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>
#include <string.h>

int N;
char s[112345];
char temp[112345];
bool Is_ans_flag = true;
char ans[112345] = "-1";

void f(int pos, char string[])
{
	if (strcmp(ans, "-1") != 0)
	{
		return;
	}
	if (pos >= N)
	{
		Is_ans_flag = true;
		for (int seek = 1; seek < N; ++seek)
		{
			if (s[seek] == 'o')
			{
				if (string[seek] == 'S')
				{
					if (string[(seek - 1) % N] != string[(seek + 1) % N])
					{
						Is_ans_flag = false;
						break;
					}
				}
				if (string[seek] == 'W')
				{
					if (string[(seek - 1) % N] == string[(seek + 1) % N])
					{
						Is_ans_flag = false;
						break;
					}
				}
			}
			if (s[seek] == 'x')
			{
				if (string[seek] == 'S')
				{
					if (string[(seek - 1) % N] == string[(seek + 1) % N])
					{
						Is_ans_flag = false;
						break;
					}
				}
				if (string[seek] == 'W')
				{
					if (string[(seek - 1) % N] != string[(seek + 1) % N])
					{
						Is_ans_flag = false;
						break;
					}
				}
			}
		}
		if (Is_ans_flag == true)
		{
			strcpy(ans, string);
			return;
		}
	}
	else
	{
		for (int seek = 1; seek < pos; ++seek)
		{
			if (s[seek] == 'o')
			{
				if (string[seek] == 'S')
				{
					if (string[(seek - 1) % N] != string[(seek + 1) % N])
					{
						Is_ans_flag = false;
						return;
					}
				}
				if (string[seek] == 'W')
				{
					if (string[(seek - 1) % N] == string[(seek + 1) % N])
					{
						Is_ans_flag = false;
						return;
					}
				}
			}
			if (s[seek] == 'x')
			{
				if (string[seek] == 'S')
				{
					if (string[(seek - 1) % N] == string[(seek + 1) % N])
					{
						Is_ans_flag = false;
						return;
					}
				}
				if (string[seek] == 'W')
				{
					if (string[(seek - 1) % N] != string[(seek + 1) % N])
					{
						Is_ans_flag = false;
						return;
					}
				}
			}
		}
		if (s[pos] == 'o')
		{
			temp[(pos - 1) % N] = 'S', temp[pos] = 'S', temp[(pos + 1) % N] = 'S';
			f(pos + 2, temp);
			temp[(pos - 1) % N] = 'W', temp[pos] = 'S', temp[(pos + 1) % N] = 'W';
			f(pos + 2, temp);
			temp[(pos - 1) % N] = 'S', temp[pos] = 'W', temp[(pos + 1) % N] = 'W';
			f(pos + 2, temp);
			temp[(pos - 1) % N] = 'W', temp[pos] = 'W', temp[(pos + 1) % N] = 'S';
			f(pos + 2, temp);
		}
		if (s[pos] == 'x')
		{
			temp[(pos - 1) % N] = 'S', temp[pos] = 'S', temp[(pos + 1) % N] = 'W';
			f(pos + 2, temp);
			temp[(pos - 1) % N] = 'W', temp[pos] = 'S', temp[(pos + 1) % N] = 'S';
			f(pos + 2, temp);
			temp[(pos - 1) % N] = 'S', temp[pos] = 'W', temp[(pos + 1) % N] = 'S';
			f(pos + 2, temp);
			temp[(pos - 1) % N] = 'W', temp[pos] = 'W', temp[(pos + 1) % N] = 'W';
			f(pos + 2, temp);
		}
	}
}

int main(void)
{
	scanf("%d%s", &N, s);
	f(1, "");
	printf("%s\n", ans);
	return 0;
}