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)

fn main() {
    let mut sc = Scanner::new();
    let n: usize = sc.read();
    let s: Vec<char> = sc.read::<String>().chars().collect();

    let check = |sheep: &mut Vec<bool>| {
        for pos in 2..n {
            if sheep[pos - 1] {
                if s[pos - 1] == 'o' {
                    sheep[pos] = sheep[pos - 2];
                } else {
                    sheep[pos] = !sheep[pos - 2];
                }
            } else {
                if s[pos - 1] != 'o' {
                    sheep[pos] = sheep[pos - 2];
                } else {
                    sheep[pos] = !sheep[pos - 2];
                }
            }
        }
        for i in 0..n {
            if sheep[i] {
                if s[i] == 'o' && sheep[(i - 1 + n) % n] != sheep[(i + 1) % n] {
                    return false;
                }
                if s[i] == 'x' && sheep[(i - 1 + n) % n] == sheep[(i + 1) % n] {
                    return false;
                }
            } else {
                if s[i] == 'x' && sheep[(i - 1 + n) % n] != sheep[(i + 1) % n] {
                    return false;
                }
                if s[i] == 'o' && sheep[(i - 1 + n) % n] == sheep[(i + 1) % n] {
                    return false;
                }
            }
        }
        return true;
    };

    let out = |sheep: &Vec<bool>| {
        for i in 0..n {
            if sheep[i] {
                print!("S");
            } else {
                print!("W");
            }
        }
        println!();
    };

    let mut sheep = vec![true; n];
    if check(&mut sheep) {
        out(&sheep);
        return;
    }

    sheep[0] = true;
    sheep[1] = false;
    if check(&mut sheep) {
        out(&sheep);
        return;
    }
    sheep[0] = false;
    sheep[1] = true;
    if check(&mut sheep) {
        out(&sheep);
        return;
    }
    sheep[0] = false;
    sheep[1] = false;
    if check(&mut sheep) {
        out(&sheep);
        return;
    }
    println!("-1");
}

struct Scanner {
    ptr: usize,
    length: usize,
    buf: Vec<u8>,
    small_cache: Vec<u8>,
}

impl Scanner {
    fn new() -> Scanner {
        Scanner {
            ptr: 0,
            length: 0,
            buf: vec![0; 1024],
            small_cache: vec![0; 1024],
        }
    }

    fn load(&mut self) {
        use std::io::Read;
        let mut s = std::io::stdin();
        self.length = s.read(&mut self.buf).unwrap();
    }

    fn byte(&mut self) -> u8 {
        if self.ptr >= self.length {
            self.ptr = 0;
            self.load();
            if self.length == 0 {
                self.buf[0] = b'\n';
                self.length = 1;
            }
        }

        self.ptr += 1;
        return self.buf[self.ptr - 1];
    }

    fn is_space(b: u8) -> bool {
        b == b'\n' || b == b'\r' || b == b'\t' || b == b' '
    }

    fn read<T>(&mut self) -> T
    where
        T: std::str::FromStr,
        T::Err: std::fmt::Debug,
    {
        let mut b = self.byte();
        while Scanner::is_space(b) {
            b = self.byte();
        }

        for pos in 0..self.small_cache.len() {
            self.small_cache[pos] = b;
            b = self.byte();
            if Scanner::is_space(b) {
                return String::from_utf8_lossy(&self.small_cache[0..(pos + 1)])
                    .parse()
                    .unwrap();
            }
        }

        let mut v = self.small_cache.clone();
        while !Scanner::is_space(b) {
            v.push(b);
            b = self.byte();
        }
        return String::from_utf8_lossy(&v).parse().unwrap();
    }
}