The skyline of Singapore as viewed from the Marina Promenade (shown on the left) is one of the iconic scenes of Singapore. Country X would also like to create an iconic skyline, and it has put up a call for proposals. Each submitted proposal is a description of a proposed skyline and one of the metrics that country X will use to evaluate a proposed skyline is the amount of overlap in the proposed sky-line. 

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As the assistant to the chair of the skyline evaluation committee, you have been tasked with determining the amount of overlap in each proposal. Each proposal is a sequence of buildings, b₁, b₂,..., b_n <tex2html_verbatim_mark>, where a building is specified by its left and right endpoint and its height. The buildings are specified in back to front order, in other words a building which appears later in the sequence appears in front of a building which appears earlier in the sequence. 

The skyline formed by the first k <tex2html_verbatim_mark>buildings is the union of the rectangles of the first k <tex2html_verbatim_mark>buildings (see Figure 4). The overlap of a building, b_i <tex2html_verbatim_mark>, is defined as the total horizontal length of the parts of b_i <tex2html_verbatim_mark>, whose height is greater than or equal to the skyline behind it. This is equivalent to the total horizontal length of parts of the skyline behind b_i<tex2html_verbatim_mark>which has a height that is less than or equal to h_i <tex2html_verbatim_mark>, where h_i <tex2html_verbatim_mark>is the height of building b_i <tex2html_verbatim_mark>. You may assume that initially the skyline has height zero everywhere. 

The input consists of a line containing the number c <tex2html_verbatim_mark>of datasets, followed by c <tex2html_verbatim_mark>datasets, followed by a line containing the number ` 0‘. 

The first line of each dataset consists of a single positive integer, n <tex2html_verbatim_mark>(0 < n < 100000) <tex2html_verbatim_mark>, which is the number of buildings in the proposal. The following n<tex2html_verbatim_mark>lines of each dataset each contains a description of a single building. The i <tex2html_verbatim_mark>-th line is a description of building b_i <tex2html_verbatim_mark>. Each building b_i <tex2html_verbatim_mark>is described by three positive integers, separated by spaces, namely, l_i <tex2html_verbatim_mark>, r_i <tex2html_verbatim_mark>and h_i <tex2html_verbatim_mark>, where l_i <tex2html_verbatim_mark>and r_j <tex2html_verbatim_mark>(0 < l_i < r_i100000) <tex2html_verbatim_mark>represents the left and right end point of the building and h_i represents the height of the building. 

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The output consists of one line for each dataset. The c <tex2html_verbatim_mark>-th line contains one single integer, representing the amount of overlap in the proposal for dataset c<tex2html_verbatim_mark>. You may assume that the amount of overlap for each dataset is at most 2000000. 

Note: In this test case, the overlap of building b₁ <tex2html_verbatim_mark>, b₂ <tex2html_verbatim_mark>and b₃ <tex2html_verbatim_mark>are 6, 4 and 4 respectively. Figure 4 shows how to compute the overlap of building b₃ <tex2html_verbatim_mark>. The grey area represents the skyline formed by b₁ <tex2html_verbatim_mark>and b₂ <tex2html_verbatim_mark>and the black rectangle represents b₃ <tex2html_verbatim_mark>. As shown in the figure, the length of the skyline covered by b₃ <tex2html_verbatim_mark>is from position 3 to position 5 and from position 11 to position 13, therefore the overlap of b₃ <tex2html_verbatim_mark>is 4. 

1 3 5 11 3 1 10 1 3 13 2 0

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