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 PHP (7.4.4) (judge verdict: Accepted)

<?php
  list($n) = explode(" ", trim(fgets(STDIN)));

  list($s) = explode(" ", trim(fgets(STDIN)));

  $PT = ['SS','WW','SW','WS'];
  for ($h=0; $h<count($PT); $h++) {
    $ans = [];
    $ans[0] = $PT[$h][0];
    $ans[1] = $PT[$h][1];
    // 3匹目～
    for ($i=2; $i<$n; $i++) {
      //o
      if($s[$i-1] == 'o'){  
        if($ans[$i-1] == 'S'){
          $ans[$i] = $ans[$i-2];
        }else{
          if($ans[$i-2] == 'S') {
            $ans[$i] = 'W';
          }else{
            $ans[$i] = 'S';
          }
        }
      }
      // x
      else{
        if($ans[$i-1] == 'S'){
          if($ans[$i-2] == 'S') {
            $ans[$i] = 'W';
          }else{
            $ans[$i] = 'S';
          }
        }else{
          $ans[$i] =  $ans[$i-2];
        }
      }      
    }
    
    $check1 = false;
    $check2 = false;
    if($s[0] == 'o'){
      if($ans[0] == 'S'){
        if($ans[1] == $ans[$n-1]){
          $check1 = true;
        }
      }else{
        if($ans[1] != $ans[$n-1]){
          $check1 = true;
        }
      }
    }else{
      if($ans[0] == 'W'){
        if($ans[1] == $ans[$n-1]){
          $check1 = true;
        }
      }else{
        if($ans[1] != $ans[$n-1]){
          $check1 = true;
        }
      }
    }

    if($s[$n-1] == 'o'){
      if($ans[$n-1] == 'S'){
        if($ans[$n-2] == $ans[0]){
          $check2 = true;
        }
      }else{
        if($ans[$n-2] != $ans[0]){
          $check2 = true;
        }
      }
    }else{
      if($ans[$n-1] == 'W'){
        if($ans[$n-2] == $ans[0]){
          $check2 = true;
        }
      }else{
        if($ans[$n-2] != $ans[0]){
          $check2 = true;
        }
      }
    }

    
    if($check1 && $check2){
      echo implode("", $ans);
      exit;
    }
  }
  echo "-1";