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문제

Consider an array $A$ of length $N$. The instability of $A$ is defined as $$\sum\limits_{i = 1}^{N - 1} (|A[i + 1] - A[i]|)\text{.}$$

Master Zhu wants to stabilize an array. In order to do that, he wants to select an integer $X$ and change every element $A[i]$ to $(A[i] \oplus X)$. Here, $u \oplus v$ is the bitwise XOR of $u$ and $v$.

Find the smallest non-negative integer $X$ Master Zhu must choose to minimize the instability of a given array, and calculate the resulting instability.

입력

The first line of input contains an integer $N$ ($1 \le N \le 10^5$). Next line contains $N$ integers $A[i]$, indicating the elements of the array ($0 \le A[i] < 2^{20}$).

출력

Print a single line containing two integers: the smallest non-negative integer $X$ which must be used in order to reach the minimum possible instability and the resulting instability itself.

예제 입력 1

3
0 3 0

예제 출력 1

1 2

예제 입력 2

3
1 3 1

예제 출력 2

0 4