| Phineas is the proud owner of an enormous new fish tank! Looking at the fish |
| tank from the side, it can be represented as an infinite 2D plane. Phineas has |
| installed **N** vertical dividers into the tank, the _i_th of which is a line |
| segment connecting points (**Xi**, **Ai**) and (**Xi**, **Bi**). No two |
| dividers overlap at any point (including at their endpoints). |
|
|
| Unfortunately, Phineas's fish tank is lacking in fish, but he'll soon rectify |
| that! He's going to place one or more fish into the tank, with each one |
| initially occupying any point of his choice (each coordinate may be non- |
| integral and arbitrarily small or large). No fish's location may overlap with |
| any of the dividers (including their endpoints), but multiple fish may be |
| placed at the same coordinates. |
|
|
| After the fish have been placed, each one may swim left and right freely |
| (continuously decreasing or increasing its x-coordinate), as long as it never |
| touches a divider (including its endpoints). Fish do not block one another |
| from swimming, so multiple fish are able to occupy the same coordinates. |
| However, no fish is able to change its y-coordinate. |
|
|
| At any given moment, each fish feels that its personal space is violated if |
| any other fish is currently at the same x-coordinate as it (either at its |
| current y-coordinate, or arbitrarily far above or below it). As such, if two |
| fish ever occupy the same x-coordinate as one another, they both become |
| unhappy. |
|
|
| Phineas suspects that someone's planning on stealing one of his dividers soon |
| after he places fish into the tank! |
|
|
| And he wants to ensure that none of his fish have any chance of becoming |
| unhappy! |
|
|
| But he still wants to have as many fish as possible! |
|
|
| As such, he'd like to determine the maximum number of fish which he can place |
| into the tank such that, no matter which single one of the **N** dividers is |
| subsequently removed, and no matter how the fish then decide to swim around, |
| none of the fish can ever become unhappy. |
|
|
| ### Input |
|
|
| Input begins with an integer **T**, the number of fish tanks. For each fish |
| tank, there is first a line containing the single integer **N**. Then, **N** |
| lines follow, the _i_th of which contains the 3 space-separated integers |
| **Xi**, **Ai**, and **Bi**. |
|
|
| ### Output |
|
|
| For the _i_th fish tank, output a line containing "Case #_i_: " followed by |
| the maximum number of fish which Phineas can place into the tank with no risk |
| of unhappiness. |
|
|
| ### Constraints |
|
|
| 1 ≤ **T** ≤ 90 |
| 1 ≤ **N** ≤ 500,000 |
| 0 ≤ **Xi** ≤ 1,000,000,000 |
| 0 ≤ **Ai** < **Bi** ≤ 1,000,000,000 |
|
|
| ### Explanation of Sample |
|
|
| In the first case, Phineas could, for example, place a fish at coordinates (5, |
| 5). If he placed another fish anywhere else in the tank (for example at |
| coordinates (-1, 2)), then if the single divider were removed, both fish would |
| be able to swim freely and might come to occupy the same x-coordinate as one |
| another. |
|
|
| In the second case, Phineas can place one fish at coordinates (-5, 5) and |
| another at coordinates (15, 5). |
|
|
| In the third case, no matter where Phineas might place two fish in the tank, |
| at least one choice of removed divider would result in them potentially |
| becoming unhappy. |
|
|
|
|
