There is an integer sequence of length 2^N: A_0, A_1, ..., A_{2^N-1}. (Note that the sequence is 0-indexed.)
For every integer K satisfying 1 \leq K \leq 2^N-1, solve the following problem:
 - Let i and j be integers. Find the maximum value of A_i + A_j where 0 \leq i < j \leq 2^N-1 and (i or j) \leq K.
Here, or denotes the bitwise OR.

-----Constraints-----
 - 1 \leq N \leq 18
 - 1 \leq A_i \leq 10^9
 - All values in input are integers.

-----Input-----
Input is given from Standard Input in the following format:
N
A_0 A_1 ... A_{2^N-1}

-----Output-----
Print 2^N-1 lines.
In the i-th line, print the answer of the problem above for K=i.

-----Sample Input-----
2
1 2 3 1

-----Sample Output-----
3
4
5

For K=1, the only possible pair of i and j is (i,j)=(0,1), so the answer is A_0+A_1=1+2=3.
For K=2, the possible pairs of i and j are (i,j)=(0,1),(0,2).
When (i,j)=(0,2), A_i+A_j=1+3=4. This is the maximum value, so the answer is 4.
For K=3, the possible pairs of i and j are (i,j)=(0,1),(0,2),(0,3),(1,2),(1,3),(2,3) .
When (i,j)=(1,2), A_i+A_j=2+3=5. This is the maximum value, so the answer is 5.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'N=int(input())\nA=list(map(int,input().split()))+[0]\n\ndata=[[] for i in range(2**N)]\n\nfor i in range(1,2**N):\n    for j in range(N):\n        if i&(1<<j)==0:\n            continue\n        else:\n            data[i].append(i-(1<<j))\n\nMAX=[0]*2**N\nsemiMAX=[0]*2**N\n\nsemiMAX[0]=2**N\n\nif MAX[0]<A[1]:\n    MAX[1]=1\n    semiMAX[1]=0\nelse:\n    MAX[1]=0\n    semiMAX[1]=1\n\nK=[A[0]+A[1]]\nfor k in range(2,2**N):\n    a,b=k,2**N\n    for u in data[k]:\n        c,d=MAX[u],semiMAX[u]\n        if A[c]<=A[b]:\n            c=c\n        elif A[d]>=A[a]:\n            a,b=c,d\n        elif A[c]>A[a]:\n            a,b=c,a\n        elif A[a]>=A[c]>A[b] and a!=c:\n            b=c\n        elif A[a]>=A[d]>A[b] and a!=d:\n            b=d\n    MAX[k]=a\n    semiMAX[k]=b\n    K.append(max(K[-1],A[a]+A[b]))\n\nfor u in K:\n    print(u)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13829