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 Go (1.6) (judge verdict: Wrong Answer)

package main

import "fmt"

func main() {
	var n int
	var s string
	fmt.Scan(&n, &s)

	for _, p := range []string{"SSS", "WSW", "SWW", "WWS"} {
		t := make([]byte, n)
		t[n-1] = p[0]
		t[0] = p[1]
		t[1] = p[2]

		for i := 1; i < n-2; i++ {
			if t[i] == 'S' && s[i] == 'o' || t[i] == 'W' && s[i] == 'x' {
				t[i+1] = t[i-1]
			} else {
				if t[i-1] == 'S' {
					t[i+1] = 'W'
				} else {
					t[i+1] = 'S'
				}
			}
		}

		ok := true
		tmp := append(t, t[0])
		for i := 1; i < n; i++ {
			l, m, r := tmp[i-1], tmp[i], tmp[i+1]
			if s[i] == 'o' && m == 'S' && l == r ||
				s[i] == 'o' && m == 'W' && l != r ||
				s[i] == 'x' && m == 'S' && l != r ||
				s[i] == 'x' && m == 'W' && l == r {
				continue
			}

			ok = false
			break
		}

		if ok {
			fmt.Println(string(t))
			return
		}
	}

	fmt.Println(-1)
}