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



Sample input:
6
ooxoox


Sample output:
SSSWWS

Submission status: Runtime Error

Solution code:
import itertools
N = int(input())
s = list(map(lambda x: True if x == "o" else False, list(input())))

# N = 6
# s = "ooxoox"
# N = 3
# s = "oox"
s = [True, True, False]

def hantei(N,s):
    f = lambda x,y: not(x^y)
    for onetwo in itertools.product((True, False), (True, False)):
        res = {}
        for n in range(N):
            if n == 0:
                res[n] = onetwo[0]
            elif n == 1:
                res[n] = onetwo[1]
            else:
                res[n] = f(res[n-2], f(res[n-1], s[n-1]))
        # check s[0]
        if not ((res[1] == res[N-1]) ^ res[0]) == s[0]:
            if not ((res[0] == res[N-2]) ^ res[N-1]) == s[N-1]:
                print(''.join(map(lambda x: "S" if x == 0 else "W", res.values())))
                return True

    return False

if not hantei(N, s):
    print(-1)

Submission status: Runtime Error

Solution code:
SHEEP = True
WOLF = False


def print_tree(tree):
    print(''.join(['S' if e else 'W' for e in tree]))


def calc_next_animal(tree, cur_pos):
    if answer[cur_pos]:
        if tree[cur_pos] == SHEEP:
            return tree[cur_pos - 1]
        else:
            return not tree[cur_pos - 1]
    else:
        if tree[cur_pos] == SHEEP:
            return not tree[cur_pos - 1]
        else:
            return tree[cur_pos - 1]


def calc_prev_animal(tree, cur_pos):
    if answer[cur_pos]:
        if tree[cur_pos] == SHEEP:
            return tree[cur_pos + 1]
        else:
            return not tree[cur_pos + 1]
    else:
        if tree[cur_pos] == SHEEP:
            return not tree[cur_pos + 1]
        else:
            return tree[cur_pos + 1]


def wfs(tree, cur_pos, N):
    tree[cur_pos + 1] = calc_next_animal(tree, cur_pos)
    cur_pos += 1
    if cur_pos == N - 1:
        return tree[0] == calc_next_animal(tree, cur_pos) and tree[cur_pos] == calc_prev_animal(tree, 0)
    else:
        return wfs(tree, cur_pos, N)


if __name__ == '__main__':
    N = int(input())
    answer = [True if i == 'o' else False for i in input().rstrip()]
    aa = [[WOLF, WOLF]
        , [WOLF, SHEEP]
        , [SHEEP, SHEEP]
        , [SHEEP, WOLF]]
    super_list = [0] * int(2E5)
    for a in aa:
        super_list[:2] = a
        if wfs(super_list, 1, N):
            print_tree(super_list[:N])
            break
    else:
        print(-1)

Submission status: Runtime Error

Solution code:
SHEEP = True
WOLF = False


def print_tree(tree):
    print(''.join(['S' if e else 'W' for e in tree]))


def calc_next_animal(tree, cur_pos):
    if answer[cur_pos]:
        if tree[cur_pos] == SHEEP:
            return tree[cur_pos - 1]
        else:
            return not tree[cur_pos - 1]
    else:
        if tree[cur_pos] == SHEEP:
            return not tree[cur_pos - 1]
        else:
            return tree[cur_pos - 1]


def calc_prev_animal(tree, cur_pos):
    if answer[cur_pos]:
        if tree[cur_pos] == SHEEP:
            return tree[cur_pos + 1]
        else:
            return not tree[cur_pos + 1]
    else:
        if tree[cur_pos] == SHEEP:
            return not tree[cur_pos + 1]
        else:
            return tree[cur_pos + 1]


def wfs(tree, cur_pos, N) -> bool:
    tree[cur_pos + 1] = calc_next_animal(tree, cur_pos)
    cur_pos += 1
    if cur_pos == N - 1:
        return tree[0] == calc_next_animal(tree, cur_pos) and tree[cur_pos] == calc_prev_animal(tree, 0)
    else:
        return wfs(tree, cur_pos, N)


if __name__ == '__main__':
    N = int(input())
    answer = [True if i == 'o' else False for i in input().rstrip()]
    aa = [[WOLF, WOLF]
        , [WOLF, SHEEP]
        , [SHEEP, SHEEP]
        , [SHEEP, WOLF]]
    super_list = [0] * int(2E5)
    for a in aa:
        super_list[:2] = a
        if wfs(super_list, 1, N):
            print_tree(super_list[:N])
            break
    else:
        print(-1)

Submission status: Runtime Error

Solution code:
SHEEP = True
WOLF = False


def print_tree(tree):
    print(''.join(['S' if e else 'W' for e in tree]))


def calc_next_animal(tree, cur_pos):
    if answer[cur_pos]:
        if tree[cur_pos] == SHEEP:
            return tree[cur_pos - 1]
        else:
            return not tree[cur_pos - 1]
    else:
        if tree[cur_pos] == SHEEP:
            return not tree[cur_pos - 1]
        else:
            return tree[cur_pos - 1]


def calc_prev_animal(tree, cur_pos):
    if answer[cur_pos]:
        if tree[cur_pos] == SHEEP:
            return tree[cur_pos + 1]
        else:
            return not tree[cur_pos + 1]
    else:
        if tree[cur_pos] == SHEEP:
            return not tree[cur_pos + 1]
        else:
            return tree[cur_pos + 1]


def wfs(tree, cur_pos, N) -> bool:
    tree[cur_pos + 1] = calc_next_animal(tree, cur_pos)
    cur_pos += 1
    if cur_pos == N - 1:
        return tree[0] == calc_next_animal(tree, cur_pos) and tree[cur_pos] == calc_prev_animal(tree, 0)
    else:
        return wfs(tree, cur_pos, N)


if __name__ == '__main__':
    N = int(input())
    answer = [True if i == 'o' else False for i in input().rstrip()]
    aa = [[WOLF, WOLF]
        , [WOLF, SHEEP]
        , [SHEEP, SHEEP]
        , [SHEEP, WOLF]]
    super_list = [0] * int(1E5)
    for a in aa:
        super_list[:2] = a
        if wfs(super_list, 1, N):
            print_tree(super_list[:N])
            break
    else:
        print(-1)

Submission status: Runtime Error

Solution code:
import itertools
N = int(input(l))
s = list(input())

# N = 6
# s = "ooxoox"
N = 3
s = "oox"

def hantei(N,s):
    for onetwo in itertools.product((0, 1), (0, 1)):
        res = {}
        for n in range(N):
            if n == 0:
                res[n] = onetwo[0]
            elif n == 1:
                res[n] = onetwo[1]
            else:
                if res[n-1] == 0 and s[n-1] == "o":
                    res[n] = res[n-2]
                elif res[n-1] == 0 and s[n-1] == "x":
                    res[n] = 1 if res[n-2] == 0 else 0
                elif res[n-1] == 1 and s[n-1] == "o":
                    res[n] = 1 if res[n-2] == 0 else 0
                elif res[n-1] == 1 and s[n-1] == "x":
                    res[n] = res[n-2]
        # check s[0]
        if (res[1] == res[N-1]) and res[0] == 0 and s[0] == "x":
            continue
        if (res[1] == res[N-1]) and res[0] == 1 and s[0] == "o":
            continue
        if (res[1] != res[N-1]) and res[0] == 0 and s[0] == "o":
            continue
        if (res[1] != res[N-1]) and res[0] == 1 and s[0] == "x":
            continue
        # check s[n-1]
        if (res[0] == res[N-2]) and res[N-1] == 0 and s[N-1] == "x":
            continue
        if (res[0] == res[N-2]) and res[N-1] == 1 and s[N-1] == "o":
            continue
        if (res[0] != res[N-2]) and res[N-1] == 0 and s[N-1] == "o":
            continue
        if (res[0] != res[N-2]) and res[N-1] == 1 and s[N-1] == "x":
            continue

        print(''.join(map(lambda x: "S" if x == 0 else "W", res.values())))
        return True

    return False

if not hantei(N, s):
    print(-1)

Submission status: Runtime Error

Solution code:
n = int(input())
s = input()
flag = False

def rec(t, i, s, n):
    global flag

    if flag:
        return

    l = len(t)
    if 2 < l:
        if t[i%l] == 'S' and (t[(i-1)%l] == t[(i+1)%l] and s[i%l] == 'x' or t[(i-1)%l] != t[(i+1)%l] and s[i%l] == 'o'):
            return
        elif t[i%l] == 'W' and (t[(i-1)%l] == t[(i+1)%l] and s[i%l] == 'o' or t[(i-1)%l] != t[(i+1)%l] and s[i%l] == 'x'):
            return
        if i == n + 1:
            print(t)
            flag = True
            return

    if l < n:
        rec(t + 'S', i+1, s, n)
        rec(t + 'W', i+1, s, n)
    else:
        rec(t, i+1, s, n)

rec('', -2, s, n)

if not flag:
    print('-1')

Submission status: Runtime Error

Solution code:
SHEEP = True
WOLF = False


def print_tree(tree):
    print(''.join(['S' if e else 'W' for e in tree]))


def calc_next_animal(tree, cur_pos):
    if answer[cur_pos]:
        if tree[cur_pos] == SHEEP:
            return tree[cur_pos - 1]
        else:
            return not tree[cur_pos - 1]
    else:
        if tree[cur_pos] == SHEEP:
            return not tree[cur_pos - 1]
        else:
            return tree[cur_pos - 1]


def calc_prev_animal(tree, cur_pos):
    if answer[cur_pos]:
        if tree[cur_pos] == SHEEP:
            return tree[cur_pos + 1]
        else:
            return not tree[cur_pos + 1]
    else:
        if tree[cur_pos] == SHEEP:
            return not tree[cur_pos + 1]
        else:
            return tree[cur_pos + 1]


def wfs(tree, cur_pos, N) -> bool:
    tree.append(calc_next_animal(tree, cur_pos))
    cur_pos += 1
    if cur_pos == N - 1:
        return tree[0] == calc_next_animal(tree, cur_pos) and tree[-1] == calc_prev_animal(tree, 0)
    else:
        return wfs(tree, cur_pos, N)


N = int(input())
answer = [True if i == 'o' else False for i in input().rstrip()]
a = [WOLF, WOLF]
b = [WOLF, SHEEP]
c = [SHEEP, SHEEP]
d = [SHEEP, WOLF]
if wfs(a, 1, N):
    print_tree(a)
elif wfs(b, 1, N):
    print_tree(b)
elif wfs(c, 1, N):
    print_tree(c)
elif wfs(d, 1, N):
    print_tree(d)
else:
    print(-1)