| **N** ladders have been set up in a room, which can be represented as a 2D plane when viewed from the side. The room's floor is the horizontal line with y-coordinate 0, and its ceiling is the horizontal line with y-coordinate **H**. The _i_th ladder is a vertical line segment between integral coordinates (**Xi**, **Ai**) and (**Xi**, **Bi**), located within the inclusive bounds of the room (such that 0 ≤ **Ai** < **Bi** ≤ **H**). Note that each ladder may be touching the floor and/or ceiling, or may be floating in mid-air (don't question it). No two ladders overlap with one another (even at their endpoints). | |
| Sneider the Snake has taken an interest in this room, and may add 0 or more | |
| snakes to it. The _j_th snake will be a vertical line segment between some | |
| coordinates (**xj**, **aj**) and (**xj**, **bj**), located strictly inside the | |
| bounds of the room (with **xj** being any non-negative real number, and **aj** | |
| and **bj** being integers such that 0 < **aj** ≤ **bj** < **H**). A snake may | |
| be a length-0 line segment, with its endpoints being equal, in which case it | |
| occupies only a single point on the plane. No snake may overlap with any other | |
| snake, nor with any ladder (even at an endpoint). | |
| Flynn the Flying Squirrel finds herself on the floor at coordinates (0, 0), | |
| and wants to reach coordinates (0, **H**) on the ceiling. At any point, she | |
| may gracefully hover horizontally (left or right) as long as she doesn't | |
| overlap with any snake (including exactly at one of its endpoints). She may | |
| also move vertically (up or down) as long as she's overlapping with a ladder | |
| (including exactly at one of its endpoints). Flynn always moves continuously | |
| around the plane (she does not skip from one integral coordinate to the next). | |
| Sneider the Snake doesn't want Flynn to reach her destination, just because he | |
| likes being mean. Determine the minimum possible sum of lengths of snakes | |
| which Sneider must place such that Flynn will be unable to reach coordinates | |
| (0, **H**) from her initial position (0, 0), if possible. | |
| ### Input | |
| Input begins with an integer **T**, the number of rooms. For each room, there | |
| is first a line containing the space-separated integers **N** and **H**. Then, | |
| **N** lines follow, the _i_th of which contains the space-separated integers | |
| **Xi**, **Ai**, and **Bi**. | |
| ### Output | |
| For the _i_th room, print a line containing "Case #_i_: " followed by 1 | |
| integer, either the minimum total length of snakes required, or -1 if Sneider | |
| cannot prevent Flynn from reaching coordinates (0, **H**). | |
| ### Constraints | |
| 1 ≤ **T** ≤ 150 | |
| 1 ≤ **N** ≤ 50 | |
| 1 ≤ **H** ≤ 100,000 | |
| 0 ≤ **Xi** ≤ 100,000 | |
| 0 ≤ **Ai** < **Bi** ≤ **H** | |
| 0 ≤ **xj** | |
| 0 < **aj** ≤ **bj** < **H** | |
| ### Explanation of Sample | |
| In the first case, one optimal way for Sneider to prevent Flynn from reaching | |
| coordinates (0, 4) involves placing a length-2 snake with endpoints (0.5, 1) | |
| and (0.5, 3), as illustrated below (with ladders indicated in brown and the | |
| snake indicated in green): | |
|  | |
| In the second case, Flynn already can't reach coordinates (0, 100) even if | |
| Sneider doesn't place any snakes. | |
| In the third case, Flynn cannot be prevented from reaching coordinates (0, 9). | |
| In the fourth case, one optimal way for Sneider to prevent Flynn from reaching | |
| coordinates (0, 30) involves placing a length-1 snake with endpoints (9, 20) | |
| and (9, 21), two length-0 snakes at coordinates (14, 20) and (16, 20), and a | |
| length-2 snake with endpoints (24, 20) and (24, 22). The sum of these snakes' | |
| lengths is 1 + 0 + 0 + 2 = 3. | |