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 JavaScript (Node.js 12.16.1) (judge verdict: Accepted)

function Main(input) {
  input=input.split("\n");
  var S=input[1];
  var array;
  var flg=false;
  ["S","W"].forEach(a=>{
    ["S","W"].forEach(b=>{
      array=new Array(S.length);
      array[0]=a;
      array[1]=b;
      for(var i=2;i<S.length;i++){
        if(array[i-1]==="W"^S[i-1]==="o"){
          array[i]=array[i-2];
        }else{
          if(array[i-2]==="W"){
            array[i]="S";
          }else{
            array[i]="W";
          }
        }
      }
      //console.log(array.join(""));
      //console.log(array[0]==="S");
      //console.log(S[0]==="o");
      //console.log(array[array.length-1]===array[1]);
      //console.log(array[0]==="S"^S[0]==="o"^array[array.length-1]===array[1]);
      //console.log(array[array.length-1]==="S"^S[array.length-1]==="o"^array[array.length-2]===array[0]);
      if(!flg&&(array[0]==="S"^S[0]==="o"^array[array.length-1]===array[1])&&(array[array.length-1]==="S"^S[array.length-1]==="o"^array[array.length-2]===array[0])){
         console.log(array.join(""));
         flg=true;
      }
    });
  });
  if(!flg)console.log(-1);
}

//*この行以降は編集しないでください（標準入出力から一度に読み込み、Mainを呼び出します）
Main(require("fs").readFileSync("/dev/stdin", "utf8"));