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)

use std::io;
use std::io::Write;

#[allow(unused_macros)]
macro_rules! input {
    ( $($x:expr ),*) => {
        {
            let temp_str = input_line_str();
            let mut split_result_iter = temp_str.split_whitespace();
                $(
                let buf_split_result = split_result_iter.next();
                let buf_split_result = buf_split_result.unwrap();
                    ($x) = buf_split_result.parse().unwrap();
                )*
        }
    };
}

#[allow(dead_code)]
fn input_line_str() -> String {
    let mut s = String::new();
    io::stdin().read_line(&mut s).unwrap();
    s.trim().to_string()
}

#[allow(dead_code)]
fn str2vec(s: &str) -> Vec<char> {
    let mut v: Vec<char> = Vec::new();
    for c in s.chars() {
        v.push(c);
    }
    v
}

fn calc(v: &mut Vec<char>, input: &Vec<char>) -> bool {
    for z in 2..v.len() {
        if v[z - 1] == 'S' {
            if input[z - 1] == 'o' {
                if v[z - 2] == 'S' {
                    v[z] = 'S';
                } else {
                    v[z] = 'W';
                }
            } else {
                if v[z - 2] == 'S' {
                    v[z] = 'W';
                } else {
                    v[z] = 'S';
                }
            }
        } else {
            if input[z - 1] == 'o' {
                if v[z - 2] == 'S' {
                    v[z] = 'W';
                } else {
                    v[z] = 'S';
                }
            } else {
                if v[z - 2] == 'S' {
                    v[z] = 'S';
                } else {
                    v[z] = 'W';
                }
            }
        }
    }

    let p = v[v.len() - 2];
    let n = v[0];

    if *v.last().unwrap() == 'W' {
        if *input.last().unwrap() == 'o' {
            if p == n {
                return false;
            }
        } else {
            if p != n {
                return false;
            }
        }
    } else {
        if *input.last().unwrap() == 'o' {
            if p != n {
                return false;
            }
        } else {
            if p == n {
                return false;
            }
        }
    }

    let p = v[v.len() - 1];
    let n = v[1];

    if v[0] == 'W' {
        if input[0] == 'o' {
            p != n
        } else {
            p == n
        }
    } else {
        if input[0] == 'o' {
            p == n
        } else {
            p != n
        }
    }
}

fn main() {
    let n: usize;
    input!(n);
    let s = str2vec(&input_line_str());
    let mut ans = vec!['x'; n];
    let mut flag = false;

    loop {
        ans[0] = 'S';
        ans[1] = 'S';
        flag = calc(&mut ans, &s);
        if flag {
            break;
        }
        ans[1] = 'W';
        flag = calc(&mut ans, &s);
        if flag {
            break;
        }
        ans[0] = 'W';
        ans[1] = 'S';
        flag = calc(&mut ans, &s);
        if flag {
            break;
        }
        ans[1] = 'W';
        flag = calc(&mut ans, &s);
        break;
    }

    if flag {
        for z in ans {
            write!(std::io::stdout(), "{}", z);
        }
        println!("");
    } else {
        println!("-1");
    }
}