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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php
  declare(strict_types=1);

  fscanf(STDIN, "%i", $n);
  $s = trim(fgets(STDIN));

  $correct = FALSE;
  for ($assumption = 3; !$correct && $assumption >= 0; --$assumption)
  {
      unset($t);
      $t[0] = (bool)($assumption & 1); // TRUE means sheep
      $t[1] = (bool)(($assumption >> 1) & 1);
      for ($i = 1; $i < $n; ++$i)
      {
          if ($t[$i])
          {
              if ($s[$i] === 'o')
              {
                  $t[$i + 1] = $t[$i - 1];
              }
              else
              {
                  $t[$i + 1] = !$t[$i - 1];
              }
          }
          else
          {
              if ($s[$i] === 'o')
              {
                  $t[$i + 1] = !$t[$i - 1];
              }
              else
              {
                  $t[$i + 1] = $t[$i - 1];
              }
          }
      }
      
      if ($t[0])
      {
          if ($s[0] === 'o')
          {
              $correct = $t[1] === $t[$n - 1];
          }
          else
          {
              $correct = $t[1] !== $t[$n - 1];
          }
      }
      else
      {
          if ($s[0] === 'o')
          {
              $correct = $t[1] !== $t[$n - 1];
          }
          else
          {
              $correct = $t[1] === $t[$n - 1];
          }
      }
      $correct = $correct && $t[0] === $t[$n];
  }

  if ($correct)
  {
      for ($i = 0; $i < $n; ++$i)
      {
          $t[$i] = $t[$i] ? 'S' : 'W';
      }

      echo substr(join($t), 0, $n),PHP_EOL;
  }
  else
  {
      echo -1,PHP_EOL;
  }