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 Lua (5.3.2) (judge verdict: Accepted)

n = io.read('*n')
_, str = io.read('*l'), io.read('*l')

function b2i(b) if b then return 1 else return 0 end end
function check(s1, s2)
    local s = { s1, s2 }
    for i = 3, n do
        s[i] = s[i - 1] ~ s[i - 2] ~ b2i(str:sub(i - 1, i - 1) == 'x')
    end
    if s1 == (s[n] ~ s[n - 1] ~ b2i(str:sub(n, n) == 'x')) and
        s2 == (s[1] ~ s[n] ~ b2i(str:sub(1, 1) == 'x'))
    then
        return s
    end
end
function print_tab(t)
    for i = 1, #t do if t[i] == 0 then io.write('S') else io.write('W') end end
    io.write('\n')
end

s = check(0, 0); if s ~= nil then print_tab(s) return end
s = check(0, 1); if s ~= nil then print_tab(s) return end
s = check(1, 0); if s ~= nil then print_tab(s) return end
s = check(1, 1); if s ~= nil then print_tab(s) return end
print('-1')