28209번 - Classical Maximization Problem 스페셜 저지다국어

문제

You are given 2ドルn$ distinct points on a plane. Point $i$ has integer coordinates $(x_i, y_i)$.

Points $i$ and $j$ are a friendly pair if either $x_i = x_j$ or $y_i = y_j$.

Form $n$ pairs of points. Every point must belong to exactly one pair. The number of friendly pairs among your $n$ pairs must be maximized.

입력

Each test contains multiple test cases. The first line contains the number of test cases $t$ (1ドル \le t \le 10^4$). The description of the test cases follows.

The first line of each test case contains a single integer $n$ (1ドル \le n \le 10^5$).

The $i$-th of the next 2ドルn$ lines contains two integers $x_i$ and $y_i,ドル denoting the coordinates of the $i$-th point ($-10^9 \le x_i, y_i \le 10^9$). All points are distinct.

It is guaranteed that the sum of $n$ over all test cases does not exceed 10ドル^5$.

출력

For each test case, print a non-negative integer $k,ドル denoting the maximum possible number of friendly pairs.

In the $i$-th of the next $n$ lines, print two integers $a_i$ and $b_i,ドル denoting a pair formed by points $a_i$ and $b_i$ (1ドル \le a_i, b_i \le 2n$; $a_i \ne b_i$).

Every integer from 1ドル$ to 2ドルn$ must appear among $a_i$ and $b_i$ exactly once. The number of indices $i$ such that points $a_i$ and $b_i$ are a friendly pair must be equal to $k$.

제한

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