{"raw_statement":[{"iden":"problem statement","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 $a$, $b$, $c$, $d$ $(a \\neq c, b \\neq d)$ 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.\n\nWe 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."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 10^5$\n*   $1 \\leq x_i, y_i \\leq 10^5$\n*   If $i \\neq j$, $x_i \\neq x_j$ or $y_i \\neq y_j$.\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$\n$x_1$ $y_1$\n$:$\n$x_N$ $y_N$"},{"iden":"sample input 1","content":"3\n1 1\n5 1\n5 5"},{"iden":"sample output 1","content":"1\n\nBy 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 $1$."},{"iden":"sample input 2","content":"2\n10 10\n20 20"},{"iden":"sample output 2","content":"0\n\nThere are only two dots, so we cannot do the operation at all."},{"iden":"sample input 3","content":"9\n1 1\n2 1\n3 1\n4 1\n5 1\n1 2\n1 3\n1 4\n1 5"},{"iden":"sample output 3","content":"16\n\nWe 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 $16$."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}