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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php
/*
    Problem URL : http://arc069.contest.atcoder.jp/tasks/arc069_b

    Score  :
    Result :
    Time   : ms
    Memory : KB
 */

// define('DEBUG', true);
define('DEBUG', false);

fscanf(STDIN, "%d", $N);
fscanf(STDIN, "%s", $s);

$from = pow(2,2);
$to = pow(2,11);

echo solve($s);
// echo solve("ooxoox");
// echo solve("oox");
// echo solve("xoooo");
// exit;
// for ($i = $from; $i < $to; $i++) {
//     $strbin = decbin($i);
//     $strbin = str_replace("0", "o", $strbin);
//     $strbin = str_replace("1", "x", $strbin);
//     echo $i . " " . $strbin . PHP_EOL;
//     printf("%s %s\n", $strbin, solve($strbin));
//     sleep(1);
// }

function solve($s) {
    $N = strlen($s);

    $s = " {$s}";

    $preset = array(
        0 => array(0 => "S", 1 => "S", 2 => "W", 3 => "W"),
        1 => array(0 => "S", 1 => "W", 2 => "S", 3 => "W"),
    );

    for ($i = 0; $i < 4; $i++) {
        $bool = true;
        $arr = array(
            0 => $preset[0][$i],
            $N => $preset[0][$i],
            1 => $preset[1][$i],
            $N+1 => $preset[1][$i]
        );
        // var_dump($arr);
        if (DEBUG) ksort($arr);
        if (DEBUG) var_dump($arr);
        for ($j = 1; $j <= $N; $j++) {
            // if (DEBUG) echo "1:{$arr[$j-1]} 2:{$arr[$j]}\n";
            switch ($arr[$j]) {
                case "S":
                    if ($arr[$j-1] == "S") {
                        if ($s[$j] == "o") {
                            $expected = "S";
                        }
                        if ($s[$j] == "x") {
                            $expected = "W";
                        }
                    }
                    if ($arr[$j-1] == "W") {
                        if ($s[$j] == "o") {
                            $expected = "W";
                        }
                        if ($s[$j] == "x") {
                            $expected = "S";
                        }
                    }
                    break;

                case "W":
                    if ($arr[$j-1] == "S") {
                        if ($s[$j] == "o") {
                            $expected = "W";
                        }
                        if ($s[$j] == "x") {
                            $expected = "S";
                        }
                    }
                    if ($arr[$j-1] == "W") {
                        if ($s[$j] == "o") {
                            $expected = "S";
                        }
                        if ($s[$j] == "x") {
                            $expected = "W";
                        }
                    }
                    break;
            }
            if (DEBUG) echo "j:{$arr[$j]} j-1:{$arr[$j-1]} \$s:$s[$j] \$expected: [{$expected}]\n";
            // if (DEBUG) echo "\$expected: [{$expected}]\n";
            if (!isset($arr[$j+1])) {
                $arr[$j+1] = $expected;
                if (DEBUG) echo ($j+1) . " {$expected}\n";
            } else {
                if ($arr[$j+1] != $expected) {
                    $bool = false;
                }
            }
        }
        if ($bool) {
            // var_dump($arr);
            ksort($arr);
            if (DEBUG) var_dump($arr);
            $arr[0] = "";
            $arr[$N+1] = "";
            return implode("", $arr) . PHP_EOL;
        }
    }
    return "-1\n";
}