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: Accepted)

package main

import (
	"bufio"
	"fmt"
	"math"
	"os"
	"strconv"
	"strings"
)

func main() {
	N := nextInt()
	s := nextString()

	s += string(s[0])
	starts := [][]string{{"S", "S"}, {"S", "W"}, {"W", "S"}, {"W", "W"}}
	for _, start := range starts {
		animals := make([]string, N+2)
		animals[0] = start[0]
		animals[1] = start[1]
		for i := 1; i <= N; i++ {
			if animals[i] == "S" {
				if s[i] == 'o' {
					if animals[i-1] == "S" {
						animals[i+1] = "S"
					} else {
						animals[i+1] = "W"
					}
				} else {
					if animals[i-1] == "S" {
						animals[i+1] = "W"
					} else {
						animals[i+1] = "S"
					}
				}
			} else {
				if s[i] == 'o' {
					if animals[i-1] == "S" {
						animals[i+1] = "W"
					} else {
						animals[i+1] = "S"
					}
				} else {
					if animals[i-1] == "S" {
						animals[i+1] = "S"
					} else {
						animals[i+1] = "W"
					}
				}
			}
		}

		if animals[0] == animals[N] && animals[1] == animals[N+1] {
			fmt.Println(strings.Join(animals[:N], ""))
			return
		}
	}

	fmt.Println(-1)
}

// Input. ----------

var sc = bufio.NewScanner(os.Stdin)

func init() {
	sc.Buffer([]byte{}, math.MaxInt64)
	sc.Split(bufio.ScanWords)
}

func nextInt() int {
	sc.Scan()
	i, err := strconv.Atoi(sc.Text())
	if err != nil {
		panic(err)
	}

	return i
}

func nextString() string {
	sc.Scan()

	return sc.Text()
}

// ---------- Input.