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>
#include<stdlib.h>
#include<string.h>
#include<math.h>
 
#define sl(x) scanf("%ld", &x)
#define ss(x) scanf("%s", x)
#define pl(x) printf("%ld\n", x)
#define pd(x) printf("%lf\n", x)
#define ps(x) printf("%s\n", x)
 
#define INF 1000000000000000000
#define MOD 1000000007
 
#define MIN(a,b) (((a)<(b))?(a):(b))
#define MAX(a,b) (((a)>(b))?(a):(b))

long N, M;
long a[300001];
char s[100010];
long i, j;
char ans[100010];
long pre, next;

int compare_long(const void *a, const void *b) {
	return *(long*)a - *(long*)b;
}

int solve_right() {
	for(i=0;i<N-2;i++) {
		pre = (i + N - 1) % N;
		next = i + 1;
		if(ans[i] == 'S') {
			if(s[i] == 'o' && ans[pre] != ans[next]) {
				ans[next] = ans[pre];
			}
			if(s[i] == 'x' && ans[pre] == ans[next]) {
				ans[next] = ans[next] == 'S' ? 'W' : 'S';
			}
		} else {
			if(s[i] == 'o' && ans[pre] == ans[next]) {
				ans[next] = ans[next] == 'S' ? 'W' : 'S';
			}
			if(s[i] == 'x' && ans[pre] != ans[next]) {
				ans[next] = ans[pre];
			}
		}
	}
	if(ans[N-1] == 'S') {
		if(s[N-1] == 'o' && ans[N-2] == ans[0]) {
			ps(ans);
			return 1;
		}
		if(s[N-1] == 'x' && ans[N-2] != ans[0]) {
			ps(ans);
			return 1;
		}
	} else {
		if(s[N-1] == 'o' && ans[N-2] != ans[0]) {
			ps(ans);
			return 1;
		}
		if(s[N-1] == 'x' && ans[N-2] == ans[0]) {
			ps(ans);
			return 1;
		}
	}
	
	return 0;
}

int solve_right2() {
	for(i=0;i<N-2;i++) {
		pre = i + 1;
		next = (i + N - 1) % N;
		if(ans[i] == 'S') {
			if(s[i] == 'o' && ans[pre] != ans[next]) {
				ans[next] = ans[pre];
			}
			if(s[i] == 'x' && ans[pre] == ans[next]) {
				ans[next] = ans[next] == 'S' ? 'W' : 'S';
			}
		} else {
			if(s[i] == 'o' && ans[pre] == ans[next]) {
				ans[next] = ans[next] == 'S' ? 'W' : 'S';
			}
			if(s[i] == 'x' && ans[pre] != ans[next]) {
				ans[next] = ans[pre];
			}
		}
	}
	if(ans[N-1] == 'S') {
		if(s[N-1] == 'o' && ans[N-2] == ans[0]) {
			ps(ans);
			return 1;
		}
		if(s[N-1] == 'x' && ans[N-2] != ans[0]) {
			ps(ans);
			return 1;
		}
	} else {
		if(s[N-1] == 'o' && ans[N-2] != ans[0]) {
			ps(ans);
			return 1;
		}
		if(s[N-1] == 'x' && ans[N-2] == ans[0]) {
			ps(ans);
			return 1;
		}
	}
	
	return 0;
}

int solve_left() {
	for(i=N-1;i>1;i--) {
		pre = (i + 1) % N;
		next = i - 1;
		if(ans[i] == 'S') {
			if(s[i] == 'o' && ans[pre] != ans[next]) {
				ans[next] = ans[pre];
			}
			if(s[i] == 'x' && ans[pre] == ans[next]) {
				ans[next] = ans[next] == 'S' ? 'W' : 'S';
			}
		} else {
			if(s[i] == 'o' && ans[pre] == ans[next]) {
				ans[next] = ans[next] == 'S' ? 'W' : 'S';
			}
			if(s[i] == 'x' && ans[pre] != ans[next]) {
				ans[next] = ans[pre];
			}
		}
	}
	if(ans[0] == 'S') {
		if(s[0] == 'o' && ans[N-1] == ans[1]) {
			ps(ans);
			return 1;
		}
		if(s[0] == 'x' && ans[N-1] != ans[1]) {
			ps(ans);
			return 1;
		}
	} else {
		if(s[0] == 'o' && ans[N-1] != ans[1]) {
			ps(ans);
			return 1;
		}
		if(s[0] == 'x' && ans[N-1] == ans[1]) {
			ps(ans);
			return 1;
		}
	}
	
	return 0;
}

int solve_left2() {
	for(i=N-1;i>1;i--) {
		pre = i - 1;
		next = (i + 1) % N;
		if(ans[i] == 'S') {
			if(s[i] == 'o' && ans[pre] != ans[next]) {
				ans[next] = ans[pre];
			}
			if(s[i] == 'x' && ans[pre] == ans[next]) {
				ans[next] = ans[next] == 'S' ? 'W' : 'S';
			}
		} else {
			if(s[i] == 'o' && ans[pre] == ans[next]) {
				ans[next] = ans[next] == 'S' ? 'W' : 'S';
			}
			if(s[i] == 'x' && ans[pre] != ans[next]) {
				ans[next] = ans[pre];
			}
		}
	}
	if(ans[0] == 'S') {
		if(s[0] == 'o' && ans[N-1] == ans[1]) {
			ps(ans);
			return 1;
		}
		if(s[0] == 'x' && ans[N-1] != ans[1]) {
			ps(ans);
			return 1;
		}
	} else {
		if(s[0] == 'o' && ans[N-1] != ans[1]) {
			ps(ans);
			return 1;
		}
		if(s[0] == 'x' && ans[N-1] == ans[1]) {
			ps(ans);
			return 1;
		}
	}
	
	return 0;
}

int main() {
	
	sl(N);
	ss(s);
	
	for(i=0;i<N;i++) ans[i] = 'S';
	ans[N] = '\0';
	
	if(solve_right()) return 0;
	
	for(i=0;i<N;i++) ans[i] = 'W';
	ans[N] = '\0';
	
	if(solve_right()) return 0;
	
	for(i=0;i<N;i++) ans[i] = 'S';
	ans[N] = '\0';
	
	if(solve_right2()) return 0;
	
	for(i=0;i<N;i++) ans[i] = 'W';
	ans[N] = '\0';
	
	if(solve_right2()) return 0;
	
	for(i=0;i<N;i++) ans[i] = 'S';
	ans[N] = '\0';
	
	if(solve_left()) return 0;
	
	for(i=0;i<N;i++) ans[i] = 'W';
	ans[N] = '\0';
	
	if(solve_left()) return 0;
	
	for(i=0;i<N;i++) ans[i] = 'S';
	ans[N] = '\0';
	
	if(solve_left2()) return 0;
	
	for(i=0;i<N;i++) ans[i] = 'W';
	ans[N] = '\0';
	
	if(solve_left2()) return 0;
	
	ps("-1");
	
	return 0;
}