Description

A very, very long time ago, Xiaoming generated some data.

His data generator used the following two functions to generate random numbers:

Define function srand(32-bit unsigned integer seed)
	Set x to seed

Define function rand()
	Set x to x XOR (x left shift by 13 bits)
	Set x to x XOR (x right shift by 17 bits)
	Set x to x XOR (x left shift by 5 bits)
	Return x

After calling $\text{srand(seed)}$, Xiaoming called $\text{rand()}$ consecutively $n$ times, and recorded the remainder $a_i$ obtained by taking the return value of each $\text{rand()}$ modulo $p$.

A very, very long time later, only the data generator still remains (see generator.cpp in the provided files), but the parameters $\text{seed}$ and $p$ have been lost.

Xiaoming wants to recover these two parameters from the data. That is, given the sequence $a_i$, you need to find any possible values of $\text{seed}$ and $p$. Can you help him?

Brief description

Xiaoming's data generator is the provided file generator.cpp. You need to deduce the generator's input from its output.

Input Format

The first line contains an integer $n$.

The second line contains $n$ $32$-bit unsigned integers $a_1, a_2, \cdots, a_n$, which are the data generated by Xiaoming.

Output Format

Output only two $32$-bit unsigned integers $\text{seed}$ and $p$ as your answer. You need to ensure that $0 < \text{seed}, p < 2^{32}$.

If there are multiple solutions, you may output any one of them.

见下发文件的 sample.in

见下发文件的 sample.out

Hint

Constraints

This problem has $50$ test cases, and each test case is worth $2$ points.

For all testdata, it is guaranteed that $n = 10^5$, $\text{seed}$ is chosen randomly, and there exists at least one solution.

Translated by ChatGPT 5