEEP && list[right] == WOLF

        if list[left] == WOLF
          list[right] = WOLF
        else
          list[right] = SHEEP
        end
      else
        return [false, list] if list[left] == WOLF && list[right] == WOLF
        return [false, list] if list[left] == SHEEP && list[right] == SHEEP

        if list[left] == WOLF
          list[right] = SHEEP
        else
          list[right] = WOLF
        end
      end
    else
      if S[i] == 'o'
        return [false, list] if list[left] == WOLF && list[right] == WOLF
        return [false, list] if list[left] == SHEEP && list[right] == SHEEP

        if list[left] == WOLF
          list[right] = SHEEP
        else
          list[right] = WOLF
        end
      else
        return [false, list] if list[left] == WOLF && list[right] == SHEEP
        return [false, list] if list[left] == SHEEP && list[right] == WOLF

        if list[left] == WOLF
          list[right] = WOLF
        else
          list[right] = SHEEP
        end
      end
    end
  end

  [true, list]
end

# case 1
list = Array.new(N, -1)
idx = S.index('o')

if idx.nil?
  puts 'S' * N
  exit
end

left = idx - 1
right = (idx + 1) % N

o_patterns = [
  [SHEEP, SHEEP, SHEEP],
  [WOLF, SHEEP, WOLF],
  [WOLF, WOLF, SHEEP],
  [SHEEP, WOLF, WOLF],
]

o_patterns.each do |p1, p2, p3|
  list[left] = p1
  list[idx] = p2
  list[right] = p3
  res, ans = check(list, right)

  if res
    puts ans.map { |v| ['W', 'S'][v] }.join
    exit
  end
end

list = Array.new(N, -1)
idx = S.index('x')

if idx.nil?
  puts 'W' * N
  exit
end

left = idx - 1
right = (idx + 1) % N

x_patterns = [
  [SHEEP, SHEEP, WOLF],
  [WOLF, SHEEP, SHEEP],
  [WOLF, WOLF, WOLF],
  [SHEEP, WOLF, SHEEP],
]

x_patterns.each do |p1, p2, p3|
  list[left] = p1
  list[idx] = p2
  list[right] = p3
  res, ans = check(list, idx)

  if res
    puts ans.map { |v| ['W', 'S'][v] }.join
    exit
  end
end

puts -1