[ICPC 2022 Jinan R] Set of Intervals

Luogu

IDLGP9674

Time2000ms

Memory512MB

DifficultyP6

2022O2优化ICPCAd-hoc分类讨论济南

Prof. Pang has a multi-set of intervals $S=\{[l_i,r_i]\}$($l_i<r_i$). Prof. Pang will perform the following operation for $|S|-1$ times: - Select two intervals $[a,b]$ and $[c,d]$ from $S$, and then choose two integers $x,y$ satisfying $x\in [a,b], y\in [c,d], x<y$. After that, delete $[a,b]$ and $[c,d]$ from $S$, and add $[x,y]$ to $S$. It's easy to find that $S$ contains exactly one interval after the operations, and Prof. Pang will get the interval as a gift. Now Prof. Pang wants you to calculate how many different intervals he can get. ## Input The first line contains one integer $T~$($1\le T \le 10^4$), the number of test cases. For each test case, the first line contains one integer $n~$($1\le n\le 10^5$) --- the size of $S$. Each of the following $n$ lines contains two integers $l_i$ and $r_i~$($1\le l_i<r_i\le 10^9$), describing the $i$-th interval in $S$. It is guaranteed that the sum of $n$ over all test cases is no more than $10^5$. ## Output For each test case, output one line containing the answer to Prof. Pang's question. [samples]

Samples

Input #1

4
1
1 1000000000
2
1 1000000000
1 1000000000
4
1 2
3 4
5 6
7 8
4
1 3
2 4
5 8
6 7

Output #1

1
499999999500000000
26
28

API Response (JSON)

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    "name": "[ICPC 2022 Jinan R] Set of Intervals",
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      "content": "Prof. Pang has a multi-set of intervals $S=\\{[l_i,r_i]\\}$($l_i<r_i$). Prof. Pang will perform the following operation for $|S|-1$ times: - Select two intervals $[a,b]$ and $[c,d]$ from $S$, and then",
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      "content": "Prof. Pang has a multi-set of intervals $S=\\{[l_i,r_i]\\}$($l_i<r_i$).\n\nProf. Pang will perform the following operation for $|S|-1$ times:\n\n- Select two intervals $[a,b]$ and $[c,d]$ from $S$, and then...",
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