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 Python (3.4.3) (judge verdict: Accepted)

def main():
  N = int(input())
  s = input()
  L = [["S","S"],["S","W"],["W","W"],["W","S"]]
  for i in range(1,N):
    for j in range(4):
      if s[i] == "o":
        if L[j][-1] == "S":
          L[j].append(L[j][-2])
        else:
          if L[j][-2] == "S":
            L[j].append("W")
          else:
            L[j].append("S")
      else:
        if L[j][-1] == "S":
          if L[j][-2] == "S":
            L[j].append("W")
          else:
            L[j].append("S")
        else:
          L[j].append(L[j][-2])
  for i in range(4):
    flg = False
    if L[i][0] != L[i][-1]:
      continue
    if s[0] == "o":
      if L[i][-1] == "S" and L[i][1] == L[i][-2]:
        flg = True
      elif L[i][-1] == "W" and L[i][1] != L[i][-2]:
        flg = True
    else:
      if L[i][-1] == "W" and L[i][1] == L[i][-2]:
        flg = True
      elif L[i][-1] == "S" and L[i][1] != L[i][-2]:
        flg = True
    if flg:
      print(*L[i][:-1],sep="")
      exit()
  print(-1)
main()