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: Wrong Answer)

import java.io.BufferedReader
import java.util.*

fun main() = arc069d()

@OptIn(ExperimentalStdlibApi::class)
fun arc069d() = SimpleFastIOWithToken_arc069d().exec {
    val n = readInt()
    val replies = readString().map { it == 'o' }.toBooleanArray()

    val allocation = BooleanArray(n).apply { this[0] = true; this[1] = true }
    allocation[n - 1] = replies.first()

    for (i in 1 until n - 1) {
        allocation[i + 1] = (replies[i] == allocation[i]) == allocation[i - 1]
    }

    for (i in 0 until n) {
        if ((replies[i] == allocation[i]) != (allocation[(i - 1 + n) % n] == allocation[(i + 1) % n]))
            return@exec println(-1)
    }

    val answer = allocation.joinToString("") { if (it) "S" else "W" }

    println(answer)
}

// region kokokara template dayo (^o^)
@Suppress("unused", "HasPlatformType", "MemberVisibilityCanBePrivate", "ClassName")
private class SimpleFastIOWithToken_arc069d(private val separator: String = System.lineSeparator()) {
    private val br: BufferedReader = System.`in`.bufferedReader()
    private var st: StringTokenizer = StringTokenizer("")
    private val sb: StringBuilder = StringBuilder()
    private fun prepareNext() = run { if (!st.hasMoreTokens()) st = StringTokenizer(br.readLine()) }

    fun readString(): String = run { prepareNext() }.run { st.nextToken() }
    fun readInt(): Int = Integer.valueOf(readString())
    fun readLong(): Long = java.lang.Long.valueOf(readString())

    fun println(): Unit = run { sb.append(separator) }
    fun print(any: Any): Unit = run { sb.append(any) }
    fun println(any: Any): Unit = run { sb.append(any.toString() + separator) }

    fun exec(action: SimpleFastIOWithToken_arc069d.() -> Unit) {
        var t: Throwable? = null
        Thread(null, { action() }, "solve", 128 * 1024 * 1024)
            .apply { setUncaughtExceptionHandler { _, t1 -> t = t1 } }
            .apply { start() }.join()
        t?.let { throw it }
        kotlin.io.print(sb)
    }

    fun readLine(): Nothing = error("readLine is disabled.")
}
// endregion kokomade template dayo (^o^)