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)

var
	n,i:Longint;
	s:String;
	a:array[0..99999]of Boolean;
function f(x,y:Boolean):Boolean;
var j:Longint;flag:Boolean;
begin
	a[0]:=x;
	a[1]:=y;
	for j:=1 to n-2 do if(s[j+1]='x')xor a[j]then a[j+1]:=a[j-1]else a[j+1]:=not a[j-1];
	flag:=true;
	if(s[1]='x')xor a[0]then flag:=flag and(a[n-1]=a[1])else flag:=flag and(a[n-1]<>a[1]);
	if(s[n]='x')xor a[n-1]then flag:=flag and(a[n-2]=a[0])else flag:=flag and(a[n-2]<>a[0]);
	f:=flag;
end;
procedure print();
var j:Longint;
begin
	for j:=0 to n-1 do if a[j] then write('S')else write('W');
	writeln;
end;
begin
	readln(n);
	readln(s);
	if f(true,true)then print()else if f(true,false)then print()else if f(false,true)then print()else if f(false,false)then print()else writeln(-1);
end.