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 (2.7.6) (judge verdict: Accepted)

def findNextAnimal(oxList, swList, index):
    nextAns = oxList[index]
    before = swList[index-1]
    animal = swList[index]
    nextAnimal = ""
    if(nextAns == "o" and before == "S" and animal == "S"):
        nextAnimal = "S"
    elif(nextAns == "o" and before == "S" and animal == "W"):
        nextAnimal = "W"
    elif(nextAns == "o" and before == "W" and animal == "S"):
        nextAnimal = "W"
    elif(nextAns == "o" and before == "W" and animal == "W"):
        nextAnimal = "S"
    elif(nextAns == "x" and before == "S" and animal == "S"):
        nextAnimal = "W"
    elif(nextAns == "x" and before == "S" and animal == "W"):
        nextAnimal = "S"
    elif(nextAns == "x" and before == "W" and animal == "S"):
        nextAnimal = "S"
    elif(nextAns == "x" and before == "W" and animal == "W"):
        nextAnimal = "W"
    return nextAnimal

def checkList(oxList, swList):
    ans = 0
    if(swList[-1] == "S"):
        if(oxList[-1] == "x" and swList[-2] != swList[0]):
            ans = 1
        elif(oxList[-1] == "o" and swList[-2] == swList[0]):
            ans = 1
    elif(swList[-1] == "W"):
        if(oxList[-1] == "x" and swList[-2] == swList[0]):
            ans = 1
        elif(oxList[-1] == "o" and swList[-2] != swList[0]):
            ans = 1
            
    ans2 = 0    
    if(swList[0] == "S"):
        if(oxList[0] == "x" and swList[1] != swList[-1]):
            ans2 = 1
        elif(oxList[0] == "o" and swList[1] == swList[-1]):
            ans2 = 1
    elif(swList[0] == "W"):
        if(oxList[0] == "x" and swList[1] == swList[-1]):
            ans2 = 1
        elif(oxList[0] == "o" and swList[1] != swList[-1]):
            ans2 = 1
    
    return ans*ans2

try:
    while True:  
        n = raw_input().strip().upper()
        oxList = raw_input().strip().lower()
        ans = -1
        for s0 in ["S", "W"]:
            for s1 in ["S","W"]:
                swList = [0]*int(n)
                swList[0] = s0
                swList[1] = s1
                for i in range(2, int(n)):
                    nextAnimal = findNextAnimal(oxList, swList, i-1)
                    swList[i] = nextAnimal
                    flag = checkList(oxList, swList)
                    if(flag == 1):
                        ans = ""
                        for s in swList:
                            ans += s
        print ans
                        
except EOFError:
    pass