Problem Statement

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 $K=i$.