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 (5.6.30) (judge verdict: Wrong Answer)

<?php

  fscanf(STDIN, "%d" ,$n);
  fscanf(STDIN, "%s" ,$s);

  $result = array();

  //一匹目が羊
  //二匹目が羊
  $result[0] = "S";
  $result[1] = "S";
  $last = "";
  $s[0] == "o" ? $last = "S" : $last = "W";

  for($i = 1;$i < $n-1;$i++){
    if($s[$i] == "o"){
      if($result[$i] == "S"){
        $result[$i+1] = $result[$i-1];
      }else{
        $result[$i-1] == "S" ? $result[$i+1] = "W" : $result[$i+1] ="S";
      }
    }else{
      if($result[$i] == "W"){
        $result[$i+1] = $result[$i-1];
      }else{
        $result[$i-1] == "S" ? $result[$i+1] = "W" : $result[$i+1] ="S";
      }
    }
  }

  if($last == $result[$n-1]){
    if($last =="S"){
      if($s[$n-1] == "o" && $result[$n-2] == $result[0]){
        echo implode($result);
        return;
      }
      if($s[$n-1] == "x" && $result[$n-2] != $result[0]){
        echo implode($result);
        return;
      }
    }else{
      if($s[$n-1] == "o" && $result[$n-2] != $result[0]){
        echo implode($result);
        return;
      }
      if($s[$n-1] == "x" && $result[$n-2] == $result[0]){
        echo implode($result);
        return;
      }
    }
  }


    //一匹目が羊
    //二匹目が狼
    $result[0] = "S";
    $result[1] = "W";
    $last = "";
    $s[0] == "o" ? $last = "W" : $last = "S";

    for($i = 1;$i < $n-1;$i++){
      if($s[$i] == "o"){
        if($result[$i] == "S"){
          $result[$i+1] = $result[$i-1];
        }else{
          $result[$i-1] == "S" ? $result[$i+1] = "W" : $result[$i+1] ="S";
        }
      }else{
        if($result[$i] == "W"){
          $result[$i+1] = $result[$i-1];
        }else{
          $result[$i-1] == "S" ? $result[$i+1] = "W" : $result[$i+1] ="S";
        }
      }
    }

    if($last == $result[$n-1]){
      if($last =="S"){
        if($s[$n-1] == "o" && $result[$n-2] == $result[0]){
          echo implode($result);
          return;
        }
        if($s[$n-1] == "x" && $result[$n-2] != $result[0]){
          echo implode($result);
          return;
        }
      }else{
        if($s[$n-1] == "o" && $result[$n-2] != $result[0]){
          echo implode($result);
          return;
        }
        if($s[$n-1] == "x" && $result[$n-2] == $result[0]){
          echo implode($result);
          return;
        }
      }
    }

    //一匹目が狼
    //二匹目が羊
    $result[0] = "W";
    $result[1] = "S";
    $last = "";
    $s[0] == "o" ? $last = "W" : $last = "S";

    for($i = 1;$i < $n-1;$i++){
      if($s[$i] == "o"){
        if($result[$i] == "S"){
          $result[$i+1] = $result[$i-1];
        }else{
          $result[$i-1] == "S" ? $result[$i+1] = "W" : $result[$i+1] ="S";
        }
      }else{
        if($result[$i] == "W"){
          $result[$i+1] = $result[$i-1];
        }else{
          $result[$i-1] == "S" ? $result[$i+1] = "W" : $result[$i+1] ="S";
        }
      }
    }

    if($last == $result[$n-1]){
      if($last =="S"){
        if($s[$n-1] == "o" && $result[$n-2] == $result[0]){
          echo implode($result);
          return;
        }
        if($s[$n-1] == "x" && $result[$n-2] != $result[0]){
          echo implode($result);
          return;
        }
      }else{
        if($s[$n-1] == "o" && $result[$n-2] != $result[0]){
          echo implode($result);
          return;
        }
        if($s[$n-1] == "x" && $result[$n-2] == $result[0]){
          echo implode($result);
          return;
        }
      }
    }

    //一匹目が狼
    //二匹目が狼
    $result[0] = "W";
    $result[1] = "W";
    $last = "";
    $s[0] == "o" ? $last = "S" : $last = "W";

    for($i = 1;$i < $n-1;$i++){
      if($s[$i] == "o"){
        if($result[$i] == "S"){
          $result[$i+1] = $result[i-1];
        }else{
          $result[$i-1] == "S" ? $result[$i+1] = "W" : $result[$i+1] ="S";
        }
      }else{
        if($result[$i] == "W"){
          $result[$i+1] = $result[i-1];
        }else{
          $result[$i-1] == "S" ? $result[$i+1] = "W" : $result[$i+1] ="S";
        }
      }
    }

    if($last == $result[$n-1]){
      if($last =="S"){
        if($s[$n-1] == "o" && $result[$n-2] == $result[0]){
          echo implode($result);
          return;
        }
        if($s[$n-1] == "x" && $result[$n-2] != $result[0]){
          echo implode($result);
          return;
        }
      }else{
        if($s[$n-1] == "o" && $result[$n-2] != $result[0]){
          echo implode($result);
          return;
        }
        if($s[$n-1] == "x" && $result[$n-2] == $result[0]){
          echo implode($result);
          return;
        }
      }
    }

    echo -1;