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 <bits/stdc++.h>
#define mp make_pair
#define eb emplace_back
#define fi first
#define se second
using namespace std;
using cd = complex <double>;
 
typedef pair <int, int> pii;
const int N = 3e3 + 5;
const long long INF = 1e18;
const int mod = 1e9 + 123;//786433;//998244353;
const double Pi = acos(-1);
const int p = 510200;
 
void Fastio()
{
	ios_base::sync_with_stdio(false);
	cin.tie(0);
	cout.tie(0);
}

int n;
char a[100005];
char b[100005];

signed main()
{
	Fastio();
	cin >> n;
	for(int i = 1; i <= n; i++)
	{
		cin >> a[i];
	}
	b[1] = 'S';
	b[2] = 'S';
	for(int i = 3; i <= n; i++)
	{
		if(b[i - 1] == 'S')
		{
			if(a[i - 1] == 'o')
			{
				b[i] = b[i - 2];
			}
			else
			{
				if(b[i - 2] == 'S')
				{
					b[i] = 'W';
				}
				else
				{
					b[i] = 'S';
				}
			}
		}
		else
		{
			if(a[i - 1] == 'x')
			{
				b[i] = b[i - 2];
			}
			else
			{
				if(b[i - 2] == 'S')
				{
					b[i] = 'W';
				}
				else
				{
					b[i] = 'S';
				}
			}
		}
	}
	if(b[n] == 'S')
	{
		if(a[n] == 'o')
		{
			if(b[n - 1] == b[1])
			{
				for(int i = 1; i <= n; i++)
				{
					cout << b[i];
				}
				return 0;
			}
		}
		else
		{
			if(b[n - 1] != b[1])
			{
				for(int i = 1; i <= n; i++)
				{
					cout << b[i];
				}
				return 0;
			}
		}
	}
	else
	{
		if(a[n] == 'o')
		{
			if(b[n - 1] != b[1])
			{
				for(int i = 1; i <= n; i++)
				{
					cout << b[i];
				}
				return 0;
			}
		}
		else
		{
			if(b[n - 1] == b[1])
			{
				for(int i = 1; i <= n; i++)
				{
					cout << b[i];
				}
				return 0;
			}
		}
	}
	b[1] = 'W';
	b[2] = 'S';
	for(int i = 3; i <= n; i++)
	{
		if(b[i - 1] == 'S')
		{
			if(a[i - 1] == 'o')
			{
				b[i] = b[i - 2];
			}
			else
			{
				if(b[i - 2] == 'S')
				{
					b[i] = 'W';
				}
				else
				{
					b[i] = 'S';
				}
			}
		}
		else
		{
			if(a[i - 1] == 'x')
			{
				b[i] = b[i - 2];
			}
			else
			{
				if(b[i - 2] == 'S')
				{
					b[i] = 'W';
				}
				else
				{
					b[i] = 'S';
				}
			}
		}
	}
	if(b[n] == 'S')
	{
		if(a[n] == 'o')
		{
			if(b[n - 1] == b[1])
			{
				for(int i = 1; i <= n; i++)
				{
					cout << b[i];
				}
				return 0;
			}
		}
		else
		{
			if(b[n - 1] != b[1])
			{
				for(int i = 1; i <= n; i++)
				{
					cout << b[i];
				}
				return 0;
			}
		}
	}
	else
	{
		if(a[n] == 'o')
		{
			if(b[n - 1] != b[1])
			{
				for(int i = 1; i <= n; i++)
				{
					cout << b[i];
				}
				return 0;
			}
		}
		else
		{
			if(b[n - 1] == b[1])
			{
				for(int i = 1; i <= n; i++)
				{
					cout << b[i];
				}
				return 0;
			}
		}
	}
	b[1] = 'S';
	b[2] = 'W';
	for(int i = 3; i <= n; i++)
	{
		if(b[i - 1] == 'S')
		{
			if(a[i - 1] == 'o')
			{
				b[i] = b[i - 2];
			}
			else
			{
				if(b[i - 2] == 'S')
				{
					b[i] = 'W';
				}
				else
				{
					b[i] = 'S';
				}
			}
		}
		else
		{
			if(a[i - 1] == 'x')
			{
				b[i] = b[i - 2];
			}
			else
			{
				if(b[i - 2] == 'S')
				{
					b[i] = 'W';
				}
				else
				{
					b[i] = 'S';
				}
			}
		}
	}
	if(b[n] == 'S')
	{
		if(a[n] == 'o')
		{
			if(b[n - 1] == b[1])
			{
				for(int i = 1; i <= n; i++)
				{
					cout << b[i];
				}
				return 0;
			}
		}
		else
		{
			if(b[n - 1] != b[1])
			{
				for(int i = 1; i <= n; i++)
				{
					cout << b[i];
				}
				return 0;
			}
		}
	}
	else
	{
		if(a[n] == 'o')
		{
			if(b[n - 1] != b[1])
			{
				for(int i = 1; i <= n; i++)
				{
					cout << b[i];
				}
				return 0;
			}
		}
		else
		{
			if(b[n - 1] == b[1])
			{
				for(int i = 1; i <= n; i++)
				{
					cout << b[i];
				}
				return 0;
			}
		}
	}
	b[1] = 'W';
	b[2] = 'W';
	for(int i = 3; i <= n; i++)
	{
		if(b[i - 1] == 'S')
		{
			if(a[i - 1] == 'o')
			{
				b[i] = b[i - 2];
			}
			else
			{
				if(b[i - 2] == 'S')
				{
					b[i] = 'W';
				}
				else
				{
					b[i] = 'S';
				}
			}
		}
		else
		{
			if(a[i - 1] == 'x')
			{
				b[i] = b[i - 2];
			}
			else
			{
				if(b[i - 2] == 'S')
				{
					b[i] = 'W';
				}
				else
				{
					b[i] = 'S';
				}
			}
		}
	}
	if(b[n] == 'S')
	{
		if(a[n] == 'o')
		{
			if(b[n - 1] == b[1])
			{
				for(int i = 1; i <= n; i++)
				{
					cout << b[i];
				}
				return 0;
			}
		}
		else
		{
			if(b[n - 1] != b[1])
			{
				for(int i = 1; i <= n; i++)
				{
					cout << b[i];
				}
				return 0;
			}
		}
	}
	else
	{
		if(a[n] == 'o')
		{
			if(b[n - 1] != b[1])
			{
				for(int i = 1; i <= n; i++)
				{
					cout << b[i];
				}
				return 0;
			}
		}
		else
		{
			if(b[n - 1] == b[1])
			{
				for(int i = 1; i <= n; i++)
				{
					cout << b[i];
				}
				return 0;
			}
		}
	}
	cout << -1;
}