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"
  "os"
)
func main() {
  var n int
  var s string
  fmt.Scan(&n,&s)
  d := map[int]string{0:"S",1:"W"}
  if m,ok := check(n,s,0,0);ok {
    for i:=0;i<n;i++ { fmt.Print(d[m[i]]) }
    fmt.Println()
    os.Exit(0)
  }
  if m,ok := check(n,s,0,1);ok {
    for i:=0;i<n;i++ { fmt.Print(d[m[i]]) }
    fmt.Println()
    os.Exit(0)
  }
  if m,ok := check(n,s,1,0);ok {
    for i:=0;i<n;i++ { fmt.Print(d[m[i]]) }
    fmt.Println()
    os.Exit(0)
  }
  if m,ok := check(n,s,1,1);ok {
    for i:=0;i<n;i++ { fmt.Print(d[m[i]]) }
    fmt.Println()
    os.Exit(0)
  }
  fmt.Println(-1)
}
func check(n int,s string,m0 int,m1 int) ([]int,bool) {
  var m []int = make([]int,n)
  m[0],m[1] = m0,m1
  for i:=1;i<n-1;i++ {
    if (m[i] == 0) == (s[i:i+1] == "o") {
      m[i+1] = m[i-1]
    } else {
      m[i+1] = 1-m[i-1]
    }
  }
  if (m[n-1] == 0) == (s[n-1:n] == "o") {
    if m[0] != m[n-2] { return nil,false }
  } else {
    if m[0] != 1-m[n-2] { return nil,false }
  }
  if (m[0] == 0) == (s[0:1] == "o") {
    if m[1] != m[n-1] { return nil,false }
  } else {
    if m[1] != 1-m[n-1] { return nil,false }
  }
  return m,true
}