Buggy python submission (verdict: Time Limit Exceeded):
import sys

sys.setrecursionlimit(10 ** 6)
int1 = lambda x: int(x) - 1
p2D = lambda x: print(*x, sep="\n")
def II(): return int(sys.stdin.readline())
def MI(): return map(int, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def SI(): return sys.stdin.readline()[:-1]

class Top2:
    def __init__(self,x=-1,y=-1):
        if x<y:x,y=y,x
        self.val=[x,y]
        self.s=x+y

    def __add__(self, other):
        i=j=0
        self.val=sorted(self.val+other.val,reverse=True)[:2]
        self.s=sum(self.val)
        return self

n=II()
aa=LI()
dp=[Top2(a) for a in aa]

for i in range(n):
    for j in range((1<<n)-1,-1,-1):
        if j>>i&1:continue
        dp[j|1<<i]+=dp[j]

mx=-1
for j in range(1,1<<n):
    mx=max(mx,int(dp[j].s))
    print(mx)


Fixed submission:
import sys

sys.setrecursionlimit(10 ** 6)
int1 = lambda x: int(x) - 1
p2D = lambda x: print(*x, sep="\n")
def II(): return int(sys.stdin.readline())
def MI(): return map(int, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def SI(): return sys.stdin.readline()[:-1]

class Top2:
    def __init__(self,x=-1,y=-1):
        if x<y:x,y=y,x
        self.val=[x,y]
        self.s=x+y

    def __add__(self, other):
        i=j=0
        self.val=sorted(self.val+other.val,reverse=True)[:2]
        self.s=sum(self.val)
        return self

n=II()
aa=LI()
dp=[Top2(a) for a in aa]

for i in range(n):
    for j in range((1<<n)-1,-1,-1):
        if j>>i&1:continue
        dp[j|1<<i]+=dp[j]

mx=-1
for j in range(1,1<<n):
    mx=max(mx,int(dp[j].s))
    print(mx)

Buggy python submission (verdict: Time Limit Exceeded):
# YouTube

def max12(x):
    if len(x) < 3:
        return x
    x.sort(reverse=True)
    return x[:2]

def f(n):
    nn = 2 ** n
    aa = list(map(int, input().split()))
    dp = [[a] for a in aa]
    # print(dp)
    for i in range(n):
        for j in range(nn - 1, -1, -1):
            if j & 1 << i == 0:
                dp[j + (1 << i)] = max12(dp[j + (1 << i)] + dp[j])
    #    print(dp)
    mx = 0
    for dk in dp[1:]:
        s = sum(dk)
        if s > mx: mx = s
        print(mx)

n = int(input())
f(n)


Fixed submission:
import sys

sys.setrecursionlimit(10 ** 6)
int1 = lambda x: int(x) - 1
p2D = lambda x: print(*x, sep="\n")
def II(): return int(sys.stdin.readline())
def MI(): return map(int, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def SI(): return sys.stdin.readline()[:-1]

class Top2:
    def __init__(self,x=-1,y=-1):
        if x<y:x,y=y,x
        self.val=[x,y]
        self.s=x+y

    def __add__(self, other):
        i=j=0
        self.val=sorted(self.val+other.val,reverse=True)[:2]
        self.s=sum(self.val)
        return self

n=II()
aa=LI()
dp=[Top2(a) for a in aa]

for i in range(n):
    for j in range((1<<n)-1,-1,-1):
        if j>>i&1:continue
        dp[j|1<<i]+=dp[j]

mx=-1
for j in range(1,1<<n):
    mx=max(mx,int(dp[j].s))
    print(mx)

Buggy python submission (verdict: Time Limit Exceeded):
# YouTube

def max12(x):
    if len(x) < 3:
        return x
    x.sort(reverse=True)
    return x[:2]

n = int(input())
nn = 2 ** n
aa = list(map(int, input().split()))
dp = [[a] for a in aa]
#print(dp)
for i in range(n):
    for j in range(nn - 1, -1, -1):
        if j & 1 << i == 0:
            dp[j + (1 << i)] = max12(dp[j + (1 << i)] + dp[j])
#    print(dp)
mx = 0
for dk in dp[1:]:
    mx = max(mx, sum(dk))
    print(mx)


Fixed submission:
import sys

sys.setrecursionlimit(10 ** 6)
int1 = lambda x: int(x) - 1
p2D = lambda x: print(*x, sep="\n")
def II(): return int(sys.stdin.readline())
def MI(): return map(int, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def SI(): return sys.stdin.readline()[:-1]

class Top2:
    def __init__(self,x=-1,y=-1):
        if x<y:x,y=y,x
        self.val=[x,y]
        self.s=x+y

    def __add__(self, other):
        i=j=0
        self.val=sorted(self.val+other.val,reverse=True)[:2]
        self.s=sum(self.val)
        return self

n=II()
aa=LI()
dp=[Top2(a) for a in aa]

for i in range(n):
    for j in range((1<<n)-1,-1,-1):
        if j>>i&1:continue
        dp[j|1<<i]+=dp[j]

mx=-1
for j in range(1,1<<n):
    mx=max(mx,int(dp[j].s))
    print(mx)

Buggy python submission (verdict: Time Limit Exceeded):
from heapq import *

n = int(input())
nn = 2 ** n
aa = list(map(int, input().split()))
hp = []
ai = []
ans = [-1] * nn
for i, a in enumerate(aa):
    ai.append([a, i])
ai.sort(reverse=True)
used = set()
heappush(hp, [-ai[0][0] - ai[1][0], ai[0][1] | ai[1][1], 0, 1])
used.add((0, 1))
ni = 2
r = nn
while ni > 1:
    s, ni, i, j = heappop(hp)
    if ans[ni] == -1:
        for ii in range(ni, r):
            ans[ii] = -s
        r = ni
    if (i, j + 1) not in used and j < nn - 1:
        heappush(hp, [-ai[i][0] - ai[j + 1][0], ai[i][1] | ai[j + 1][1], i, j + 1])
        used.add((i, j + 1))
    if i + 1 < j and (i + 1, j) not in used:
        heappush(hp, [-ai[i + 1][0] - ai[j][0], ai[i + 1][1] | ai[j][1], i + 1, j])
        used.add((i + 1, j))
for x in ans[1:]:
    print(x)


Fixed submission:
import sys

sys.setrecursionlimit(10 ** 6)
int1 = lambda x: int(x) - 1
p2D = lambda x: print(*x, sep="\n")
def II(): return int(sys.stdin.readline())
def MI(): return map(int, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def SI(): return sys.stdin.readline()[:-1]

class Top2:
    def __init__(self,x=-1,y=-1):
        if x<y:x,y=y,x
        self.val=[x,y]
        self.s=x+y

    def __add__(self, other):
        i=j=0
        self.val=sorted(self.val+other.val,reverse=True)[:2]
        self.s=sum(self.val)
        return self

n=II()
aa=LI()
dp=[Top2(a) for a in aa]

for i in range(n):
    for j in range((1<<n)-1,-1,-1):
        if j>>i&1:continue
        dp[j|1<<i]+=dp[j]

mx=-1
for j in range(1,1<<n):
    mx=max(mx,int(dp[j].s))
    print(mx)

Buggy python submission (verdict: Time Limit Exceeded):
from heapq import *

n = int(input())
nn = 2 ** n
aa = list(map(int, input().split()))
hp = []
ans = [-1] * nn
for i in range(nn-1):
    for j in range(i+1,nn):
        heappush(hp, [-(aa[i]+aa[j]), i|j])
r=nn
i=2
while i>1:
    s, i = heappop(hp)
    if ans[i]==-1:
        for ii in range(i,r):
            ans[ii]=-s
        r=i
for x in ans[1:]:
    print(x)


Fixed submission:
import sys

sys.setrecursionlimit(10 ** 6)
int1 = lambda x: int(x) - 1
p2D = lambda x: print(*x, sep="\n")
def II(): return int(sys.stdin.readline())
def MI(): return map(int, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def SI(): return sys.stdin.readline()[:-1]

class Top2:
    def __init__(self,x=-1,y=-1):
        if x<y:x,y=y,x
        self.val=[x,y]
        self.s=x+y

    def __add__(self, other):
        i=j=0
        self.val=sorted(self.val+other.val,reverse=True)[:2]
        self.s=sum(self.val)
        return self

n=II()
aa=LI()
dp=[Top2(a) for a in aa]

for i in range(n):
    for j in range((1<<n)-1,-1,-1):
        if j>>i&1:continue
        dp[j|1<<i]+=dp[j]

mx=-1
for j in range(1,1<<n):
    mx=max(mx,int(dp[j].s))
    print(mx)