n = int(input())
s = input() + "#"

izon = [0] * n
teisu = [0] * (n+1)

dp = [0] * (n+1)
for i in range(n-2,-1,-1):
	# dp[i] = izon dp[i] + teisu
	# teisu / (1 - izon)
	if s[i] == "#": continue
	
	if s[i+1] == "#":
		izon[i] += 1/3
	else:
		teisu[i] += teisu[i+1] / 3
		izon[i] += izon[i+1] / 3

	if s[i+2] == "#":
		izon[i] += 1/3
	else:
		teisu[i] += teisu[i+2] / 3
		izon[i] += izon[i+2] / 3
	
	teisu[i] += 1.0
	dp[i] = teisu[i] / (1 - izon[i] - 1/3)
	teisu[i] += dp[i] / 3

print(dp[0])

#print(dp)
#print(izon)