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 LuaJIT (2.0.4) (judge verdict: Accepted)

local n = io.read("*n", "*l")
local str = io.read()
local t = {}
for i = 1, n do
  t[i] = str:sub(i, i) == "o"
end
local found = false
for c = 1, 4 do
  local res = {}
  res[1] = c <= 2
  res[2] = c % 2 == 1
  for i = 3, n do
    if res[i - 1] then
      if t[i - 1] then
        res[i] = res[i - 2]
      else
        res[i] = not res[i - 2]
      end
    else
      if t[i - 1] then
        res[i] = not res[i - 2]
      else
        res[i] = res[i - 2]
      end
    end
  end
  local cand1 = false
  if res[n] then
    if t[n] then
      cand1 = res[n - 1]
    else
      cand1 = not res[n - 1]
    end
  else
    if t[n] then
      cand1 = not res[n - 1]
    else
      cand1 = res[n - 1]
    end
  end
  local cand2 = false
  if res[1] then
    if t[1] then cand2 = res[n] else cand2 = not res[n] end
  else
    if t[1] then cand2 = not res[n] else cand2 = res[n] end
  end
  if res[1] == cand1 and res[2] == cand2 then
    for k = 1, n do
      io.write(res[k] and "S" or "W")
    end
    io.write("\n")
    found = true
    break
  end
end
if not found then print(-1) end