{"raw_statement":[{"iden":"problem statement","content":"You are given a sequence of non-negative integers $A=(a_1,\\ldots,a_N)$.\nLet us perform the following operation on $A$ just once.\n\n*   Choose a non-negative integer $x$. Then, for every $i=1, \\ldots, N$, replace the value of $a_i$ with the bitwise XOR of $a_i$ and $x$.\n\nLet $M$ be the maximum value in $A$ after the operation. Find the minimum possible value of $M$.\nWhat is bitwise XOR? The bitwise XOR of non-negative integers $A$ and $B$, $A \\oplus B$, is defined as follows.\n\n*   When $A \\oplus B$ is written in binary, the $k$\\-th lowest bit ($k \\geq 0$) is $1$ if exactly one of the $k$\\-th lowest bits of $A$ and $B$ is $1$, and $0$ otherwise.\n\nFor instance, $3 \\oplus 5 = 6$ (in binary: $011 \\oplus 101 = 110$)."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 1.5 \\times 10^5$\n*   $0 \\leq a_i \\lt 2^{30}$\n*   All values in the input are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$\n$a_1$ $\\ldots$ $a_N$"},{"iden":"sample input 1","content":"3\n12 18 11"},{"iden":"sample output 1","content":"16\n\nIf we do the operation with $x=2$, the sequence becomes $(12 \\oplus 2,18 \\oplus 2, 11 \\oplus 2) = (14,16,9)$, where the maximum value $M$ is $16$.  \nWe cannot make $M$ smaller than $16$, so this value is the answer."},{"iden":"sample input 2","content":"10\n0 0 0 0 0 0 0 0 0 0"},{"iden":"sample output 2","content":"0"},{"iden":"sample input 3","content":"5\n324097321 555675086 304655177 991244276 9980291"},{"iden":"sample output 3","content":"805306368"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}