import sys
readline=sys.stdin.readline

N=int(readline())
S=readline().rstrip()
mod=998244353
dp=[None]*(N+1)
dp[N]=(0,1,0)
dp[N-1]=(0,0,0)
for i in range(N-2,-1,-1):
    if S[i]=="#":
        dp[i]=(-1,1,0)
    else:
        a=2
        b=3
        for j in (i+1,i+2):
            a-=dp[j][1]
            b+=dp[j][2]
        x=b/a
        A,B=0,3+x
        for j in (i+1,i+2):
            A+=dp[j][1]
            B+=dp[j][2]
        A/=3
        B/=3
        dp[i]=(x,A,B)
ans=dp[0][0]
print(ans)