#CF1895B. Points and Minimum Distance
Points and Minimum Distance
Description
You are given a sequence of integers $a$ of length $2n$. You have to split these $2n$ integers into $n$ pairs; each pair will represent the coordinates of a point on a plane. Each number from the sequence $a$ should become the $x$ or $y$ coordinate of exactly one point. Note that some points can be equal.
After the points are formed, you have to choose a path $s$ that starts from one of these points, ends at one of these points, and visits all $n$ points at least once.
The length of path $s$ is the sum of distances between all adjacent points on the path. In this problem, the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is defined as $|x_1-x_2| + |y_1-y_2|$.
Your task is to form $n$ points and choose a path $s$ in such a way that the length of path $s$ is minimized.
The first line contains a single integer $t$ ($1 \le t \le 100$) — the number of testcases.
The first line of each testcase contains a single integer $n$ ($2 \le n \le 100$) — the number of points to be formed.
The next line contains $2n$ integers $a_1, a_2, \dots, a_{2n}$ ($0 \le a_i \le 1\,000$) — the description of the sequence $a$.
For each testcase, print the minimum possible length of path $s$ in the first line.
In the $i$-th of the following $n$ lines, print two integers $x_i$ and $y_i$ — the coordinates of the point that needs to be visited at the $i$-th position.
If there are multiple answers, print any of them.
题面翻译
给定长度为 的序列 ，你需要把这些数分为 对，得到 个坐标轴上的点。 中的每个数都要是某一个点的 或 坐标。注意有些点可能会重合。
之后，你可以选择从一个点出发，选择一条路径走过所有 个点至少一次，在某个点处停下。
你需要求出路径总长度的最小值。本题中两点间距离为曼哈顿距离，即 和 间距离为 。
Input
The first line contains a single integer $t$ ($1 \le t \le 100$) — the number of testcases.
The first line of each testcase contains a single integer $n$ ($2 \le n \le 100$) — the number of points to be formed.
The next line contains $2n$ integers $a_1, a_2, \dots, a_{2n}$ ($0 \le a_i \le 1\,000$) — the description of the sequence $a$.
Output
For each testcase, print the minimum possible length of path $s$ in the first line.
In the $i$-th of the following $n$ lines, print two integers $x_i$ and $y_i$ — the coordinates of the point that needs to be visited at the $i$-th position.
If there are multiple answers, print any of them.
2
2
15 1 10 5
3
10 30 20 20 30 10
9
10 1
15 5
20
20 20
10 30
10 30
Note
In the first testcase, for instance, you can form points $(10, 1)$ and $(15, 5)$ and start the path $s$ from the first point and end it at the second point. Then the length of the path will be $|10 - 15| + |1 - 5| = 5 + 4 = 9$.
In the second testcase, you can form points $(20, 20)$, $(10, 30)$, and $(10, 30)$, and visit them in that exact order. Then the length of the path will be $|20 - 10| + |20 - 30| + |10 - 10| + |30 - 30| = 10 + 10 + 0 + 0 = 20$.
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