Xor Minimization

AtCoder

IDabc281_f

Time2500ms

Memory256MB

Difficulty—

You are given a sequence of non-negative integers $A=(a_1,\ldots,a_N)$. Let us perform the following operation on $A$ just once. * 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 $x$. Let $M$ be the maximum value in $A$ after the operation. Find the minimum possible value of $M$. What is bitwise XOR? The bitwise XOR of non-negative integers $A$ and $B$, $A \oplus B$, is defined as follows. * 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. For instance, $3 \oplus 5 = 6$ (in binary: $011 \oplus 101 = 110$). ## Constraints * $1 \leq N \leq 1.5 \times 10^5$ * $0 \leq a_i \lt 2^{30}$ * All values in the input are integers. ## Input The input is given from Standard Input in the following format: $N$ $a_1$ $\ldots$ $a_N$ [samples]

Samples

Input #1

3
12 18 11

Output #1

16

If 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 $16$.  
We cannot make $M$ smaller than $16$, so this value is the answer.

Input #2

10
0 0 0 0 0 0 0 0 0 0

Output #2

Input #3

5
324097321 555675086 304655177 991244276 9980291

Output #3

805306368

API Response (JSON)

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    "name": "Xor Minimization",
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      "content": "You are given a sequence of non-negative integers $A=(a_1,\\ldots,a_N)$. Let us perform the following operation on $A$ just once. *   Choose a non-negative integer $x$. Then, for every $i=1, \\ldots, N",
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      "statement_type": "Markdown",
      "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...",
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