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 (1.0.0) (judge verdict: Accepted)

import java.util.*
import kotlin.*

import java.io.InputStream
import java.lang.NumberFormatException
import java.lang.StringBuilder


fun main(args: Array<String>) {
    Program().solve()
}

class Program {
    fun solve() {
        val sc = FastScanner()
        val n = sc.nextInt()
        val s = sc.next()

        // 2つ決めたら残りも全部決まる
        // 矛盾しなかったらOK
        // SS
        if (c('S', 'S', n, s)) return
        // SW
        if (c('S', 'W', n, s)) return
        // WS
        if (c('W', 'S', n, s)) return
        // WW
        if (c('W', 'W', n, s)) return
        println("-1")
    }

    fun c(first: Char, second: Char, n: Int, s: String): Boolean {
        val ar = Array(n) { '0' }
        ar[0] = first
        ar[1] = second
        for (i in 1 until n - 1) {
            if (ar[i] == 'S') {
                if (s[i] == 'o') {
                    ar[i + 1] = ar[i - 1]
                } else {
                    ar[i + 1] = if (ar[i - 1] == 'S') 'W' else 'S'
                }
            } else if (ar[i] == 'W') {
                if (s[i] == 'x') {
                    ar[i + 1] = ar[i - 1]
                } else {
                    ar[i + 1] = if (ar[i - 1] == 'S') 'W' else 'S'
                }
            }
        }

        // 矛盾しないか?
        if (ar[n - 1] == 'S') {
            if (s[n - 1] == 'o') {
                if (ar[n - 2] != ar[0]) return false
            } else {
                if (ar[n - 2] == ar[0]) return false
            }
        } else {
            if (s[n - 1] == 'x') {
                if (ar[n - 2] != ar[0]) return false
            } else {
                if (ar[n - 2] == ar[0]) return false
            }
        }

        if (ar[0] == 'S') {
            if (s[0] == 'o') {
                if (ar[n - 1] != ar[1]) return false
            } else {
                if (ar[n - 1] == ar[1]) return false
            }
        } else {
            if (s[0] == 'x') {
                if (ar[n - 1] != ar[1]) return false
            } else {
                if (ar[n - 1] == ar[1]) return false
            }
        }
        println(String(ar.toCharArray()))
        return true
    }
}


class FastScanner {
    companion object {
        val input: InputStream = System.`in`
        val buffer = ByteArray(1024) { 0 }
        fun isPrintableChar(c: Int): Boolean = c in 33..126
    }

    var ptr = 0
    var buflen = 0
    private fun hasNextByte(): Boolean {
        if (ptr < buflen) {
            return true
        } else {
            ptr = 0
            buflen = input.read(buffer)
            if (buflen <= 0) {
                return false
            }
        }
        return true
    }

    private fun readByte(): Int = if (hasNextByte()) buffer[ptr++].toInt() else -1

    private fun skipUnprintable() {
        while (hasNextByte() && !isPrintableChar(buffer[ptr].toInt())) ptr++
    }

    fun hasNext(): Boolean {
        skipUnprintable()
        return hasNextByte()
    }

    fun next(): String {
        if (!hasNext()) throw NoSuchElementException()
        val sb = StringBuilder()
        var b = readByte()
        while (isPrintableChar(b)) {
            sb.appendCodePoint(b)
            b = readByte()
        }
        return sb.toString()
    }

    fun nextInt(): Int {
        if (!hasNext()) throw NoSuchElementException()
        var n = 0
        var b = readByte()
        // '-' = 45
        val minus = b == 45
        if (minus) {
            b = readByte()
        }

        // '0' = 48 '9' = 57
        if (b !in 48..57) {
            throw NumberFormatException()
        }

        while (true) {
            if (b in 48..57) {
                n *= 10
                n += b - 48
            } else if (b == -1 || !isPrintableChar(b)) {
                return if (minus) -n else n
            } else {
                throw NumberFormatException()
            }
            b = readByte()
        }
    }

    fun nextLong(): Long {
        if (!hasNext()) throw NoSuchElementException()
        var n = 0L
        var b = readByte()
        // '-' = 45
        val minus = b == 45
        if (minus) {
            b = readByte()
        }

        // '0' = 48 '9' = 57
        if (b !in 48..57) {
            throw NumberFormatException()
        }

        while (true) {
            if (b in 48..57) {
                n *= 10
                n += b - 48
            } else if (b == -1 || !isPrintableChar(b)) {
                return if (minus) -n else n
            } else {
                throw NumberFormatException()
            }
            b = readByte()
        }
    }

    fun nextDouble(): Double = next().toDouble()
}