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: Wrong Answer)


local sub = string.sub
local n = io.read('*n', '*l')
local s = io.read('*l')
ss = {}
for i = 1, n do
	ss[i] = sub(s, i, i)
end
local ret = {
	{[1] = 1, [2] = 1},
	{[1] = 1, [2] = 0},
	{[1] = 0, [2] = 0},
	{[1] = 0, [2] = 1},
}
for i = 2, n-1 do
	for j = 1, 4 do
		local ans = ret[j]
		ans[i + 1] = ((ss[i] == 'o') == (ans[i] == 1)) and ans[i - 1] or 1 - ans[i - 1]
	end
end

local function isOK(a, b, c, ch)
	return ((ch == 'o') == (b == 1)) and (a == c) or (a ~= c)
end

local sum = 0
local result = nil
for j = 1, 4 do
	local ans = ret[j]
	if isOK(ans[n], ans[1], ans[2], ss[1]) and isOK(ans[n-1], ans[n], ans[1], ss[n]) then
		sum = sum  + 1
		result = ans
		break
	end
end

if sum >= 1 then
	for i = 1, n do
		result[i] = result[i] == 1 and "S" or "W"
	end
	print(table.concat(result))
else
	print(-1)
end