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 JavaScript (node.js v5.12) (judge verdict: Accepted)

function Main(input) {
	input = input.split("\n");
	var s = input[1];
	var n = parseInt(input[0], 10);
    var toTest = [['S', 'S'], ['S', 'W'], ['W', 'S'], ['W', 'W']];
    for (var t = 0; t < 4; t++) {
        var arr = toTest[t];
        for (var i = 1; i < n-1; i++) {
            if (s[i] == 'o') {
                if (arr[i] == 'S') {
                    if (arr[i-1] == 'S') {
                        arr.push('S');
                    } else {
                        arr.push('W');
                    }
                } else {
                    if (arr[i-1] == 'S') {
                        arr.push('W');
                    } else {
                        arr.push('S');
                    }
                }
            } else {
                if (arr[i] == 'S') {
                    if (arr[i-1] == 'S') {
                        arr.push('W');
                    } else {
                        arr.push('S');
                    }
                } else {
                    if (arr[i-1] == 'S') {
                        arr.push('S')
                    } else {
                        arr.push('W');
                    }
                }
            }
        }
    }
    var failCount = 0;
    for (var t = 0; t < 4; t++) {
        var fail = false;
        var arr = toTest[t];
        for (var i = 0; i < n; i++) {
            var prev = i - 1;
            var next = i + 1;
            if (i == 0) {
                prev = n - 1;
            }
            if (i == n - 1) {
                next = 0;
            }
            if (arr[i] == 'S') {
                if (s[i] == 'o' && arr[prev] != arr[next]) {
                    fail = true;
                    break;
                } else if (s[i] == 'x' && arr[prev] == arr[next]) {
                    fail = true;
                    break;
                }
            } else {
                if (s[i] == 'o' && arr[prev] == arr[next]) {
                    fail = true;
                    break;
                } else if (s[i] == 'x' && arr[prev] != arr[next]) {
                    fail = true;
                    break;
                }
            }
        }
        if (!fail) {
            console.log(arr.join(""));
            break;
        }
        failCount++;
    }
    if (failCount >= 4) console.log(-1);
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));