import sys,random,bisect
from collections import deque,defaultdict
from heapq import heapify,heappop,heappush
from itertools import permutations
from math import gcd,log

input = lambda :sys.stdin.readline().rstrip()
mi = lambda :map(int,input().split())
li = lambda :list(mi())

N = int(input())
S = input().rstrip()
S += "#"

dp = [10**15] * N
dp[N-1] = 0

dp_save = [0] * N
dp_save_p = [0] * N

dp_back_p = [0] * N
dp_back_e = [0] * N

for i in range(N-1)[::-1]:
    if S[i]=="#":
        continue

    if i+1 <= N and S[i+1]==".":
        if i+1 != N-1:
            dp_back_p[i] += dp_back_p[i+1]/3
            dp_back_e[i] += (dp_back_p[i+1]+dp_back_e[i+1])/3
            dp_save[i] += 1/9 * (2+dp[i+1]) + 1/3 * (dp_save_p[i+1]+dp_save[i+1])
            dp_save_p[i] += 1/9 + 1/3 * dp_save_p[i+1]
        else:
            dp_save[i] += 1/3
            dp_save_p[i] += 1/3
    elif i+1 <= N:
        dp_back_p[i] += 1/3
        dp_back_e[i] += 1/3

    if i+2 <= N and S[i+2]==".":
        if i+2 != N-1:
            dp_back_p[i] += dp_back_p[i+2]/3
            dp_back_e[i] += (dp_back_p[i+2]+dp_back_e[i+2])/3
            dp_save[i] += 1/9 * (2+dp[i+2]) + 1/3 * (dp_save_p[i+2]+dp_save[i+2])
            dp_save_p[i] += 1/9 + 1/3 * dp_save_p[i+2]
        else:
            dp_save[i] += 1/3
            dp_save_p[i] += 1/3
    elif i+2 <= N:
        dp_back_p[i] += 1/3
        dp_back_e[i] += 1/3
    
    """
    dp[i] = 1/3 * (1+dp[i]) + dp_save[i] + dp_back_p[i] * dp[i] + dp_back_e[i]
    """

    #print(dp_save[i],dp_back_e[i],dp_back_p[i])
    #print(dp_save_p[i]+dp_back_p[i])

    dp[i] = (1/3+dp_save[i]+dp_back_e[i]) / (2/3-dp_back_p[i])
    #print(dp[i])

print(dp[0])