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
reply = gets.chomp.split("").map{ |n| n == "o"}

answer1 = Array.new(n+1)
answer2 = Array.new(n+1)
answer3 = Array.new(n+1)
answer4 = Array.new(n+1)

if reply[0]
  answer1[0],answer1[1],answer2[0],answer3[1] = false,false,false,false
  answer2[1],answer3[0],answer4[0],answer4[1] = true,true,true,true
else
  answer1[0],answer1[1],answer2[1],answer4[0] = false,false,false,false
  answer2[0],answer3[0],answer3[1],answer4[1] = true,true,true,true
end

for i in 2..n do
  answer1[i] = (reply[i-1] ^ answer1[i-1]) ? answer1[i-2] : answer1[i-2] ^ true
  answer2[i] = (reply[i-1] ^ answer2[i-1]) ? answer2[i-2] : answer2[i-2] ^ true
  answer3[i] = (reply[i-1] ^ answer3[i-1]) ? answer3[i-2] : answer3[i-2] ^ true
  answer4[i] = (reply[i-1] ^ answer4[i-1]) ? answer4[i-2] : answer4[i-2] ^ true
end

if answer1[n] == answer1[0]
  answer = answer1[0..n-1]
elsif answer2[n] == answer2[0]
  answer = answer2[0..n-1]
elsif answer3[n] == answer3[0]
  answer = answer3[0..n-1]
elsif answer4[n] == answer4[0]
  answer = answer4[0..n-1]
else
  answer = nil
end

puts answer ? answer.map{ |n| n ? "W" : "S"}.join : -1