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 (3.8.2) (judge verdict: Wrong Answer)

import sys

read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

in_n = lambda: int(readline())
in_nn = lambda: map(int, readline().split())
in_s = lambda: readline().rstrip().decode('utf-8')
in_nl = lambda: list(map(int, readline().split()))
in_nl2 = lambda H: [in_nl() for _ in range(H)]
in_map = lambda: [s == ord('o') for s in readline() if s != ord('\n')]
in_map2 = lambda H: [in_map() for _ in range(H)]
in_all = lambda: map(int, read().split())


def solve(N, S, ans):

    for i in range(N - 2):
        if S[i]:
            if ans[i] == 0 and ans[i - 1] == 0:
                ans[i + 1] = 0
            elif ans[i] == 0 and ans[i - 1] == 1:
                ans[i + 1] = 1
            elif ans[i] == 1 and ans[i - 1] == 0:
                ans[i + 1] = 1
            elif ans[i] == 1 and ans[i - 1] == 1:
                ans[i + 1] = 0
        else:
            if ans[i] == 0 and ans[i - 1] == 0:
                ans[i + 1] = 1
            elif ans[i] == 0 and ans[i - 1] == 1:
                ans[i + 1] = 0
            elif ans[i] == 1 and ans[i - 1] == 0:
                ans[i + 1] = 0
            elif ans[i] == 1 and ans[i - 1] == 1:
                ans[i + 1] = 1

    ret = True
    for i in range(N - 1, N):

        if S[i]:
            if ans[i] == 0 and ans[i - 1] == 0:
                ret &= ans[(i + 1) % N] == 0
            elif ans[i] == 0 and ans[i - 1] == 1:
                ret &= ans[(i + 1) % N] == 1
            elif ans[i] == 1 and ans[i - 1] == 0:
                ret &= ans[(i + 1) % N] == 1
            elif ans[i] == 1 and ans[i - 1] == 1:
                ret &= ans[(i + 1) % N] == 0
        else:
            if ans[i] == 0 and ans[i - 1] == 0:
                ret &= ans[(i + 1) % N] == 1
            elif ans[i] == 0 and ans[i - 1] == 1:
                ret &= ans[(i + 1) % N] == 0
            elif ans[i] == 1 and ans[i - 1] == 0:
                ret &= ans[(i + 1) % N] == 0
            elif ans[i] == 1 and ans[i - 1] == 1:
                ret &= ans[(i + 1) % N] == 1

    return ret


def main():

    N = in_n()
    S = in_map()

    pattern = [(0, 0), (0, 1), (1, 0), (1, 1)]

    for p in pattern:
        ans = [0] * N
        ans[0], ans[-1] = p[0], p[1]
        if(solve(N, S, ans)):
            p = ''
            for i in range(N):
                if ans[i] == 0:
                    p += 'S'
                else:
                    p += 'W'
            print(p)
            exit()
    else:
        print(-1)


if __name__ == '__main__':
    main()