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 Pascal (FPC 2.6.2) (judge verdict: Accepted)

program j01;
var s:ansistring;
    ans:array[0..100086]of longint;
    c:array[0..1]of char;
    flag:boolean;
    i,n:longint;

procedure check;
var i:longint;dd,dd2:longint;ch:longint;
begin
  dd:=ord(s[1]='o');
  if ((dd=1)and(ans[1]=0))or((dd=0)and(ans[1]=1)) then
    ch:=ans[2] else ch:=1-ans[2];
  for i:=2 to n-1 do
  begin
    dd:=ord(s[i]='o');
    if((dd=1)and(ans[i]=0))or((dd=0)and(ans[i]=1)) then
      ans[i+1]:=ans[i-1] else ans[i+1]:=1-ans[i-1];
  end;
  dd:=ord(s[n]='o');
  dd2:=ord(ans[n-1]=ans[1]);
  if((ans[n]=0)and(dd<>dd2))or((ans[n]=1)and(dd=dd2)) then exit; 
  if ch=ans[n] then
  begin
    for i:=1 to n do
      if ans[i]=0 then write('S') else write('W');
    halt;
  end;
end;

begin
  readln(n);readln(s);
  ans[1]:=0;ans[2]:=0;
  check;
  ans[1]:=0;ans[2]:=1;
  check;
  ans[1]:=1;ans[2]:=0;
  check;
  ans[1]:=1;ans[2]:=1;
  check;
  writeln(-1);
end.