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 (2.4.0) (judge verdict: Accepted)

N = int(input())
S = input()

isF = [False for i in range(N)]
isT = [False for i in range(N)]

def isSatisfied():
    for i in range(2, N+2):
        different = (S[(i - 1) % N] == "x" and isT[(i - 1) % N]) or (S[(i - 1) % N] == "o" and isF[(i - 1) % N])
        if different:
            isF[i % N] |= not isF[(i-2) % N]
            isT[i % N] |= not isT[(i-2) % N]
        else:
            isF[i % N] |= isF[(i-2) % N]
            isT[i % N] |= isT[(i-2) % N]
    for j in range(2, N+2):
        i = 1-i
        different = (S[(i + 1) % N] == "x" and isT[(i + 1) % N]) or (S[(i + 1) % N] == "o" and isF[(i + 1) % N])
        if different:
            isF[i % N] |= not isF[(i+2) % N]
            isT[i % N] |= not isT[(i+2) % N]
        else:
            isF[i % N] |= isF[(i+2) % N]
            isT[ i% N] |= isT[(i+2) % N]
    for i in range(N):
        if isF[i] and isT[i]: return False
    return True

for a in [False, True]:
    for b in [False, True]:
        isF = [False for i in range(N)]
        isT = [False for i in range(N)]
        isF[0] = a
        isT[0] = not a
        isF[1] = b
        isT[1] =  not b
        if isSatisfied():
            print("".join(["S" if isT[i] else "W" for i in range(N)]))
            quit()
print(-1)