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: Wrong Answer)

def check(s,ans_d):
	for i in range(1,len(s)):
		if ans_d[i]=="S":
			if s[i]=="o":
				ans_d+=ans_d[i-1]
			else:
				if ans_d[i-1]=="S":
					ans_d+="W"
				else:
					ans_d+="S"
		else:
			if s[i]=="x":
				ans_d+=ans_d[i-1]
			else:
				if ans_d[i-1]=="S":
					ans_d+="W"
				else:
					ans_d+="S"
	#check index=-1
	if ans_d[-1]==ans_d[0]:
		if ans_d[0]=="S":
			if s[0]=="o":
				if s[1]==s[-1]:
					return ans_d
			else:
				if s[1]!=s[-1]:
					return ans_d
		else:
			if s[0]=="x":
				if s[1]==s[-1]:
					return ans_d
			else:
				if s[1]!=s[-1]:
					return ans_d
	return False

N=int(input())
s=input()
flag=False

ans=check(s,"SS")
if ans==False and flag==False:
	ans=check(s,"SW")
else:
	flag=True
if ans==False and flag==False:
	ans=check(s,"WS")
else:
	flag=True
if ans==False and flag==False:
	ans=check(s,"WW")
else:
	flag=True

if flag==False:
	print("-1")
else:
	print(ans[0:-1])