| Oh boy, Sid's family has taken him to Pizza Planet today! Pizza Planet is a | |
| fun family restaurant with lots of arcade games, but the highlight for Sid is | |
| Space Crane, a crane game with cool toy prizes. He'd love to win some to add | |
| to his collection! | |
| Looking at Space Crane from the front, it can be represented as a 2D plane. At | |
| the top, there's a horizontal crane track, a line segment running from (0, | |
| **M**) to (1,000,000, **M**). There's a claw attached to this track by an | |
| extendible wire. The claw is initially located at coordinates (0, **M**) and | |
| may be moved anywhere within the inclusive range of x-coordinates [0, | |
| 1,000,000] and the inclusive range of y-coordinates [0, **M**]. At all points | |
| in time, the connecting wire runs vertically upwards from the claw's position | |
| to the track. That is, when the claw is at some point (**x**, **y**), the wire | |
| forms a line segment from (**x**, **y**) to (**x**, **M**). | |
| Space Crane works differently than most crane games — rather than using the | |
| claw to directly pick up prizes, the player's objective is to navigate the | |
| claw to a series of targets. There are **N** targets, all with distinct | |
| x-coordinates, with the _i_th target at coordinates (**Xi**, **Yi**). If Sid | |
| manages to move the claw to touch the **N** targets in order from 1 to **N**, | |
| and then return the claw to its original position at (0, **M**), he'll win a | |
| prize! Targets are not collected along the way (they're only touched by the | |
| claw), meaning that all **N** targets will remain in place for the duration of | |
| the game. | |
| The claw may never be anywhere directly underneath a target (at the same | |
| x-coordinate but with a strictly smaller y-coordinate), as it would interfere | |
| with the crane's wire. However, the claw may occupy exactly the same position | |
| as a target, including passing directly through targets which Sid is not | |
| currently trying to touch. | |
| Before the game starts, Sid is given an opportunity to adjust each of the | |
| **N** targets. There are two possible choices for each target: it may either | |
| be left in its original position, or its y-coordinate may be increased by | |
| exactly 1 unit. These adjustments may only be performed in advance, and the | |
| targets must then all remain in their chosen positions for the duration of the | |
| game. | |
| Completing the game normally isn't much of a challenge for Sid, but he's heard | |
| a rumour that Space Crane awards double prizes if completed as efficiently as | |
| possible! The game measures efficiency based on how much the claw's wire | |
| expands and contracts. As such, Sid would like to adjust the targets and then | |
| move the claw around such that the total amount of vertical movement (changes | |
| in y-coordinate) performed by the claw is minimized. Note that the claw's | |
| horizontal movement (changes in x-coordinate) is ignored. Help Sid determine | |
| the minimum total amount of vertical claw movement which might be required! | |
| ### Input | |
| Input begins with an integer **T**, the number of times Sid plays Space Crane. | |
| For each game, there is first a line containing the space-separated integers | |
| **N** and **M**. Then **N** lines follow, the _i_th of which contains the | |
| space-separated integers **Xi** and **Yi**. | |
| ### Output | |
| For the _i_th game, output a line containing "Case #_i_: " followed by the the | |
| minimum total amount of vertical claw movement, in units. | |
| ### Constraints | |
| 1 ≤ **T** ≤ 100 | |
| 1 ≤ **N** ≤ 1,000,000 | |
| 3 ≤ **M** ≤ 1,000,000 | |
| 0 ≤ **Xi** ≤ 1,000,000 | |
| 1 ≤ **Yi** ≤ **M** \- 2 | |
| ### Explanation of Sample | |
| In the first case, the single target's height should be increased from 1 to 2. | |
| Then, aside from moving right and left by 1,000,000 units, the crane will need | |
| to move downwards by 8 units to reach the target and upwards by 8 units to | |
| return to its original position, for a total of 16 units of vertical movement. | |
| In the second case, if the targets are all left at their original heights, 10 | |
| units of vertical movement will be required. If their heights are all | |
| increased by 1, 8 units will be required. However, if just the first two | |
| targets are raised, then only 6 units will be required, which is the minimum | |
| achievable amount. | |