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 <bits/stdc++.h>

using namespace std;

typedef long long int ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;

const int INF = 1000000000; //
const ll LINF = (ll) 4000000000000000000; //
const ll MOD = (ll) 1000000007; //
const double PI = 3.1415926535898; //
const int limit = 100010;

#define REP(i,m,n) for(int i=m;i<(int)(n);i++)
#define rep(i,n) REP(i,0,n)
#define rep2(i,n) REP(i,1,n+1)
#define rep3(i,n) REP(i,0,n+1)
#define REPLL(i,m,n) for(ll i=m;i<(ll)(n);i++)
#define repll(i,n) REPLL(i,0,n)
#define repll2(i,n) REPLL(i,1,n+1)
#define MP make_pair
#define YES(n) cout << ((n) ? "YES" : "NO") << endl
#define Yes(n) cout << ((n) ? "Yes" : "No") << endl
#define Possible(n) cout << ((n) ? "Possible" : "Impossible") << endl
#define NP(v) next_permutation(v.begin(),v.end())

//------------------------------------------------------
int n;

int mod(int a) {  //inlineの有無による実行時間のテスト
    return (a + n) % n;
}

int main() {
    string s;
    cin >> n >> s;

    rep(a, 2) {

        rep(b, 2) {
            bool sheep[n];
            sheep[0] = (a == 0);
            sheep[1] = (b == 0);

            REP(i, 1, n) {
                if ((s[mod(i)] == 'o') == sheep[mod(i)]) sheep[mod(i + 1)] = sheep[mod(i - 1)];
                else sheep[mod(i + 1)] = !sheep[mod(i - 1)];
            }

            bool can = true;

            rep(i, n) {
                if ((sheep[i] == (s[i] == 'o')) != (sheep[mod(i - 1)] == sheep[mod(i + 1)])) {
                    can = false;
                    break;
                }
            }

            if (can) {
                rep(i, n) cout << (sheep[i] ? 'S' : 'W');
                cout << endl;
                return 0;
            }

        }
    }

    cout << -1 << endl;

    return 0;
}