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{ |rep| rep == "o"}

answer = Array.new(3){Array.new(n+1)}
makerep = Array.new(3){Array.new(n)}

if reply[0]
  answer[0][0],answer[0][1],answer[1][0],answer[2][1] = false,false,false,false
  answer[1][1],answer[2][0] = true,true
else
  answer[0][0],answer[0][1],answer[1][1] = false,false,false
  answer[1][0],answer[2][0],answer[2][1] = true,true,true
end

for i in 2..n do
  for j in 0..2 do
  answer[j][i] = (reply[i-1] ^ answer[j][i-1]) ? answer[j][i-2] : answer[j][i-2] ^ true
  end
end

for k in 0..n-1 do
  for l in 0..2 do
    makerep[l][k] = (answer[l][k-1] == answer[l][(k+1)%n]) ^ answer[l][k]
  end
end

if makerep[0] == reply
  ans = answer[0][0..n-1]
elsif makerep[1] == reply
  ans = answer[1][0..n-1]
elsif makerep[2] == reply
  ans = answer[2][0..n-1]
else
  ans = nil
end

puts ans ? ans.map{ |boolans| boolans ? "W" : "S"}.join : -1