28210번 - Classical Minimization Problem 스페셜 저지다국어

You are given $2n$ 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 minimized.

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

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

The $i$-th of the next $2n$ lines contains two integers $x_i$ and $y_i$, 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 $10^5$.

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

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

Every integer from $1$ to $2n$ 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 $k$.