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)

n = gets.chomp.to_i
s = gets.chomp.split('')

def next_animal(last2_animal, last_animal, last_o_or_x)
  if last2_animal == 'S'
    if last_animal == 'S'
      if last_o_or_x == 'o'
        return 'S'
      else
        return 'W'
      end
    else
      if last_o_or_x == 'o'
        return 'W'
      else
        return 'S'
      end
    end
  else
    if last_animal == 'S'
      if last_o_or_x == 'o'
        return 'W'
      else
        return 'S'
      end
    else
      if last_o_or_x == 'o'
        return 'S'
      else
        return 'W'
      end
    end
  end
end

def check(ans, s, n)
  if next_animal(ans[n-2], ans[n-1], s[n-1]) == ans[0] && next_animal(ans[n-1], ans[0], s[0] == ans[1])
    puts ans.join('')
    exit
  end
end

['SS', 'SW', 'WS', 'WW'].each do |uu|
  ans = []
  fi, se = uu.split('')
  ans.push(fi)
  ans.push(se)
  2.upto(n-1) do |i|
    ans.push(next_animal(ans[i-2], ans[i-1], s[i-1]))
  end
  check(ans, s, n)
end
p -1