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)


def choose_animal(last_animal:, last_say:, two_last_animal:)
  if last_animal == 0
    if last_say == 0
      two_last_animal
    else
      (two_last_animal + 1) % 2
    end
  else
    if last_say == 0
      (two_last_animal + 1) % 2
    else
      two_last_animal
    end
  end
end

N = gets.to_i
string = gets.chomp.split("")
arr = string.map do |i|
  if i == 'o'
    0
  else
    1
  end
end

# 0:羊　1:狼
flag = false
[[0, 0], [0, 1], [1, 0],[1, 1]].each do |first, second|
  tmp = Array.new(N)
  tmp[0] = first
  tmp[1] = second

  (2..(N-1)).each do |i|
    tmp[i] = choose_animal(last_animal: tmp[i-1], last_say: arr[i-1], two_last_animal: tmp[i-2])
  end
  last_animal = choose_animal(last_animal: tmp[N-1], last_say: arr[N-1], two_last_animal: tmp[N-2])
  if last_animal == first
    flag = true
    result = tmp.map do |j|
      if j == 0
        'S'
      else
        'W'
      end
    end.join
    puts result
    break
  end
end

if !flag
  puts -1
end