{"raw_statement":[{"iden":"problem statement","content":"There is an integer sequence of length $2^N$: $A_0, A_1, ..., A_{2^N-1}$. (Note that the sequence is $0$\\-indexed.)\nFor every integer $K$ satisfying $1 \\leq K \\leq 2^N-1$, solve the following problem:\n\n*   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."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 18$\n*   $1 \\leq A_i \\leq 10^9$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$\n$A_0$ $A_1$ $...$ $A_{2^N-1}$"},{"iden":"sample input 1","content":"2\n1 2 3 1"},{"iden":"sample output 1","content":"3\n4\n5\n\nFor $K=1$, the only possible pair of $i$ and $j$ is $(i,j)=(0,1)$, so the answer is $A_0+A_1=1+2=3$.\nFor $K=2$, 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 $4$.\nFor $K=3$, 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 $5$."},{"iden":"sample input 2","content":"3\n10 71 84 33 6 47 23 25"},{"iden":"sample output 2","content":"81\n94\n155\n155\n155\n155\n155"},{"iden":"sample input 3","content":"4\n75 26 45 72 81 47 97 97 2 2 25 82 84 17 56 32"},{"iden":"sample output 3","content":"101\n120\n147\n156\n156\n178\n194\n194\n194\n194\n194\n194\n194\n194\n194"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}