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 = STDIN.gets.chomp.to_i
s = STDIN.gets.chomp.chars

def predict(s, init)
  (1...(s.size - 1)).each do |i|
    if s[i] == 'o'
      if init[i]
        init[i + 1] = init[i - 1]
      else
        init[i + 1] = !init[i - 1]
      end
    else
      if init[i]
        init[i + 1] = !init[i - 1]
      else
        init[i + 1] = init[i - 1]
      end
    end
  end
  init
end

def valid?(s, result)
  a = if s[0] == 'o'
    if result[0]
      result[1] == result[-1]
    else
      result[1] != result[-1]
    end
  else
    if result[0]
      result[1] != result[-1]
    else
      result[1] == result[-1]
    end
  end

  b = if s[-1] == 'o'
    if result[-1]
      result[0] == result[-2]
    else
      result[0] != result[-2]
    end
  else
    if result[-1]
      result[0] != result[-2]
    else
      result[0] == result[-2]
    end
  end
  a && b
end

def output(result)
  result.map{|r|
    if r
      "S"
    else
      "W"
    end
  }.join('')
end

init = [true, true]
result = predict(s, init)
if valid?(s, result)
  puts output(result)
  exit
end

init = [true, false]
result = predict(s, init)
if valid?(s, result)
  puts output(result)
  exit
end

init = [false, true]
result = predict(s, init)
if valid?(s, result)
  puts output(result)
  exit
end

init = [false, false]
result = predict(s, init)
if valid?(s, result)
  puts output(result)
  exit
end
puts -1