XOR Inverse

Problem Description

You are given an array $a$ of $n$ non-negative integers. You must choose a non-negative integer $x$ and XOR every $a_i$ with $x$ to form a new array $b$. You want the number of inversions in $b$ to be minimized. If multiple $x$ achieve the minimum, output the smallest $x$.

An inversion is a pair $(i, j)$ in array $b$ satisfying $1 \le i < j \le n$ and $b_i > b_j$.

Input Format

The first line contains a positive integer $n$.

The next line contains $n$ non-negative integers $a_1, a_2, \dots, a_n$.

Output Format

Output two numbers: the minimum number of inversions in $b$, and the smallest $x$ achieving it.

Sample Input 1

4
0 1 3 2

Sample Output 1

1 0

Sample Input 2

9
10 7 9 10 7 5 5 3 5

Sample Output 2

4 14

Sample Input 3

3
8 10 3

Sample Output 3

0 8

Constraints

$1 \le n \le 3 \cdot 10^5$, $0 \le a_i \le 10^9$.