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: Wrong Answer)

#include <stdio.h>

int main(void)
{
	int n, i, j, v;
	char k[114514];
	char a[114514];
	scanf("%d", &n);
	scanf("%s", &k);

	for(i = 0; i < n; i++)
	{
		k[i] = (k[i] == 'o');
	}

	k[n] = k[0];

	for(a[1] = 'S'; a[1] != 'W'; a[1] = 'W')
	{
		for(a[0] = 'S'; a[0] != 'W'; a[0] = 'W')
		{
			a[n] = a[0];
			for(j = 0; j < n - 2; j++)
			{
				if((a[j + 1] == 'S' && k[j + 1]) ||
						(a[j + 1] == 'W' && !k[j + 1])
				)
				{
					a[j + 2] = a[j];
				}
				else
				{
					a[j + 2] = (a[j] == 'S' ? 'W' : 'S');
				}
			}

			if((a[n - 1] == 'S' && k[n - 1]) || (a[n - 1] == 'W' && !k[n - 1]))
			{
				if(a[n - 2] == a[n])
				{
					for(v = 0; v < n; v++)
					{
						printf("%c", a[v]);
					}
					return 0;
				}
			}
			else
			{
				if(a[n - 2] != a[n])
				{
					for(v = 0; v < n; v++)
					{
						printf("%c", a[v]);
					}
					return 0;
				}
			}
		}
	}
	printf("-1");
	return 0;
}