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)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
use competitive::prelude::*;

fn ok(c0: char, c1: char, c2: char, s1: char) -> bool {
    if s1 == 'o' {
        if c1 == 'S' {
            c0 == c2
        } else {
            c0 != c2
        }
    } else {
        if c1 == 'S' {
            c0 != c2
        } else {
            c0 == c2
        }
    }
}

fn make_ans(c0: char, c1: char, s: &[char]) -> Option<Vec<char>> {
    let n = s.len();
    let mut ans: Vec<char> = vec!['0'; n];
    ans[0] = c0;
    ans[1] = c1;
    let mut i = 2;
    while i < n {
        ans[i] = match (ans[i - 2], ans[i - 1], s[i - 1]) {
            ('S', 'S', 'o') => 'S',
            ('S', 'S', 'x') => 'W',
            ('S', 'W', 'o') => 'W',
            ('S', 'W', 'x') => 'S',
            ('W', 'S', 'o') => 'W',
            ('W', 'S', 'x') => 'S',
            ('W', 'W', 'o') => 'S',
            ('W', 'W', 'x') => 'W',
            _ => unreachable!(),
        };
        i += 1;
    }
    if ok(ans[n - 1], ans[0], ans[1], s[0]) && ok(ans[n - 2], ans[n - 1], ans[0], s[n - 1]) {
        Some(ans)
    } else {
        // dbg!(ans.into_iter().collect::<String>());
        None
    }
}

fn solve(s: &[char]) -> Option<Vec<char>> {
    let ans = make_ans('S', 'S', s);
    if ans != None {
        return ans;
    }
    let ans = make_ans('S', 'W', s);
    if ans != None {
        return ans;
    }
    let ans = make_ans('W', 'S', s);
    if ans != None {
        return ans;
    }
    make_ans('W', 'W', s)
}

#[proconio::fastout]
fn main() {
    input! {
        _: usize,
        s: Chars,
    }
    match solve(&s) {
        Some(ans) => println!("{}", ans.into_iter().collect::<String>()),
        None => println!("-1"),
    }
}
*/

fn main() {
    let exe = "/tmp/bin9FE50254";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "<base64-encoded ELF executable removed>";