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(Python)
def a(n, v):
R = dict() # index of each reachable subset is [card(s)-1][s]
for i in range(n): R[i] = dict()
for i in range(n): R[0][(v[i], )] = {v[i]}
reach = set(v)
for j in range(1, n):
for i in range((j+1)//2):
for s1 in R[i]:
for s2 in R[j-1-i]:
if set(s1) & set(s2) == set():
s12 = tuple(sorted(set(s1) | set(s2)))
if s12 not in R[len(s12)-1]:
R[len(s12)-1][s12] = set()
for a in R[i][s1]:
for b in R[j-1-i][s2]:
allowed = [a+b, a*b, a-b, b-a]
if a!=0 and b%a==0: allowed.append(b//a)
if b!=0 and a%b==0: allowed.append(a//b)
R[len(s12)-1][s12].update(allowed)
reach.update(allowed)
k = 1
while k in reach: k += 1
return k
alst = [1]
[alst.append(a(n, alst)) for n in range(1, 8)]
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