200691: [AtCoder]ARC069 D - Menagerie

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