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=[[true,true],[true,false],[false,true],[false,false]]
n=gets.to_i
s=gets.chomp
1.upto(n-2) do |i|
  4.times do |j|
    if s[i]==?o
      if a[j][i]==true
        a[j]<< a[j][i-1]
      else
        a[j]<< !a[j][i-1]
      end
    else
      if a[j][i]==true
        a[j]<< !a[j][i-1]
      else
        a[j]<< a[j][i-1]
      end
    end
  end
end
u=[]
4.times do |j|
  g=a[j]
  if (g[-1]&&((s[-1]==?o&&(g[-2]==g[0])) || (s[-1]==?x&&(g[-2]!=g[0]))))||(!g[-1]&&((s[-1]==?x&&(g[-2]==g[0])) || (s[-1]==?o&&(g[-2]!=g[0]))))
    if (g[0]&&((s[0]==?o&&(g[-1]==g[1])) || (s[0]==?x&&(g[-1]!=g[1]))))||(!g[0]&&((s[0]==?x&&(g[-1]==g[1])) || (s[0]==?o&&(g[-1]!=g[1]))))
      u=g
      break
    end
  end
end

puts u==[] ? -1:u.map{|i|i ? ?S:?W}.*("")