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 (GCC 5.4.1) (judge verdict: Runtime Error)

#include <stdio.h>
char s[4][11111];
char s1[11111];
int n;
int i, j, k;
int flag;
int pp()
{
	for (i = 1; i < n-1; i++)
	{
		if (s1[i] == 'o')
		{
			if (s[k][i - 1] == 'W'&&s[k][i] == 'S')
			{
				if (i + 1 != n - 1)
				{
					s[k][i + 1] = 'W';
				}
				else
				{
					if (s[k][i + 1] != 'W')
					{
						return 0;
						break;
					}
				}
			}
			else if (s[k][i - 1] == 'S'&&s[k][i] == 'S')
			{
				if (i + 1 != n - 1)
				{
					s[k][i + 1] = 'S';
				}
				else
				{
					if (s[k][i + 1] != 'S')
					{
						return 0;
						break;
					}
				}
			}
			else if (s[k][i - 1] == 'S'&&s[k][i] == 'W')
			{
				if (i + 1 != n - 1)
				{
					s[k][i + 1] = 'W';
				}
				else
				{
					if (s[k][i + 1] != 'W')
					{
						return 0;
						break;
					}
				}
			}
			else if (s[k][i - 1] == 'W'&&s[k][i] == 'W')
			{
				if (i + 1 != n - 1)
				{
					s[k][i + 1] = 'S';
				}
				else
				{
					if (s[k][i + 1] != 'S')
					{
						return 0;
						break;
					}
				}
			}
		}
		else
		{
			if (s[k][i - 1] == 'S'&&s[k][i] == 'S')
			{
				if (i + 1 != n - 1)
				{
					s[k][i + 1] = 'W';
				}
				else
				{
					if (s[k][i + 1] != 'W')
					{
						return 0;
						break;
					}
				}
			}
			else if (s[k][i - 1] == 'W'&&s[k][i] == 'S')
			{
				if (i + 1 != n - 1)
				{
					s[k][i + 1] = 'S';
				}
				else
				{
					if (s[k][i + 1] != 'S')
					{
						return 0;
						break;
					}
				}
			}
			else if (s[k][i - 1] == 'S'&&s[k][i] == 'W')
			{
				if (i + 1 != n - 1)
				{
					s[k][i + 1] = 'S';
				}
				else
				{
					if (s[k][i + 1] != 'S')
					{
						return 0;
						break;
					}
				}
			}
			else if (s[k][i - 1] == 'W'&&s[k][i] == 'W')
			{
				if (i + 1 != n - 1)
				{
					s[k][i + 1] = 'W';
				}
				else
				{
					if (s[k][i + 1] != 'W')
					{
						return 0;
						break;
					}
				}
			}
		}
	}
	if (s1[n - 1] == 'o')
	{
		if (s[k][n - 2] == 'S'&&s[k][n - 1] == 'S')
		{
			if (s[k][0] != 'S')
			{
				return 0;
			}
		}
		else if (s[k][n - 2] == 'W'&&s[k][n - 1] == 'S')
		{
			if (s[k][0] != 'W')
			{
				return 0;
			}
		}
		else if (s[k][n - 2] == 'S'&&s[k][n - 1] == 'W')
		{
			if (s[k][0] != 'W')
			{
				return 0;
			}
		}
		else if (s[k][n - 2] == 'W'&&s[k][n - 1] == 'W')
		{
			if (s[k][0] != 'S')
			{
				return 0;
			}
		}
	}
	else
	{
		if (s[k][n - 2] == 'W'&&s[k][n - 1] == 'S')
		{
			if (s[k][0] != 'S')
			{
				return 0;
			}
		}
		else if (s[k][n - 2] == 'S'&&s[k][n - 1] == 'S')
		{
			if (s[k][0] != 'W')
			{
				return 0;
			}
		}
		else if (s[k][n - 2] == 'S'&&s[k][n - 1] == 'W')
		{
			if (s[k][0] != 'S')
			{
				return 0;
			}
		}
		else if (s[k][n - 2] == 'W'&&s[k][n - 1] == 'W')
		{
			if (s[k][0] != 'W')
			{
				return 0;
			}
		}
	}
	return 1;
}
int main()
{
	int a1, a2, a3, a4;
	while (~scanf("%d", &n))
	{
		flag = 0;
		scanf("%s", s1);
		k = 0;
		if (s1[0] == 'o')
		{
			s[k][0] = 'S', s[k][1] = 'W', s[k][n - 1] = 'W';
			a1 = pp(); k++;
			s[k][0] = 'W', s[k][1] = 'W', s[k][n - 1] = 'S';
			a2 = pp(); k++;
			s[k][0] = 'W', s[k][1] = 'S', s[k][n - 1] = 'W';
			a3 = pp(); k++;
			s[k][0] = 'S', s[k][1] = 'S', s[k][n - 1] = 'S';
			a4 = pp(); k++;
		}
		else
		{
			s[k][0] = 'S', s[k][1] = 'S', s[k][n - 1] = 'W';
			a1 = pp(); k++;
			s[k][0] = 'S', s[k][1] = 'W', s[k][n - 1] = 'S';
			a2 = pp(); k++;
			s[k][0] = 'W', s[k][1] = 'S', s[k][n - 1] = 'S';
			a3 = pp(); k++;
			s[k][0] = 'W', s[k][1] = 'W', s[k][n - 1] = 'W';
			a4 = pp(); k++;
		}
		if (a1 == 1 || a2 == 1 || a3 == 1 || a4 == 1)
		{
			if (a1 == 1)
			{
				printf("%s\n", s[0]);
			}
			else if (a2 == 1)
			{
				printf("%s\n", s[1]);
			}
			else if (a3 == 1)
			{
				printf("%s\n", s[2]);
			}
			else if (a4 == 1)
			{
				printf("%s\n", s[3]);
			}
		}
		else
		{
			printf("-1\n");
		}
	}
	return 0;
}