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

n = ii()
s = input()

dp = [[0, 0] for _ in range(n + 1)]

dp[n] = [1, 0]
for i in range(n - 2, -1, -1):
    if s[i] == '#':
        dp[i] = [1, 0]
    else:
        p = (dp[i+1][1] + dp[i+2][1] + 3) / (-dp[i+1][0]-dp[i+2][0] + 2)
        dp[i][0] = (dp[i+1][0] + dp[i+2][0]) / 3
        dp[i][1] = (dp[i+1][1] + dp[i+2][1] + p) / 3 + 1
print(p)