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.
import sys
input = sys.stdin.readline

N = int(input())
A = list(map(int, input().split()))

Max = [[(0, A[0])]]
ans = 0
for bit in range(1, (1<<N)):
    dic = {bit: A[bit]}
    for i in range(N):
        if bit&(1<<i) != 0:
            for ind, val in Max[bit-(1<<i)]:
                dic[ind] = val
    com = []
    for ind, val in dic.items():
        if len(com) < 2:
            com.append((ind, val))
        else:
            if com[0][1] < com[1][1]:
                if com[0][1] < val:
                    com[0] = (ind, val)
                elif com[1][1] < val:
                    com[1] = (ind, val)
            else:
                if com[1][1] < val:
                    com[1] = (ind, val)
                elif com[0][1] < val:
                    com[0] = (ind, val)               
    Max.append(com)
    tmp = com[0][1] + com[1][1]
    if tmp > ans:
        ans = tmp
    print(ans)
import sys
input = sys.stdin.readline

N = int(input())
A = list(map(int, input().split()))

Max = [[(0, A[0])]]
ans = 0
for bit in range(1, (1<<N)):
    dic = {bit: A[bit]}
    for i in range(N):
        if bit&(1<<i) != 0:
            for ind, val in Max[bit-(1<<i)]:
                dic[ind] = val
    com = []
    for ind, val in dic.items():
        if len(com) < 2:
            com.append((ind, val))
        else:
            if com[0][1] < com[1][1]:
                if com[0][1] < val:
                    com[0] = (ind, val)
                elif com[1][1] < val:
                    com[1] = (ind, val)
            else:
                if com[1][1] < val:
                    com[1] = (ind, val)
                elif com[0][1] < val:
                    com[0] = (ind, val)               
    Max.append(com)
    tmp = com[0][1] + com[1][1]
    if tmp > ans:
        ans = tmp
    print(ans)