import sys
from collections import deque, Counter
import time
input = lambda: sys.stdin.readline().rstrip()
ii = lambda: int(input())
mi = lambda: map(int, input().split())
li = lambda: list(mi())
inf = 2 ** 63 - 1
mod = 998244353
import random


n = ii()

s = input()
s += '##'
def roll():
    now = 0
    save = 0
    cnt = 0
    while True:
        c = random.choice([0, 1, 2])
        cnt += 1
        if c == 0:
            now += 1
            if s[now] == '#':
                now = save
        if c == 1:
            now += 2
            if s[now] == '#':
                now = save
        if c == 2:
            save = now
        if now == n - 1:
            return cnt

t = time.time()

cnt = 0
c = 0
while time.time() - t < 1.8:
    c += roll()
    cnt += 1
print(c / cnt)