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)

#![allow(unused, non_snake_case, dead_code, non_upper_case_globals)]
#![macro_use]

use std::cmp::*;
use std::collections::*;
use std::io::*;
use std::mem::*;
use std::num::*;
use std::slice::*;

fn main() {
    let mut io = IO::new(stdin(), stdout(), stderr());
    // ===================================== //
    let n: usize = io.read();
    let mut s = io.chars();
    let k = s[0];
    s.push(k);

    let mut vv = vec![false; n + 2];
    vv[0] = true;
    vv[1] = true;
    for i in 1..n + 1 {
        if (s[i] == 'o' && !vv[i]) || (s[i] == 'x' && vv[i]) {
            vv[i + 1] = vv[i - 1];
        } else {
            vv[i + 1] = !vv[i - 1];
        }
    }
    io.debug(&vv);
    if vv[0] == vv[n] && vv[1] == vv[n + 1] {
        for i in 0..n {
            io.write(if vv[i] { "W" } else { "S" });
        }
        return;
    }

    let mut vv = vec![false; n + 2];
    vv[0] = true;
    vv[1] = false;
    for i in 1..n + 1 {
        if (s[i] == 'o' && !vv[i]) || (s[i] == 'x' && vv[i]) {
            vv[i + 1] = vv[i - 1];
        } else {
            vv[i + 1] = !vv[i - 1];
        }
    }
    io.debug(&vv);
    if vv[0] == vv[n] && vv[1] == vv[n + 1] {
        for i in 0..n {
            io.write(if vv[i] { "W" } else { "S" });
        }
        return;
    }
    let mut vv = vec![false; n + 2];
    vv[0] = false;
    vv[1] = false;
    for i in 1..n + 1 {
        if (s[i] == 'o' && !vv[i]) || (s[i] == 'x' && vv[i]) {
            vv[i + 1] = vv[i - 1];
        } else {
            vv[i + 1] = !vv[i - 1];
        }
    }
    io.debug(&vv);
    if vv[0] == vv[n] && vv[1] == vv[n + 1] {
        for i in 0..n {
            io.write(if vv[i] { "W" } else { "S" });
        }
        return;
    }
    let mut vv = vec![false; n + 2];
    vv[0] = false;
    vv[1] = true;
    for i in 1..n + 1 {
        if (s[i] == 'o' && !vv[i]) || (s[i] == 'x' && vv[i]) {
            vv[i + 1] = vv[i - 1];
        } else {
            vv[i + 1] = !vv[i - 1];
        }
    }
    io.debug(&vv);
    if vv[0] == vv[n] && vv[1] == vv[n + 1] {
        for i in 0..n {
            io.write(if vv[i] { "W" } else { "S" });
        }
        return;
    }
    io.writeln("-1");
}

// IO
struct IO<R: Read, W: Write, E: Write> {
    Read: R,
    Write: BufWriter<W>,
    Error: BufWriter<E>,
}
impl<R: Read, W: Write, E: Write> IO<R, W, E> {
    fn new(r: R, w: W, e: E) -> IO<R, W, E> {
        IO {
            Read: r,
            Write: BufWriter::new(w),
            Error: BufWriter::new(e),
        }
    }
    fn read<T>(&mut self) -> T
    where
        T: std::str::FromStr,
    {
        let next: String = self
            .Read
            .by_ref()
            .bytes()
            .map(|c| c.unwrap() as char)
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect();
        next.parse().ok().unwrap()
    }
    fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
    fn readn<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read::<T>()).collect::<Vec<_>>()
    }
    fn readmat<T: std::str::FromStr>(&mut self, n: usize, m: usize) -> Vec<Vec<T>> {
        (0..n).map(|_| self.readn(m)).collect()
    }
    fn write<S: ToString>(&mut self, val: S) {
        self.Write.write(val.to_string().as_bytes());
    }
    fn writeln<S: ToString>(&mut self, val: S) {
        self.Write.write(val.to_string().as_bytes());
        self.Write.write(b"\n");
    }
    fn debug<S: std::fmt::Debug>(&mut self, val: S) {
        writeln!(self.Error, "(debug) {:?}", &val);
    }
}