{"problem":{"name":"[EC Final 2022] Rectangle","description":{"content":"Prof. Pang has $n$ rectangles, the coordinate of the lower left corner of the $i$-th rectangle is $(x_{i,1}, y_{i,1})$, and the coordinate of the upper right corner is $(x_{i,2}, y_{i,2})$. Rectangles","description_type":"Markdown"},"platform":"Luogu","limit":{"time_limit":8000,"memory_limit":1048576},"difficulty":{"LuoguStyle":"P7"},"is_remote":true,"is_sync":true,"sync_url":null,"sign":"LGP9722"},"statements":[{"statement_type":"Markdown","content":"Prof. Pang has $n$ rectangles, the coordinate of the lower left corner of the $i$-th rectangle is $(x_{i,1}, y_{i,1})$, and the coordinate of the upper right corner is $(x_{i,2}, y_{i,2})$. Rectangles may overlap.\n\nYou need to choose three straight lines such that:\n\n- Each line should be parallel to the $x$-axis or the $y$-axis, which means its formula is $x = a$ or $y = a$.\n- In the formula $x = a$ or $y = a$, $a$ should be an integer in $[1, 10^9]$.\n- These three lines should be distinct.\n- Each rectangle is $\\textbf{touched}$ by at least one line. A line touches a rectangle if it intersects with the boundary and/or the interior of the rectangle.\n\nYou need to compute the number of ways to choose three lines. Since the answer can be very large, output it modulo $998244353$. Two ways are considered the same if only the order of three lines differs in these two ways. \n\n## Input\n\nThe first line contains a single integer $T~(1 \\le T \\le 10^5)$, denoting the number of test cases.\n\nFor each test case, the first line contains an integer $n~(1 \\le n \\le 10^5)$. The $i$-th line of the next $n$ lines contains four integers $x_{i,1}, y_{i,1},x_{i,2}, y_{i,2}~(1\\le x_{i,1}