Maximum Xor Secondary · Interview Problem

Codeforces

Medium

Arrays

Bit Manipulation

Stacks

Google

Maximum Xor Secondary

Find the maximum value of $a_i \oplus a_j$ over pairs of elements where the chosen pair must satisfy the constraints of the original problem’s ordering rule.

Acceptance 0%

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Problem Statement

You are given an array of integers. Consider all valid pairs of positions that can be formed according to the problem’s ordering constraint, and compute the bitwise XOR of the two values in each valid pair.

Your task is to determine the maximum XOR value among all valid pairs.

The key challenge is that checking every pair directly is too slow for large arrays, so the solution must exploit structure in the way valid pairs are formed.

Input Format

Input

The first line contains an integer $n$ — the number of array elements.
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ .

Interpretation

All values are treated as integers suitable for bitwise XOR.

Output Format

Output

Print a single integer: the maximum XOR value among all valid pairs.

Constraints

$2 \le n$
The array size is large enough that an $O(n^2)$ approach is not intended.
Values fit in standard 32-bit signed integer ranges unless otherwise stated by the platform.

Examples

Sample cases returned by the problem API.

Example 1

Input

3
1 2 3

Output

Explanation

Among the valid candidate pairs considered by the ordering rule, the best XOR value is $2 \oplus 3 = 1$ .

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