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

class Problem
  def initialize
    @array = []
  end
  
  def first(char1, char2)
    @array.clear()
    @array.push(char1)
    @array.push(char2)
  end
  
  def reverse(char)
    if char == "W"
      return "S"
    elsif char == "S"
      return "W"
    end
  end
  
  def maru(i)
    if @array[i] == "S"
      @array.push(@array[i-1])
    elsif @array[i] == "W"
      @array.push(reverse(@array[i-1]))
    end
  end
  
  def batsu(i)
    if @array[i] == "S"
      @array.push(reverse(@array[i-1]))
    elsif @array[i] == "W"
      @array.push(@array[i-1])
    end
  end
  
  def input(str)
    for i in 1..$n-1
      if str[i] == "o" 
        maru(i)
      elsif str[i] == "x"
        batsu(i)
      end
    end
  end
  
  def checkFirst()
      if @array.first == "S"
        if $str[0] == "o"
          if @array[1] == @array.last
            return true
          end
        else
          if @array[1] != @array.last
            return true
          end
        end
      else
        if $str[0] == "o"
          if @array[1] != @array.last
            return true
          end
        else
          if @array[1] == @array.last
            return true
          end
        end
      end        

      return false
  end
  
  def ans
    if @array.first == @array.last
      @array.pop()
      if checkFirst == true
        @array.length.times{|i|
          print @array[i]
        }
        return true
      end
    end
    
    return false
  end
end


problem = Problem.new()
$str = gets
4.times{|i|
    if i == 0
     problem.first("S", "S")
    elsif i == 1
     problem.first("S", "W")
    elsif i == 2
     problem.first("W", "S")
    elsif i == 3
     problem.first("W", "W") 
    end
    
    problem.input($str)
    if problem.ans() == true
      break
    end
    
    if i == 3
      print "-1"
    end
}