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)

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

fn solve(n: usize, s: String) -> Vec<bool> {
    let input = s.chars().map(|v| v == 'o').collect::<Vec<_>>();

    for [s0, s1] in [[true, true], [true, false], [false, true], [false, false]].iter() {
        let mut sheeps = vec![false; n];
        sheeps[0] = *s0;
        sheeps[1] = *s1;

        for i in 2..n {
            if sheeps[i - 1] && input[i - 1] {
                sheeps[i] = sheeps[i - 2];
            } else if sheeps[i - 1] && !input[i - 1] {
                sheeps[i] = !sheeps[i - 2];
            } else if !sheeps[i - 1] && input[i - 1] {
                sheeps[i] = !sheeps[i - 2];
            } else {
                sheeps[i] = sheeps[i - 2];
            }
        }

        if sheeps[n - 1] && input[n - 1] && sheeps[n - 2] != sheeps[0] {
            continue;
        }
        if sheeps[n - 1] && !input[n - 1] && sheeps[n - 2] == sheeps[0] {
            continue;
        }
        if !sheeps[n - 1] && input[n - 1] && sheeps[n - 2] == sheeps[0] {
            continue;
        }
        if !sheeps[n - 1] && !input[n - 1] && sheeps[n - 2] != sheeps[0] {
            continue;
        }

        return sheeps;
    }

    return Vec::new();
}

fn main() {
    input! {
        n: usize,
        s: String,
    }

    let rs = solve(n, s);
    if rs.is_empty() {
        println!("-1");
    } else {
        use std::iter::FromIterator;

        println!(
            "{}",
            String::from_iter(rs.into_iter().map(|b| if b { 'S' } else { 'W' }))
        );
    }
}
*/

fn main() {
    let exe = "/tmp/binBD18303A";
    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>";