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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<iostream>
#include<string>
#include<vector>
#include<set>
#include<algorithm>
#include<queue>
#include<functional>
#include<numeric>
#include<sstream>
#include<math.h>
#include <iomanip>
#define ll long long
#define PLL pair<ll,ll>
#define VS vector<string>
#define VL vector<ll>
#define rep(i,a) for (ll i=0;i<a;i++)
#define nrep(i,n,a) for (ll i=n;i<a;i++)
#define mrep(i,a) for(ll i=a;i>=0;i--)
#define INF 1145141919810
#define VMIN(vec) *std::max_element(vec.begin(),vec.end())
#define VMIN(vec) *std::max_element(vec.begin(),vec.end())
#define VSUM(vec) std::accumulate(vec.begin(),vec.end(),0LL)
#define LTS(n) to_string(n)
#define STL(str) stoll(str);

using namespace std;

ll n;
string s;


//s_or_w:0->s  s_or_w:1->w
void fun(string str){
	ll next, prev,i;
	nrep(x, 1, n+1){
		i = x%n;
		next = (i + 1) % n;
		prev = (i == 0 ? n - 1 : i - 1);
		if (s[i]=='o' && str[i] == 'S' || s[i]=='x' && str[i]=='W') str += str[prev];
		else str += (str[prev] == 'S' ? 'W' : 'S');
	}//cout << str << endl;
	if (str[n] == str[0] && str[n+1]==str[1]){
		cout << str.substr(0, n) << endl;
		exit(0);
	}
}


int main() {
	cin >> n;
	cin >> s;
	fun("SS");
	fun("SW");
	fun("WS");
	fun("WW");
	cout << -1 << endl;
	return 0;
}