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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>
int main()
{

	int n = 0, i, j, k;
	char ans[100005] = { 0 };
	// スペース区切りの整数の入力
	scanf("%d", &n);
	char s[100005];
	scanf("%s", s);
	for (j = 0; j < 4; j++)
	{

		switch (j) {
		case 0:
			ans[0] = 'S';
			ans[1] = 'S';
			break;
		case 1:
			ans[0] = 'S';
			ans[1] = 'W';
			break;
		case 2:
			ans[0] = 'W';
			ans[1] = 'S';
			break;
		case 3:
			ans[0] = 'W';
			ans[1] = 'W';
			break;

		}
		for (i = 0; i < n; i++)
		{
			if (ans[i+1] == 'S')
			{
				if (s[(i+1)%n] == 'o')
				{
					ans[i+2] = ans[i+0];
				}
				else
				{
					if (ans[i+0] == 'S')
					{
						ans[i+2] = 'W';
					}
					else
					{
						ans[i+2] = 'S';
					}
				}
			}
			else
			{
				if (s[(i+1)%n] == 'x')
				{
					ans[i+2] = ans[i+0];
				}
				else
				{
					if (ans[i+0] == 'S')
					{
						ans[i+2] = 'W';
					}
					else
					{
						ans[i+2] = 'S';
					}
				}

			}
			/*
			if (ans[i] == 'S'&&s[i + 1] == 'o')
			{

			}
			if (s[i + 1] == 'o')
			{

			}
			*/
		}
		if ((ans[0] == ans[n])&&(ans[1]==ans[n+1]))
		{
			for (i = 0; i < n; i++)
			{
				printf("%c", ans[i]);
			}
			return 0;
		}
		if (j == 3)
		{
			printf("-1");
			return 0;
		}
		printf("%s\n", ans);
	}

	// 出力
	return 0;
}