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code_segments/segment_73.txt

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+Turtle just received $n$ segments and a sequence $a_1, a_2, \ldots, a_n$. The $i$-th segment is $[l_i, r_i]$.
+
+Turtle will create an undirected graph $G$. If segment $i$ and segment $j$ intersect, then Turtle will add an undirected edge between $i$ and $j$ with a weight of $|a_i - a_j|$, for every $i \ne j$.
+
+Turtle wants you to calculate the sum of the weights of the edges of the minimum spanning tree of the graph $G$, or report that the graph $G$ has no spanning tree.
+
+We say two segments $[l_1, r_1]$ and $[l_2, r_2]$ intersect if and only if $\max(l_1, l_2) \le \min(r_1, r_2)$.
+
+Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 10^5$). The description of the test cases follows.
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+The first line of each test case contains a single integer $n$ ($2 \le n \le 5 \cdot 10^5$) — the number of segments.
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+The $i$-th of the following $n$ lines contains three integers $l_i, r_i, a_i$ ($1 \le l_i \le r_i \le 10^9, 1 \le a_i \le 10^9$) — the $i$-th segment and the $i$-th element of the sequence.
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+It is guaranteed that the sum of $n$ over all test cases does not exceed $5 \cdot 10^5$.
+
+For each test case, output a single integer — the sum of the weights of the edges of the minimum spanning tree of the graph $G$. If the graph $G$ has no spanning tree, output $-1$.
+
+In the first test case, the graph $G$ is as follows:
+
+![](CDN_BASE_URL/7b0a32f8f1d54a5dbbaffee1efd8ece1)
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+One of the minimum spanning trees of $G$ is as follows:
+
+![](CDN_BASE_URL/7a035af2d5227648781d0c24b81c076e)
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+The sum of the weights of the edges of the minimum spanning tree is $9$.
+
+In the second test case, the graph $G$ is as follows:
+
+![](CDN_BASE_URL/62be880a08fa85071b491d6badd5f58e)
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+$G$ is already a tree, and the sum of the weights of the tree is $13$.
+
+In the third test case, the graph $G$ is as follows:
+
+![](CDN_BASE_URL/b667aa771d019e3a8a3a4c4372200f03)
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+In the fourth test case, the graph $G$ is as follows:
+
+![](CDN_BASE_URL/45bc2d052677dbf032ff37fd1d723d83)
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+It's easy to see that $G$ is no