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)

/// Thank you tanakh!!!
/// https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let mut s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};

    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };

    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };

    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };

    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };

    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}

fn solve(s: &Vec<char>, first: bool, second: bool) -> Option<Vec<bool>> {
    let n = s.len();
    let mut is_wolf = vec![false; n];
    is_wolf[0] = first;
    is_wolf[1] = second;
    for i in 1..(n - 1) {
        let prev = i - 1;
        let next = i + 1;
        match (s[i], is_wolf[i]) {
            ('o', true) => {
                is_wolf[next] = !is_wolf[prev];
            }
            ('x', true) => {
                is_wolf[next] = is_wolf[prev];
            }
            ('o', false) => {
                is_wolf[next] = is_wolf[prev];
            }
            ('x', false) => {
                is_wolf[next] = !is_wolf[prev];
            }
            _ => unreachable!(),
        }
    }
    let honest = (s[n - 1] == 'o') == (is_wolf[n - 2] == is_wolf[0]);
    if (!honest) != is_wolf[n - 1] {
        return None;
    }

    let honest = (s[0] == 'o') == (is_wolf[n - 1] == is_wolf[1]);
    if (!honest) != is_wolf[0] {
        return None;
    }
    Some(is_wolf)
}

fn main() {
    input!(n: usize, s: chars);
    if let Some(is_wolf) = solve(&s, true, true) {
        for &is_wolf in is_wolf.iter() {
            print!("{}", if is_wolf { "W" } else { "S" });
        }
        println!();
    } else if let Some(is_wolf) = solve(&s, true, false) {
        for &is_wolf in is_wolf.iter() {
            print!("{}", if is_wolf { "W" } else { "S" });
        }
        println!();
    } else if let Some(is_wolf) = solve(&s, false, true) {
        for &is_wolf in is_wolf.iter() {
            print!("{}", if is_wolf { "W" } else { "S" });
        }
        println!();
    } else if let Some(is_wolf) = solve(&s, false, false) {
        for &is_wolf in is_wolf.iter() {
            print!("{}", if is_wolf { "W" } else { "S" });
        }
        println!();
    } else {
        println!("-1");
    }
}