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 PyPy3 (7.3.0) (judge verdict: Accepted)

import sys
# from collections import defaultdict, deque
# import math
# import copy
# from bisect import bisect_left, bisect_right
# import heapq

# sys.setrecursionlimit(1000000)

# input aliases
input = sys.stdin.readline

getS = lambda: input().strip()
getN = lambda: int(input())
getList = lambda: list(map(int, input().split()))
getZList = lambda: [int(x) - 1 for x in input().split()]

INF = 10 ** 20
MOD = 1000000007

def nt(n):
    if n == "1":
        return "0"
    else:
        return "1"

def check(seed, n, s):
    ans = seed
    for i in range(1, n):
        a, b = ans[-1], ans[-2]
        if int(s[i]) ^ int(b) == 0:
            ans.append(a)
        else:
            ans.append(nt(a))

    if ans[-1] != ans[0]:
        return []
    else:
        del(ans[-1])
        # print(ans)
        if int(s[0]) ^ int(ans[0]) == 0:
            if ans[-1] != ans[1]:
                return []
        else:
            if ans[-1] == ans[1]:
                return []

    return "".join(ans).replace("1", "S").replace("0", "W")

def solve():
    n = getN()
    S = getS()
    S = S.replace("o", "1").replace("x", "0")
    for seed in  [["1","1"], ["1","0"], ["0","1"], ["0","0"]]:
        ans = check(seed, n, S)
        if ans:
            print(ans)
            return

    print(-1)
    return

def main():
    n = getN()
    for _ in range(n):
        solve()
if __name__ == "__main__":
    # main()
    solve()