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 Python (3.4.3) (judge verdict: Accepted)

N = int(input())
s = input()

pat1 = [-1] * N
pat2 = [-1] * N
pat3 = [-1] * N
pat4 = [-1] * N

pat1[1] = pat2[1] = 1
pat3[1] = pat4[1] = 0

if s[1] == 'o':
	pat1[0] = pat1[2] = 0
	pat2[0] = pat2[2] = 1
	pat3[0] = pat4[2] = 0
	pat3[2] = pat4[0] = 1

else:
	pat1[0] = pat2[2] = 0
	pat2[0] = pat1[2] = 1
	pat3[0] = pat3[2] = 0
	pat4[2] = pat4[0] = 1


#print([pat1,pat2,pat3,pat4])

for i in range(2,N-1):
	for lis in [pat1,pat2,pat3,pat4]:
		if lis[i] == 1:
			if s[i] == 'o':
				lis[i+1] = lis[i-1]

			else:
				lis[i+1] = (lis[i-1] + 1)%2
		else:
			if s[i] == 'x':
				lis[i+1] = lis[i-1]

			else:
				lis[i+1] = (lis[i-1] + 1)%2

#print([pat1,pat2,pat3,pat4])

def ok1(List):
	global s
	if List[N-1] == 1:
		if s[N-1] == 'o':
			return List[N-2] == List[0]
		else:
			return List[N-2] != List[0]

	else:
		if s[N-1] == 'x':
			return List[N-2] == List[0]
		else:
			return List[N-2] != List[0]

def ok2(List):
	global s
	if List[0] == 1:
		if s[0] == 'o':
			return List[N-1] == List[1]
		else:
			return List[N-1] != List[1]

	else:
		if s[0] == 'x':
			return List[N-1] == List[1]
		else:
			return List[N-1] != List[1]





flg = []
for lis in [pat1,pat2,pat3,pat4]:
	if ok1(lis) and ok2(lis):
		flg = lis
		break
	
#print(flg)
ans = ""
if flg != []:
	for num in flg:
		if num ==  0:
			ans += 'W'
		else:
			ans += 'S'

	print(ans)

else:
	print(-1)