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: Time Limit Exceeded)

#[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(vs: &str, a: &mut Vec<&str>) -> bool {
    for i in 1..vs.len() - 1 {
        let b = a[i - 1];
        a[i + 1] = if a[i] == "S" {
            if vs.chars().nth(i).unwrap() == 'o' {
                b
            } else {
                if b == "S" {
                    "W"
                } else {
                    "S"
                }
            }
        } else {
            if vs.chars().nth(i).unwrap() == 'o' {
                if b == "S" {
                    "W"
                } else {
                    "S"
                }
            } else {
                b
            }
        }
    }

    for i in 0..a.len() {
        let ret = if a[i] == "S" {
            if vs.chars().nth(i).unwrap() == 'o' {
                a[(i + a.len() - 1) % a.len()] == a[(i + 1) % a.len()]
            } else {
                a[(i + a.len() - 1) % a.len()] != a[(i + 1) % a.len()]
            }
        } else {
            if vs.chars().nth(i).unwrap() == 'o' {
                a[(i + a.len() - 1) % a.len()] != a[(i + 1) % a.len()]
            } else {
                a[(i + a.len() - 1) % a.len()] == a[(i + 1) % a.len()]
            }
        };

        if !ret {
            return false;
        }
    }
    true
}

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

    let mut a = vec![""; n];

    a[0] = "S";
    a[1] = "S";
    if check(&vs, &mut a) {
        println!("{}", a.join(""));
        return;
    }

    a[0] = "S";
    a[1] = "W";
    if check(&vs, &mut a) {
        println!("{}", a.join(""));
        return;
    }

    a[0] = "W";
    a[1] = "S";
    if check(&vs, &mut a) {
        println!("{}", a.join(""));
        return;
    }

    a[0] = "W";
    a[1] = "W";
    if check(&vs, &mut a) {
        println!("{}", a.join(""));
        return;
    }
    println!("-1")
}