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)

# -*- coding: utf-8 -*-
n = int(input())
s = input()

def check(l):
    if s[0]=="o":
        if l[0]=="S":
            if l[-1]!=l[1]:
                return False
        else:
            if l[-1]==l[1]:
                return False
    else:
        if l[0]=="S":
            if l[-1]==l[1]:
                return False
        else:
            if l[-1]!=l[1]:
                return False
    for i in range(1,n-1):
        if s[i]=="o":
            if l[i]=="S":
                if l[i-1]!=l[i+1]:
                    return False
            else:
                if l[i-1]==l[i+1]:
                    return False
        else:
            if l[i]=="S":
                if l[i-1]==l[i+1]:
                    return False
            else:
                if l[i-1]!=l[i+1]:
                    return False
    if s[n-1]=="o":
        if l[n-1]=="S":
            if l[n-2]!=l[0]:
                return False
        else:
            if l[n-2]==l[0]:
                return False
    else:
        if l[n-1]=="S":
            if l[n-2]==l[0]:
                return False
        else:
            if l[n-2]!=l[0]:
                return False
    return True

def flip(x):
    if x=="S":
        return "W"
    else:
        return "S"

def fill(s0,s1):
    ret = [None for _ in range(n)]
    ret[0] = s0
    ret[1] = s1
    for i in range(1,n-1):
        if ret[i]=="S" and s[i]=="o":
            ret[i+1] = ret[i-1]
        elif ret[i]=="S" and s[i]=="x":
            ret[i+1] = flip(ret[i-1])
        elif ret[i]=="W" and s[i]=="o":
            ret[i+1] = flip(ret[i-1])
        elif ret[i]=="W" and s[i]=="x":
            ret[i+1] = ret[i-1]
    # print(ret)
    if check(ret):
        return ret
    else:
        return None

ret = fill("S","S")
if ret is not None:
    print("".join(ret))
    exit()

ret = fill("S","W")
if ret is not None:
    print("".join(ret))
    exit()

ret = fill("W","S")
if ret is not None:
    print("".join(ret))
    exit()

ret = fill("W","W")
if ret is not None:
    print("".join(ret))
    exit()
print(-1)