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: Wrong Answer)

fn main() {
    let (r, w) = (std::io::stdin(), std::io::stdout());
    let mut sc = IO::new(r.lock(), w.lock());
    let n: usize = sc.read();
    let s = sc.chars();

    let mut ans = vec![0; n];

    ans[0] = 0;
    ans[0] = 0;
    create_ans(&mut ans, &s);
    if is_valid(&ans, &s) {
        for i in 0..n {
            if ans[i] == 0 {
                sc.write("S");
            } else {
                sc.write("W");
            }
        }
        sc.write("\n");
        return;
    }
    ans[0] = 0;
    ans[0] = 1;
    create_ans(&mut ans, &s);
    if is_valid(&ans, &s) {
        for i in 0..n {
            if ans[i] == 0 {
                sc.write("S");
            } else {
                sc.write("W");
            }
        }
        sc.write("\n");
        return;
    }
    ans[0] = 1;
    ans[0] = 0;
    create_ans(&mut ans, &s);
    if is_valid(&ans, &s) {
        for i in 0..n {
            if ans[i] == 0 {
                sc.write("S");
            } else {
                sc.write("W");
            }
        }
        sc.write("\n");
        return;
    }
    ans[0] = 1;
    ans[0] = 1;
    create_ans(&mut ans, &s);
    if is_valid(&ans, &s) {
        for i in 0..n {
            if ans[i] == 0 {
                sc.write("S");
            } else {
                sc.write("W");
            }
        }
        sc.write("\n");
        return;
    }
    sc.write("-1\n");
}

fn is_valid(ans: &Vec<usize>, s: &Vec<char>) -> bool {
    let n = ans.len();
    for i in 0..n {
        match (s[i], ans[i]) {
            ('o', 0) => {
                if ans[(i + 1) % n] != ans[(n + i - 1) % n] {
                    return false;
                }
            }
            ('x', 0) => {
                if ans[(i + 1) % n] != ans[(n + i - 1) % n] ^ 1 {
                    return false;
                }
            }
            ('o', 1) => {
                if ans[(i + 1) % n] != ans[(n + i - 1) % n] ^ 1 {
                    return false;
                }
            }
            ('x', 1) => {
                if ans[(i + 1) % n] != ans[(n + i - 1) % n] {
                    return false;
                }
            }
            _ => unreachable!(),
        }
    }
    true
}

fn create_ans(ans: &mut Vec<usize>, s: &Vec<char>) {
    let n = s.len();
    for i in 1..(n - 1) {
        match (s[i], ans[i]) {
            ('o', 0) => {
                ans[i + 1] = ans[i - 1];
            }
            ('x', 0) => {
                ans[i + 1] = ans[i - 1] ^ 1;
            }
            ('o', 1) => {
                ans[i + 1] = ans[i - 1] ^ 1;
            }
            ('x', 1) => {
                ans[i + 1] = ans[i - 1];
            }
            _ => unreachable!(),
        }
    }
}

pub struct IO<R, W: std::io::Write>(R, std::io::BufWriter<W>);

impl<R: std::io::Read, W: std::io::Write> IO<R, W> {
    pub fn new(r: R, w: W) -> IO<R, W> {
        IO(r, std::io::BufWriter::new(w))
    }
    pub fn write<S: std::ops::Deref<Target = str>>(&mut self, s: S) {
        use std::io::Write;
        self.1.write(s.as_bytes()).unwrap();
    }
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .0
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n' || b == b'\r' || b == b'\t')
            .take_while(|&b| b != b' ' && b != b'\n' && b != b'\r' && b != b'\t')
            .collect::<Vec<_>>();
        unsafe { std::str::from_utf8_unchecked(&buf) }
            .parse()
            .ok()
            .expect("Parse error.")
    }
    pub fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    pub fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}