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)

#[allow(unused_macros)]
macro_rules! scan {
    () => {
        {
            let mut line: String = String::new();
            std::io::stdin().read_line(&mut line).unwrap();
            line.trim().to_string()
        }
    };
    (;;) => {
        {
            let mut line: String = String::new();
            std::io::stdin().read_line(&mut line).unwrap();
            line.trim().split_whitespace().map(|s| s.to_string()).collect::<Vec<String>>()
        }
    };
    (;;$n:expr) => {
        {
            (0..$n).map(|_| scan!()).collect::<Vec<_>>()
        }
    };
    ($t:ty) => {
        {
            let mut line: String = String::new();
            std::io::stdin().read_line(&mut line).unwrap();
            line.trim().parse::<$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(),)*
            )
        }
    };
    ($t:ty;;) => {
        {
            let mut line: String = String::new();
            std::io::stdin().read_line(&mut line).unwrap();
            line.split_whitespace()
                .map(|t| t.parse::<$t>().unwrap())
                .collect::<Vec<_>>()
        }
    };
    ($t:ty;;$n:expr) => {
        (0..$n).map(|_| scan!($t;;)).collect::<Vec<_>>()
    };
    ($t:ty; $n:expr) => {
        (0..$n).map(|_|
                    scan!($t)
        ).collect::<Vec<_>>()
    };
    ($($t:ty),*; $n:expr) => {
        (0..$n).map(|_|
                    scan!($($t),*)
        ).collect::<Vec<_>>()
    };
}

fn check(s: &str, pat: &mut [Option<char>]) -> bool {
    let n = s.len();
    for (i, c) in s.chars().enumerate() {
        if let Some(a) = pat[i] {
            if let Some(next) = pat[(i + 1) % n] {
                if let Some(pred) = pat[(i + n - 1) % n] {
                    if a == 'S' && c == 'o' {
                        if next != pred {
                            return false;
                        }
                    } else if a == 'S' && c == 'x' {
                        if next == pred {
                            return false;
                        }
                    } else if a == 'W' && c == 'o' {
                        if next == pred {
                            return false;
                        }
                    } else {
                        if next != pred {
                            return false;
                        }
                    }
                } else {
                    pat[(i + n - 1) % n] = if a == 'S' && c == 'o' || a == 'W' && c == 'x' {
                        Some(next)
                    } else {
                        Some(if next == 'S' { 'W' } else { 'S' })
                    }
                }
            } else {
                if let Some(pred) = pat[(i + n - 1) % n] {
                    pat[(i + 1) % n] = if a == 'S' && c == 'o' || a == 'W' && c == 'x' {
                        Some(pred)
                    } else {
                        Some(if pred == 'S' { 'W' } else { 'S' })
                    }
                }
            }
        }
    }
    true
}

fn print(vs: &[Option<char>]) {
    for &v in vs {
        if let Some(c) = v {
            print!("{}", c)
        }
    }
    println!()
}

fn main() {
    let n = scan!(usize);
    let s = scan!();

    let mut vs0 = vec![None; n];
    vs0[0] = Some('S');
    vs0[1] = Some('S');
    if check(&s, &mut vs0) {
        print(&vs0);
        return;
    }

    let mut vs0 = vec![None; n];
    vs0[0] = Some('S');
    vs0[1] = Some('W');
    if check(&s, &mut vs0) {
        print(&vs0);
        return;
    }

    let mut vs0 = vec![None; n];
    vs0[0] = Some('W');
    vs0[1] = Some('S');
    if check(&s, &mut vs0) {
        print(&vs0);
        return;
    }

    let mut vs0 = vec![None; n];
    vs0[0] = Some('W');
    vs0[1] = Some('W');
    if check(&s, &mut vs0) {
        print(&vs0);
        return;
    }
    println!("-1");
}