Description

Given n numbers, you need to find a number k such that SUM is minimum,

where we define SUM = ( a₁ ^ k ) + ( a₂ ^ k ) + ... + ( a_n ^ k )

(^ stands for the "xor" bitwise operation of the two operand)

original problem: https://acm.cs.nthu.edu.tw/problem/11770/

Input

The first line contains an integer n, representing the number of numbers.

The next line contains n integers a_i, representing each given number.

It is guaranteed that:

• n ≤ 10⁵
• 0 ≤ a_i ≤ 10⁶
• All numbers ( a_i and k ) are unsigned numbers

Output

Please output the value of SUM.

Note SUM may exceed INT.

Sample Input  Download

Sample Output  Download

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