A polyglot is a computer program that can be successfully compiled in different languages while still behaving the same. But what would a polyglot testcase in competitive programming look like? Let's take two random Division 3 problems from Codeforces:

Problem X: Karina and Array

Karina has an array of $$$n$$$ integers $$$a_1, a_2, a_3, \ldots, a_n$$$. She loves multiplying numbers, so she decided that the beauty of a pair of numbers is their product. And the beauty of an array is the maximum beauty of a pair of adjacent elements in the array.

For example, for $$$n=4$$$, $$$a=[3,5,7,4]$$$, the beauty of the array is $$$\max(3 \cdot 5, 5 \cdot 7, 7 \cdot 4) = \max(15, 35, 28) = 35$$$.

Karina wants her array to be as beautiful as possible. In order to achieve her goal, she can remove some elements (possibly zero) from the array. After Karina removes all elements she wants to, the array must contain at least two elements.

Unfortunately, Karina doesn't have enough time to do all her tasks, so she asks you to calculate the maximum beauty of the array that she can get by removing any number of elements (possibly zero).

Input

The first line of the input contains an integer $$$t$$$ $$$(1 \leq t \leq 10^4)$$$ — the number of test cases.

The description of the test cases follows.

For each test case:

• The first line contains an integer $$$n$$$ $$$(2 \leq n \leq 2 \times 10^5)$$$ — the length of the array $$$a$$$.
• The second line contains $$$n$$$ integers $$$a_1, a_2, a_3, \ldots, a_n$$$ $$$(-10^9 \leq a_i \leq 10^9)$$$ — the elements of the array $$$a$$$.

The sum of all values of $$$n$$$ across all test cases does not exceed $$$2 \times 10^5$$$.

Output

Output $$$t$$$ integers, each of which is the answer to the corresponding test case — the maximum beauty of the array that Karina can get.

Problem Y: Boats Competition

There are $$$n$$$ people who want to participate in a boat competition. The weight of the $$$i$$$-th participant is $$$w_i$$$. Only teams consisting of two people can participate in this competition. As an organizer, you think that it's fair to allow only teams with the same total weight.

So, if there are $$$k$$$ teams $$$(a_1, b_1), (a_2, b_2), \ldots, (a_k, b_k)$$$, where $$$a_i$$$ is the weight of the first participant of the $$$i$$$-th team and $$$b_i$$$ is the weight of the second participant of the $$$i$$$-th team, then the condition $$$a_1 + b_1 = a_2 + b_2 = \ldots = a_k + b_k = s$$$, where $$$s$$$ is the total weight of each team, should be satisfied.

Your task is to choose such $$$s$$$ that the number of teams people can create is the maximum possible. Note that each participant can be in no more than one team.

Input

The first line of the input contains one integer $$$t$$$ $$$(1 \leq t \leq 1000)$$$ — the number of test cases. Then $$$t$$$ test cases follow.

For each test case:

• The first line contains one integer $$$n$$$ $$$(1 \leq n \leq 50)$$$ — the number of participants.
• The second line contains $$$n$$$ integers $$$w_1, w_2, \ldots, w_n$$$ $$$(1 \leq w_i \leq n)$$$, where $$$w_i$$$ is the weight of the $$$i$$$-th participant.

Output

For each test case, print one integer $$$k$$$: the maximum number of teams people can compose with the total weight $$$s$$$, if you choose $$$s$$$ optimally.

Actual Problem

Now, you are given an integer $$$x$$$, and your job is to make a testcase that is valid for both problems above, and such that a correct solution for both problems would output the single integer $$$x$$$.