B"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) <= min(r_1, r_2) . Each test contains multiple test cases. The first line contains the number of test cases t ( 1 <= t <= 10^5 ). The description of the test cases follows. The first line of each test case contains a single integer n ( 2 <= n <= 5 cdot 10^5 ) -- the number of segments. The i -th of the following n lines contains three integers l_i, r_i, a_i ( 1 <= l_i <= r_i <= 10^9, 1 <= a_i <= 10^9 ) -- the i -th segment and the i -th element of the sequence. 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: One of the minimum spanning trees of G is as follows: 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: 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: In the fourth test case, the graph G is as follows: It's easy to see that G is not connected, so G has no spanning tree. "...