Must Be Rectangular!

AtCoder

IDabc131_f

Time2000ms

Memory256MB

Difficulty—

There are $N$ dots in a two-dimensional plane. The coordinates of the $i$\-th dot are $(x_i, y_i)$. We will repeat the following operation as long as possible: * Choose four integers $a$, $b$, $c$, $d$ $(a \neq c, b \neq d)$ such that there are dots at exactly three of the positions $(a, b)$, $(a, d)$, $(c, b)$ and $(c, d)$, and add a dot at the remaining position. We can prove that we can only do this operation a finite number of times. Find the maximum number of times we can do the operation. ## Constraints * $1 \leq N \leq 10^5$ * $1 \leq x_i, y_i \leq 10^5$ * If $i \neq j$, $x_i \neq x_j$ or $y_i \neq y_j$. * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $x_1$ $y_1$ $:$ $x_N$ $y_N$ [samples]

Samples

Input #1

Output #1

1

By choosing $a = 1$, $b = 1$, $c = 5$, $d = 5$, we can add a dot at $(1, 5)$. We cannot do the operation any more, so the maximum number of operations is $1$.

Input #2

2
10 10
20 20

Output #2

0

There are only two dots, so we cannot do the operation at all.

Input #3

Output #3

16

We can do the operation for all choices of the form $a = 1$, $b = 1$, $c = i$, $d = j$ $(2 \leq i,j \leq 5)$, and no more. Thus, the maximum number of operations is $16$.

API Response (JSON)

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      "content": "There are $N$ dots in a two-dimensional plane. The coordinates of the $i$\\-th dot are $(x_i, y_i)$. We will repeat the following operation as long as possible: *   Choose four integers $a$, $b$, $c$,",
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      "statement_type": "Markdown",
      "content": "There are $N$ dots in a two-dimensional plane. The coordinates of the $i$\\-th dot are $(x_i, y_i)$.\nWe will repeat the following operation as long as possible:\n\n*   Choose four integers $a$, $b$, $c$,...",
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