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: Accepted)

n = gets.to_i
s = gets.strip

patterns = []

poss = if s[0] == 'o'
  [
    ['S','S','S'],
    ['S','W','W'],
    ['W','S','W'],
    ['W','W','S'],
  ]
else
  [
    ['S','S','W'],
    ['S','W','S'],
    ['W','S','S'],
    ['W','W','W'],
  ]
end

poss.each do |first, second, last|
  a = Array.new(n)
  a[0] = first
  a[1] = second
  a[-1] = last
  patterns << a    
end


patterns.each do |ar|
  impossible = false
  1.upto(n-1) do |i|
    if s[i] == 'o' && ar[i] == 'S' && ar[i-1] == 'S'
      cand = 'S'
    elsif s[i] == 'o' && ar[i] == 'S' && ar[i-1] == 'W'
      cand = 'W'
    elsif s[i] == 'o' && ar[i] == 'W' && ar[i-1] == 'S'
      cand = 'W'
    elsif s[i] == 'o' && ar[i] == 'W' && ar[i-1] == 'W'
      cand = 'S'
    elsif s[i] == 'x' && ar[i] == 'S' && ar[i-1] == 'S'
      cand = 'W'
    elsif s[i] == 'x' && ar[i] == 'S' && ar[i-1] == 'W'
      cand = 'S'
    elsif s[i] == 'x' && ar[i] == 'W' && ar[i-1] == 'S'
      cand = 'S'
    elsif s[i] == 'x' && ar[i] == 'W' && ar[i-1] == 'W'
      cand = 'W'
    end
    
    if (ar[i+1] && ar[i+1] != cand) || (i == n-1 && ar[0] != cand)
      impossible = true 
      break
    elsif i+1 < n
      ar[i+1] = cand
    end
  end
  next if impossible
  puts ar.join('')
  exit 0
end

puts -1