{"problem":{"name":"Max of Medians","description":{"content":"You are given a sequence of length $2N$: $A = (A_1, A_2, \\ldots, A_{2N})$. Find the maximum value that can be obtained as the median of the length-$N$ sequence $(A_1 \\oplus A_2, A_3 \\oplus A_4, \\ldots","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":5000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc304_g"},"statements":[{"statement_type":"Markdown","content":"You are given a sequence of length $2N$: $A = (A_1, A_2, \\ldots, A_{2N})$.\nFind the maximum value that can be obtained as the median of the length-$N$ sequence $(A_1 \\oplus A_2, A_3 \\oplus A_4, \\ldots, A_{2N-1} \\oplus A_{2N})$ by rearranging the elements of the sequence $A$.\nHere, $\\oplus$ represents bitwise exclusive OR.\nWhat is bitwise exclusive OR? The bitwise exclusive OR of non-negative integers $A$ and $B$, denoted as $A \\oplus B$, is defined as follows:\n\n*   The number at the $2^k$ position ($k \\geq 0$) in the binary representation of $A \\oplus B$ is $1$ if and only if exactly one of the numbers at the $2^k$ position in the binary representation of $A$ and $B$ is $1$, and it is $0$ otherwise.\n\nFor example, $3 \\oplus 5 = 6$ (in binary notation: $011 \\oplus 101 = 110$).Also, for a sequence $B$ of length $L$, the median of $B$ is the value at the $\\lfloor \\frac{L}{2} \\rfloor + 1$\\-th position of the sequence $B'$ obtained by sorting $B$ in ascending order.\n\n## Constraints\n\n*   $1 \\leq N \\leq 10^5$\n*   $0 \\leq A_i < 2^{30}$\n*   All input values are integers.\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$N$\n$A_1$ $A_2$ $\\ldots$ $A_{2N}$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc304_g","tags":[],"sample_group":[["4\n4 0 0 11 2 7 9 5","14\n\nBy rearranging $A$ as $(5, 0, 9, 7, 11, 4, 0, 2)$, we get $(A_1 \\oplus A_2, A_3 \\oplus A_4, A_5 \\oplus A_6, A_7 \\oplus A_8) = (5, 14, 15, 2)$, and the median of this sequence is $14$.  \nIt is impossible to rearrange $A$ so that the median of $(A_1 \\oplus A_2, A_3 \\oplus A_4, A_5 \\oplus A_6, A_7 \\oplus A_8)$ is $15$ or greater, so we print $14$."],["1\n998244353 1000000007","1755654"],["5\n1 2 4 8 16 32 64 128 256 512","192"]],"created_at":"2026-03-03 11:01:13"}}