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(
	"fmt"
)
func main(){
	var n int
	fmt.Scanln(&n)
	var in [100000] bool
	var c string
	fmt.Scanln(&c)
	for i := 0; i < n; i++ {
		if c[i] == 'o' {
			in[i] = true
		}else{
			in[i] = false
		}
	}
	if doesExist(n, in, true, true) {
		answer(n, in, true, true);
		return
	}
	if doesExist(n, in, true, false) {
		answer(n, in, true, false);
		return
	}
	if doesExist(n, in, false, true) {
		answer(n, in, false, true);
		return
	}
	if doesExist(n, in, false, false) {
		answer(n, in, false, false);
		return
	}
	fmt.Println(-1)
}

func doesExist(n int, in [100000]bool, first bool, second bool) bool {
	var res [100000] bool
	res[0] = first
	res[1] = second
	for i := 1; i < n-1; i++ {
		if res[i]==in[i] {
			res[i+1] = res[i-1]
		} else {
			res[i+1] = !res[i-1]
		}
	}
	return (((in[n-1]==res[n-1])==(res[0] == res[n-2])) && ((in[0]==res[0])==(res[1] == res[n-1])) )
}

func answer(n int, in [100000]bool, first bool, second bool) {
	var res [100000] bool
	res[0] = first
	res[1] = second
	outSW(res[0])
	outSW(res[1])
	for i := 1; i < n-1; i++ {
		if res[i]==in[i] {
			res[i+1] = res[i-1]
		} else {
			res[i+1] = !res[i-1]
		}
		outSW(res[i+1])
	}
	fmt.Println()
}
func outSW(in bool) {
	if in {
		fmt.Print("S")
	} else {
		fmt.Print("W")
	}
}