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 Rust (1.15.1) (judge verdict: Accepted)

macro_rules! get {
    ($t:ty) => {
        {
            let mut line: String = String::new();
            std::io::stdin().read_line(&mut line).unwrap();
            line.trim().parse::<$t>().unwrap()
        }
    };
    ($($t:ty),*) => {
        {
            let mut line: String = String::new();
            std::io::stdin().read_line(&mut line).unwrap();
            let mut iter = line.split_whitespace();
            (
                $(iter.next().unwrap().parse::<$t>().unwrap(),)*
            )
        }
    };
    ($t:ty; $n:expr) => {
        (0..$n).map(|_|
            get!($t)
        ).collect::<Vec<_>>()
    };
    ($($t:ty),*; $n:expr) => {
        (0..$n).map(|_|
            get!($($t),*)
        ).collect::<Vec<_>>()
    };
}

fn solve(n: usize, s: &Vec<char>, mut r: Vec<char>) -> Option<String> {
    for i in 1..n-1 {
        let a = r[i];
        let b = r[i-1];
        if (a == 'S' && s[i] == 'o') || (a == 'W' && s[i] == 'x') {
            r.push(b);
        } else {
            r.push(if b == 'S' { 'W' } else { 'S' });
        }
    }
    let mut a = false;
    let mut b = false;
    if  (r[0] == 'S' && s[0] == 'o' && r[1] == r[n-1]) ||
        (r[0] == 'S' && s[0] == 'x' && r[1] != r[n-1]) ||
        (r[0] == 'W' && s[0] == 'o' && r[1] != r[n-1]) ||
        (r[0] == 'W' && s[0] == 'x' && r[1] == r[n-1]) { a = true; };
    if  (r[n-1] == 'S' && s[n-1] == 'o' && r[n-2] == r[0]) ||
        (r[n-1] == 'S' && s[n-1] == 'x' && r[n-2] != r[0]) ||
        (r[n-1] == 'W' && s[n-1] == 'o' && r[n-2] != r[0]) ||
        (r[n-1] == 'W' && s[n-1] == 'x' && r[n-2] == r[0]) { b = true; };
    
    if a && b {
        Some(r.into_iter().collect::<String>())
    } else {
        None
    }
}

fn main() {
    let n = get!(usize);
    let s = get!(String).chars().collect::<Vec<_>>();

    if let Some(r) = solve(n, &s, vec!['S', 'S']) { println!("{}", r); return; };
    if let Some(r) = solve(n, &s, vec!['S', 'W']) { println!("{}", r); return; };
    if let Some(r) = solve(n, &s, vec!['W', 'S']) { println!("{}", r); return; };
    if let Some(r) = solve(n, &s, vec!['W', 'W']) { println!("{}", r); return; };
    println!("-1");
}