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: Accepted)

#include<stdio.h>


enum
{
	SSx,
	SWx,
	WSx,
	WWx,
};


int inv(char c)
{
	if(c=='S') return 'W';
	return 'S';
}


int solve(char *s, char *r, int n)
{
	int i;

	for(i=1;i<n;i++)
	{
		if(s[i]=='o')
		{
			if(r[i]=='S')
			{
				r[i+1]=r[i-1];
			}
			else
			{
				r[i+1]=inv(r[i-1]);
			}
		}
		else
		{
			if(r[i]=='S')
			{
				r[i+1]=inv(r[i-1]);
			}
			else
			{
				r[i+1]=r[i-1];
			}
		}
	}
	if(r[0]!=r[n]) return 0;

	if(r[0]=='S')
	{
		if(s[0]=='o') return (r[n-1]==r[1]);
		else return (r[n-1]==inv(r[1]));
	}
	else
	{
		if(s[0]=='o') return (r[n-1]==inv(r[1]));
		else return (r[n-1]==r[1]);
	}
}


int main(void)
{
	int N;
	static char s[100000+1];
	static char r[100000+2];

	while(scanf("%d%100000s", &N, s)==2)
	{
		r[N]='\0';

		r[0]=r[1]='S';
		if(solve(s, r, N))
		{
			r[N]='\0';
			printf("%s\n", r);
			continue;
		}
		r[0]='S';
		r[1]='W';
		if(solve(s, r, N))
		{
			r[N]='\0';
			printf("%s\n", r);
			continue;
		}
		r[0]='W';
		r[1]='S';
		if(solve(s, r, N))
		{
			r[N]='\0';
			printf("%s\n", r);
			continue;
		}
		r[0]='W';
		r[1]='W';
		if(solve(s, r, N))
		{
			r[N]='\0';
			printf("%s\n", r);
			continue;
		}
		printf("-1\n");
	}

	return 0;
}