Buggy python submission (verdict: Time Limit Exceeded):
def max2(p, q):
    e, b = p[0], p[1]
    c, d = q[0], q[1]
    s = list(set([e, b, c, d]))
    s.sort(key = lambda x:a[x])
    return (s[-1], s[-2])

n = int(input())
a = list(map(int, input().split()))
g = [(i, (1<<n)) for i in range(1<<n)]
a+=[0]
res = 0
for i in range(n):
    for j in range(1<<n):
        if (1<<i)&j: g[j] = max2(g[j], g[j^(1<<i)])
ans = []
for i in range(1, 1<<n):
    res = max(res, a[g[i][0]]+a[g[i][1]])
    ans.append(res)
print(*ans, sep = '\n')

Fixed submission:
def max2(p, q):
    e, b = p[0], p[1]
    c, d = q[0], q[1]
    s = list(set([e, b, c, d]))
    m1, m2 = 1<<n, 1<<n
    for i in s:
        if a[m1]<a[i]:
            m2 = m1
            m1 = i
        elif a[m2]<a[i]:
            m2 = i
    return (m1, m2)

n = int(input())
a = list(map(int, input().split()))
g = [(i, (1<<n)) for i in range(1<<n)]
a+=[0]
res = 0
for i in range(n):
    for j in range(1<<n):
        if (1<<i)&j: g[j] = max2(g[j], g[j^(1<<i)])
ans = []
for i in range(1, 1<<n):
    res = max(res, a[g[i][0]]+a[g[i][1]])
    ans.append(res)
print(*ans, sep = '\n')

Buggy python submission (verdict: Time Limit Exceeded):
def max2(p, q):
    s = list(set(p+q))
    s.sort(key = lambda x:a[x], reverse = True)
    return s[:2]

n = int(input())
a = list(map(int, input().split()))
g = [[i, (1<<n)] for i in range(1<<n)]
a+=[0]
res = 0
for i in range(n):
    for j in range(1<<n):
        if (1<<i)&j: g[j] = max2(g[j], g[j^(1<<i)])
ans = []
for i in range(1, 1<<n):
    res = max(res, a[g[i][0]]+a[g[i][1]])
    ans.append(res)
print(*ans, sep = '\n')

Fixed submission:
def max2(p, q):
    e, b = p[0], p[1]
    c, d = q[0], q[1]
    s = list(set([e, b, c, d]))
    m1, m2 = 1<<n, 1<<n
    for i in s:
        if a[m1]<a[i]:
            m2 = m1
            m1 = i
        elif a[m2]<a[i]:
            m2 = i
    return (m1, m2)

n = int(input())
a = list(map(int, input().split()))
g = [(i, (1<<n)) for i in range(1<<n)]
a+=[0]
res = 0
for i in range(n):
    for j in range(1<<n):
        if (1<<i)&j: g[j] = max2(g[j], g[j^(1<<i)])
ans = []
for i in range(1, 1<<n):
    res = max(res, a[g[i][0]]+a[g[i][1]])
    ans.append(res)
print(*ans, sep = '\n')

Buggy python submission (verdict: Time Limit Exceeded):
def max2(p, q):
    s = list(set(p+q))
    s.sort(key = lambda x:a[x], reverse = True)
    return s[:2]

n = int(input())
a = list(map(int, input().split()))
g = [[i, (1<<n)] for i in range(1<<n)]
a+=[0]
res = 0
for i in range(n):
    for j in range(1<<n):
        if (1<<i)&j: g[j] = max2(g[j], g[j^(1<<i)])
for i in range(1, 1<<n):
    res = max(res, a[g[i][0]]+a[g[i][1]])
    print(res)

Fixed submission:
def max2(p, q):
    e, b = p[0], p[1]
    c, d = q[0], q[1]
    s = list(set([e, b, c, d]))
    m1, m2 = 1<<n, 1<<n
    for i in s:
        if a[m1]<a[i]:
            m2 = m1
            m1 = i
        elif a[m2]<a[i]:
            m2 = i
    return (m1, m2)

n = int(input())
a = list(map(int, input().split()))
g = [(i, (1<<n)) for i in range(1<<n)]
a+=[0]
res = 0
for i in range(n):
    for j in range(1<<n):
        if (1<<i)&j: g[j] = max2(g[j], g[j^(1<<i)])
ans = []
for i in range(1, 1<<n):
    res = max(res, a[g[i][0]]+a[g[i][1]])
    ans.append(res)
print(*ans, sep = '\n')