Random Numbers

Yuuka has $n$ integers $a\_1, a\_2, \dots, a\_n$ generated uniformly and independently between $1$ and $10^{18}$, inclusive.

Yuuka chooses an integer $m$. Next, an integer $k$ is generated uniformly between $0$ and $(m - 1)$, inclusive. After that, Yuuka changes every $a\_i$ to $(a\_i + k) \bmod m$. Finally, she randomly shuffles the integers. The resulting integers are $b\_1, b\_2, \ldots, b\_n$.

Now, given $a\_1, a\_2, \ldots, a\_n$ and $b\_1, b\_2, \ldots, b\_n$, you need to figure out the values of $m$ and $k$.

The first line contains an integer $n$, the number of integers ($10^5 \le n \le 2 \cdot 10^5$).

The second line contains $n$ integers $a\_1, a\_2, \dots, a\_n$: the $n$ randomly generated integers ($1 \le a\_i \le 10^{18}$).

The third line contains $n$ integers $b\_1, b\_2, \dots, b\_n$: the resulting integers ($0 \le b\_i < 10^{10}$).

It is guaranteed that there exists a solution such that $0 \le k < m \le 10^{10}$.

Output two integers $m$ and $k$ on a single line. If there are several possible answers, output any one of them.

Please note that the example in the problem statement is only to show the format! The tests in the system will not include this example (test 1 will be some other test), as it violates the constraints.