#python -m pdb a.py

R=range
I=input
J=lambda:list(map(int,I().split()))
N=sum(J())+1
S=I()
A=[0]+J()
s=[0]
p=[0]*N
l=1
for c in S:
	if c<')':p[l]=s[-1];s+=[l];l+=1
	else:s.pop()
import heapq as h
s=[0]*N
q=[]
P=list(R(N))
H=[0]*N
def r(i):
	m=P[i]
	while i!=m:P[i]=i=P[m];m=P[i]
	return i
w=[1]*N
def f(w,a):return w/a if a else 9**6
for i in R(1,N):s[i]=f(1,A[i]);h.heappush(q,[s[i],i])
a=0
while q:
	t,v=h.heappop(q);v=r(v)
	if t!=s[v]:continue
	s[v]=0;u=r(p[v]);a+=w[u]*A[v];p[v]=p[u]
	if H[u]<H[v]:u,v=v,u
	H[u]+=H[u]==H[v];P[v]=u;A[u]+=A[v];w[u]+=w[v]
	if u!=r(0):s[u]=f(w[u],A[u]);h.heappush(q,[s[u],u])
print(a)