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)

a = gets.chomp.to_i
b = []
b = gets.chomp.split("")
c = ["S", "W"]
for i in 0..1
for k in 0..1
  d = Array.new
  #puts d.join("")
  d[0] = c[i]
  d.push(c[k])
  for j in 1..a-2
    if d[j-1] == "S" && d[j] == "S"
      if b[j] == "o"
        d.push("S")
      else
        d.push("W")
      end
    elsif d[j-1] == "S" && d[j] == "W"
      if b[j] == "o"
        d.push("W")
      else
        d.push("S")
      end
    elsif d[j-1] == "W" && d[j] =="S"
      if b[j] == "o"
        d.push("W")
      else
        d.push("S")
      end
    elsif d[j-1] == "W" && d[j] =="W"
      if b[j] == "o"
        d.push("S")
      else
        d.push("W")
      end
    end
  end
  #puts d.join("")
    if d[-2] == d[0]
      if d[-1] == "S" && b[-1] == "o"
        if d[-1] == d[1]
          if d[0] =="S" && b[0] =="o"
            puts d.join("")
            exit
          elsif d[0] == "W" && b[0] == "x"
            puts d.join("")
            exit
          end
        elsif d[-1] != d[1]
          if d[0] == "S" && b[0] == "x"
            puts d.join("")
            exit
          elsif d[0] == "W" && b[0] == "o"
            puts d.join("")
            exit
          end
        end
      elsif d[-1] == "W" && b[-1] == "x"
        if d[-1] == d[1]
          if d[0] =="S" && b[0] =="o"
            puts d.join("")
            exit
          elsif d[0] == "W" && b[0] == "x"
            puts d.join("")
            exit
          end
        elsif d[-1] != d[1]
          if d[0] == "S" && b[0] == "x"
            puts d.join("")
            exit
          elsif d[0] == "W" && b[0] == "o"
            puts d.join("")
            exit
          end
        end
      end
    elsif d[-2] != d[0]
      if d[-1] == "S" && b[-1] == "x"
        if d[-1] == d[1]
          if d[0] =="S" && b[0] =="o"
            puts d.join("")
            exit
          elsif d[0] == "W" && b[0] == "x"
            puts d.join("")
            exit
          end
        elsif d[-1] != d[1]
          if d[0] == "S" && b[0] == "x"
            puts d.join("")
            exit
          elsif d[0] == "W" && b[0] == "o"
            puts d.join("")
            exit
          end
        end
      elsif d[-1] == "W" && b[-1] == "o"
        if d[-1] == d[1]
          if d[0] =="S" && b[0] =="o"
            puts d.join("")
            exit
          elsif d[0] == "W" && b[0] == "x"
            puts d.join("")
            exit
          end
        elsif d[-1] != d[1]
          if d[0] == "S" && b[0] == "x"
            puts d.join("")
            exit
          elsif d[0] == "W" && b[0] == "o"
            puts d.join("")
            exit
          end
        end
      end
    end
end
end
puts "-1"