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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Linq;
using System.Text;
using System.Numerics;

namespace ABC055.D
{
	using static Util;

	public class Solver : SolverBase
	{
		int N;
		string S;
		public void Run() {
			N = ReadInt();
			S = ReadLine();
			//Dump(new string(animals));

			// 4通り試して、OKパターンが出たら終了
			// 出なかったら -1 出力

			var ani = new char[N];
			if (S[0] == 'o') {
				//     ○-> SSS
				ani[N - 1] = 'S';
				ani[0] = 'S';
				ani[1] = 'S';
				if (Test(ani)) return;

				//         WSW
				InitArray(ani, default(char));
				ani[N - 1] = 'W';
				ani[0] = 'S';
				ani[1] = 'W';
				if (Test(ani)) return;

				//     ○-> SWW
				InitArray(ani, default(char));
				ani[N - 1] = 'S';
				ani[0] = 'W';
				ani[1] = 'W';
				if (Test(ani)) return;

				//         WWS
				InitArray(ani, default(char));
				ani[N - 1] = 'W';
				ani[0] = 'W';
				ani[1] = 'S';
				if (Test(ani)) return;

			} else {
				//     ×-> WSS
				ani[N - 1] = 'W';
				ani[0] = 'S';
				ani[1] = 'S';
				if (Test(ani)) return;
				//         SSW
				InitArray(ani, default(char));
				ani[N - 1] = 'S';
				ani[0] = 'S';
				ani[1] = 'W';
				if (Test(ani)) return;
				//     ×-> SWS
				InitArray(ani, default(char));
				ani[N - 1] = 'S';
				ani[0] = 'W';
				ani[1] = 'S';
				if (Test(ani)) return;
				//         WWW
				InitArray(ani, default(char));
				ani[N - 1] = 'W';
				ani[0] = 'W';
				ani[1] = 'W';
				if (Test(ani)) return;
			}

			// ここまで来た＝解無し
			WriteLine("-1");
		}

		bool Test(char[] ani) {
			if (Check(ani)) {
				WriteLine(new string(ani));
				return true;
			} else {
				return false;
			}
		}
		bool Check(char[] ani) {
			for (int i = 1; i < N; i++) {
				if ((S[i] == 'o' && ani[i] == 'S') ||
					(S[i] == 'x' && ani[i] == 'W')) {
					if (i < N - 2) {
						ani[i + 1] = ani[i - 1];
					} else if (i < N - 1) {
						if (ani[i + 1] != ani[i - 1])
							return false;
					} else {
						if (ani[0] != ani[i - 1])
							return false;
					}
				} else {
					if (i < N - 2) {
						ani[i + 1] = ani[i - 1] == 'S' ? 'W' : 'S';
					} else if (i < N - 1) {
						if (ani[i + 1] == ani[i - 1])
							return false;
					} else {
						if (ani[0] == ani[i - 1])
							return false;
					}
				}
			}
			return true;
		}

#if !MYHOME
		static void Main(string[] args) {
			new Solver().Run();
		}
#endif
	}

	public static class Util
	{
		public static int Gcd(int a, int b) {
			if (a < b)
				// 引数を入替えて自分を呼び出す
				return Gcd(b, a);
			while (b != 0) {
				var remainder = a % b;
				a = b;
				b = remainder;
			}
			return a;
		}
		public readonly static long MOD = 1000000007;

		public static string DumpToString<T>(IEnumerable<T> array) where T : IFormattable {
			var sb = new StringBuilder();
			foreach (var item in array) {
				sb.Append(item);
				sb.Append(", ");
			}
			return sb.ToString();
		}

		public static void InitArray<T>(T[] ary, T value) {
			for (int i = 0; i < ary.Length; i++) {
				ary[i] = value;
			}
		}
		public static void InitDP2<T>(T[,] dp, T value) {
			for (int i = 0; i < dp.GetLength(0); i++) {
				for (int j = 0; j < dp.GetLength(1); j++) {
					dp[i, j] = value;
				}
			}
		}
		public static void InitDP3<T>(T[,,] dp, T value) {
			for (int i = 0; i < dp.GetLength(0); i++) {
				for (int j = 0; j < dp.GetLength(1); j++) {
					for (int k = 0; k < dp.GetLength(2); k++) {
						dp[i, j, k] = value;
					}
				}
			}
		}

		public static T Max<T>(params T[] nums) where T : IComparable {
			if (nums.Length == 0) return default(T);

			T max = nums[0];
			for (int i = 1; i < nums.Length; i++) {
				max = max.CompareTo(nums[i]) > 0 ? max : nums[i];
			}
			return max;
		}
		public static T Min<T>(params T[] nums) where T : IComparable {
			if (nums.Length == 0) return default(T);

			T min = nums[0];
			for (int i = 1; i < nums.Length; i++) {
				min = min.CompareTo(nums[i]) < 0 ? min : nums[i];
			}
			return min;
		}

		/// <summary>
		/// ソート済み配列 ary に同じ値の要素が含まれている？
		/// ※ソート順は昇順/降順どちらでもよい
		/// </summary>
		public static bool HasDuplicateInSortedArray<T>(T[] ary) where T : IComparable, IComparable<T> {
			if (ary.Length <= 1) return false;

			var lastNum = ary[ary.Length - 1];

			foreach (var n in ary) {
				if (lastNum.CompareTo(n) == 0) {
					return true;
				} else {
					lastNum = n;
				}
			}
			return false;
		}

		public static bool ReplaceIfBigger<T>(ref T r, T v) where T : IComparable {
			if (r.CompareTo(v) < 0) {
				r = v;
				return true;
			} else {
				return false;
			}
		}
		public static bool ReplaceIfSmaller<T>(ref T r, T v) where T : IComparable {
			if (0 < r.CompareTo(v)) {
				r = v;
				return true;
			} else {
				return false;
			}
		}

		/// <summary>
		/// dic[key]にadderを加算する。keyが存在しなかった場合はdic[key]=adder をセットする。
		/// </summary>
		public static void AddTo<TKey>(this Dictionary<TKey, int> dic, TKey key, int adder) {
			if (dic.ContainsKey(key)) {
				dic[key] += adder;
			} else {
				dic[key] = adder;
			}
		}

		/// <summary>
		/// 二分探索
		/// ※条件を満たす最小のidxを返す
		/// ※満たすものがない場合は ary.Length を返す
		/// ※『aryの先頭側が条件を満たさない、末尾側が条件を満たす』という前提
		/// ただし、IsOK(...)の戻り値を逆転させれば、逆でも同じことが可能。
		/// </summary>
		/// <param name="ary">探索対象配列 ★ソート済みであること</param>
		/// <param name="key">探索値 ※これ以上の値を持つ（IsOKがtrueを返す）最小のindexを返す</param>
		public static int BinarySearch<T>(T[] ary, T key) where T : IComparable, IComparable<T> {
			int left = -1;
			int right = ary.Length;

			while (1 < right - left) {
				var mid = left + (right - left) / 2;

				if (IsOK(ary, mid, key)) {
					right = mid;
				} else {
					left = mid;
				}
			}

			// left は条件を満たさない最大の値、right は条件を満たす最小の値になっている
			return right;
		}
		public static bool IsOK<T>(T[] ary, int idx, T key) where T : IComparable, IComparable<T> {
			// key <= ary[idx] と同じ意味
			return key.CompareTo(ary[idx]) <= 0;
		}
	}

	public class SolverBase
	{
		virtual protected string ReadLine() => Console.ReadLine();
		virtual protected string ReadString() => ReadLine();
		virtual protected int ReadInt() => int.Parse(ReadLine());
		//virtual protected void ReadInt2(out int x, out int y) {
		//	var aryS = ReadLine().Split(' ');
		//	x = int.Parse(aryS[0]);
		//	y = int.Parse(aryS[1]);
		//}
		virtual protected long ReadLong() => long.Parse(ReadLine());
		virtual protected string[] ReadStringArray() => ReadLine().Split(' ');
		virtual protected int[] ReadIntArray() => ReadLine().Split(' ').Select<string, int>(s => int.Parse(s)).ToArray();
		virtual protected void ReadInt2(out int a, out int b) {
			var ary = ReadIntArray();
			a = ary[0];
			b = ary[1];
		}
		virtual protected void ReadInt3(out int a, out int b, out int c) {
			var ary = ReadIntArray();
			a = ary[0];
			b = ary[1];
			c = ary[2];
		}
		virtual protected void ReadInt4(out int a, out int b, out int c, out int d) {
			var ary = ReadIntArray();
			a = ary[0];
			b = ary[1];
			c = ary[2];
			d = ary[3];
		}
		virtual protected long[] ReadLongArray() => ReadLine().Split(' ').Select<string, long>(s => long.Parse(s)).ToArray();
		virtual protected void ReadLong2(out long a, out long b) {
			var ary = ReadLongArray();
			a = ary[0];
			b = ary[1];
		}
		virtual protected void ReadLong3(out long a, out long b, out long c) {
			var ary = ReadLongArray();
			a = ary[0];
			b = ary[1];
			c = ary[2];
		}
		virtual protected void ReadLong4(out long a, out long b, out long c, out long d) {
			var ary = ReadLongArray();
			a = ary[0];
			b = ary[1];
			c = ary[2];
			d = ary[3];
		}
		virtual protected double[] ReadDoubleArray() => ReadLine().Split(' ').Select<string, double>(s => double.Parse(s)).ToArray();
		virtual protected void WriteLine(string line) => Console.WriteLine(line);
		virtual protected void WriteLine(double d) => Console.WriteLine($"{d:F9}");
		virtual protected void WriteLine<T>(T value) where T : IFormattable => Console.WriteLine(value);
		virtual protected void WriteGrid(IEnumerable<IEnumerable<char>> arrayOfArray) {
			var sb = new StringBuilder();
			foreach (var a in arrayOfArray) {
				foreach (var c in a) {
					sb.Append(c);
				}
				sb.AppendLine();
			}
			WriteLine(sb.ToString());
		}

		[Conditional("DEBUG")]
		protected void Dump(string s) => Console.WriteLine(s);
		[Conditional("DEBUG")]
		protected void Dump(char c) => Console.WriteLine(c);
		[Conditional("DEBUG")]
		protected void Dump(int x) => Console.WriteLine(x);
		[Conditional("DEBUG")]
		protected void Dump(double d) => Console.WriteLine($"{d:F9}");
		[Conditional("DEBUG")]
		protected void Dump<T>(IEnumerable<T> array) where T : IFormattable {
			string s = Util.DumpToString(array);
			// Consoleに出力すると、UnitTestの邪魔をしないというメリットあり。
			Console.WriteLine(s);
			//_writer.WriteLine(s);
		}
		[Conditional("DEBUG")]
		protected void DumpGrid(IEnumerable<IEnumerable<char>> arrayOfArray) {
			var sb = new StringBuilder();
			foreach (var a in arrayOfArray) {
				foreach (var c in a) {
					sb.Append(c);
				}
				sb.AppendLine();
			}
			// Consoleに出力すると、UnitTestの邪魔をしないというメリットあり。
			Console.WriteLine(sb.ToString());
			//_writer.WriteLine(sb.ToString());
		}
		[Conditional("DEBUG")]
		protected void DumpGrid<T>(IEnumerable<IEnumerable<T>> arrayOfArray) where T : IFormattable {
			var sb = new StringBuilder();
			foreach (var a in arrayOfArray) {
				sb.AppendLine(Util.DumpToString(a));
			}
			// Consoleに出力すると、UnitTestの邪魔をしないというメリットあり。
			Console.WriteLine(sb.ToString());
			//_writer.WriteLine(sb.ToString());
		}
		[Conditional("DEBUG")]
		protected void DumpGrid(bool[,] grid) {
			var sb = new StringBuilder();
			for (int i = 0; i < grid.GetLength(0); i++) {
				for (int j = 0; j < grid.GetLength(1); j++) {
					sb.Append(grid[i, j] ? "x " : ". ");
				}
				sb.AppendLine();
			}
			Console.WriteLine(sb.ToString());
		}
		[Conditional("DEBUG")]
		protected void DumpGrid(char[,] grid) {
			var sb = new StringBuilder();
			for (int i = 0; i < grid.GetLength(0); i++) {
				for (int j = 0; j < grid.GetLength(1); j++) {
					sb.Append(grid[i, j]);
					sb.Append(" ");
				}
				sb.AppendLine();
			}
			Console.WriteLine(sb.ToString());
		}
		[Conditional("DEBUG")]
		protected void DumpDP<T>(T[,] dp) where T : IFormattable {
			var sb = new StringBuilder();
			for (int i = 0; i < dp.GetLength(0); i++) {
				for (int j = 0; j < dp.GetLength(1); j++) {
					sb.Append(dp[i, j]);
					sb.Append(", ");
				}
				sb.AppendLine();
			}
			Console.WriteLine(sb.ToString());
		}
	}
}