Upload code_segments/segment_238.txt with huggingface_hub

code_segments/segment_238.txt

@@ -0,0 +1,25 @@
+This is a hard version of this problem. The differences between the versions are the constraint on $m$ and $r_i < l_{i + 1}$ holds for each $i$ from $1$ to $m - 1$ in the easy version. You can make hacks only if both versions of the problem are solved.
+
+Turtle gives you $m$ intervals $[l_1, r_1], [l_2, r_2], \ldots, [l_m, r_m]$. He thinks that a permutation $p$ is interesting if there exists an integer $k_i$ for every interval ($l_i \le k_i < r_i$), and if he lets $a_i = \max\limits_{j = l_i}^{k_i} p_j, b_i = \min\limits_{j = k_i + 1}^{r_i} p_j$ for every integer $i$ from $1$ to $m$, the following condition holds:
+
+$$\max\limits_{i = 1}^m a_i < \min\limits_{i = 1}^m b_i$$
+
+Turtle wants you to calculate the maximum number of inversions of all interesting permutations of length $n$, or tell him if there is no interesting permutation.
+
+An inversion of a permutation $p$ is a pair of integers $(i, j)$ ($1 \le i < j \le n$) such that $p_i > p_j$.
+
+Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 10^3$). The description of the test cases follows.
+
+The first line of each test case contains two integers $n, m$ ($2 \le n \le 5 \cdot 10^3, 0 \le m \le 5 \cdot 10^3$) — the length of the permutation and the number of intervals.
+
+The $i$-th of the following $m$ lines contains two integers $l_i, r_i$ ($1 \le l_i < r_i \le n$) — the $i$-th interval. Note that there may exist identical intervals (i.e., there may exist two different indices $i, j$ such that $l_i = l_j$ and $r_i = r_j$).
+
+It is guaranteed that the sum of $n$ over all test cases does not exceed $5 \cdot 10^3$ and the sum of $m$ over all test cases does not exceed $5 \cdot 10^3$.
+
+For each test case, if there is no interesting permutation, output a single integer $-1$.
+
+Otherwise, output a single integer — the maximum number of inversions.
+
+In the third test case, the interesting permutation with the maximum number of inversions is $[5, 2, 4, 3, 1]$.
+
+In the fourth test case, the interesting permutation