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 Kotlin (1.3.71) (judge verdict: Accepted)

import java.io.*
import java.util.*
import java.lang.*
import java.lang.Math.*


data class CharPair(val first: Char, val second: Char)

fun pattern(S: String, tail: Char, head: Char): String {
    val N = S.length
    var t1 = Array<Char>(N){'_'}
    t1[N-1] = tail
    t1[0] = head
    var ok = true
    for (i in 0 until N) {
        val ip1 = (i+1)%N
        val im1 = (i-1+N)%N
        when(CharPair(t1[i], S[i])) {
            CharPair('S', 'o') -> {
                if (t1[ip1] == '_' || t1[ip1] == t1[im1]) {
                    t1[ip1] = t1[im1]
                } else {
                    ok = false
                }
            }
            CharPair('S', 'x') -> {
                if (t1[ip1] == '_' || t1[ip1] != t1[im1]) {
                    t1[ip1] = if (t1[im1] == 'S') 'W' else 'S'
                } else {
                    ok = false
                }
            }
            CharPair('W', 'o') -> {
                if (t1[ip1] == '_' || t1[ip1] != t1[im1]) {
                    t1[ip1] = if (t1[im1] == 'S') 'W' else 'S'
                } else {
                    ok = false
                }
            }
            CharPair('W', 'x') -> {
                if (t1[ip1] == '_' || t1[ip1] == t1[im1]) {
                    t1[ip1] = t1[im1]
                } else {
                    ok = false
                }
            }
        }
    }

    return if (ok) t1.joinToString("") else ""
}

fun solve() {
    val N = rd.readInt()
    val S = rd.readString()
    assert(S.length == N){"S.length == N"}

    val sw = arrayOf('S', 'W')
    for (i in 0..1) {
        for (j in 0..1) {
            val ans = pattern(S, sw[i], sw[j])
            if (ans != "") {
                println(ans)
                return
            }
        }
    }

    println(-1)
}


//val rd = debug.Reader("arc", "069", "b", "sample-1")
val rd = Reader()


fun main(args: Array<String>) {
    try {
        var exception: Throwable? = null
        val sth = Thread(null, SolveThread(), "solveThread", 128 * 1024 * 1024)
        sth.setUncaughtExceptionHandler { _, e -> exception = e }
        sth.start(); sth.join()
        if (exception != null) throw exception!!
    } catch (e: Exception) { throw e }
}
const val MOD = 1_000_000_007L; const val INF = Int.MAX_VALUE/2; const val LINF = Long.MAX_VALUE/2
data class IntPair(val first: Int, val second: Int)
val errPrintln: (Any) -> Unit = { msg -> System.err.println(msg) }
fun rAssert(exp: Boolean, lazyMsg: () -> String = {""}) {
    if (!exp) { val msg = lazyMsg(); errPrintln("EAssert Error: $msg"); throw Error(msg) }
}
fun tAssert(exp: Boolean, lazyMsg: () -> String = {""}) {
    if (!exp) { val msg = lazyMsg(); errPrintln("TAssert Error: $msg"); Thread.sleep(3000) }
}
class SolveThread : Runnable {
    override fun run() { solve() }
}
class Reader {
    private val br = BufferedReader(InputStreamReader(System.`in`))
    val readString: () -> String = { br.readLine() }
    val readInt: () -> Int = { br.readLine().toInt() }
    val readLong: () -> Long = { br.readLine().toLong() }
    val readIntArray: () -> IntArray = { br.readLine().split(' ').map { it.toInt() }.toIntArray() }
    val readLongArray: () -> LongArray = { br.readLine().split(' ').map { it.toLong() }.toLongArray() }
    val readListInt: () -> List<Int> = { br.readLine().split(' ').map { it.toInt() } }
    val readListLong: () -> List<Long> = { br.readLine().split(' ').map { it.toLong() } }
}