| The starship Enterprise, bravely captained by Jean-Luc Picard, is on yet |
| another mission to explore strange new worlds, seek out new life and new |
| civilizations, and boldly go where no one has gone before! Equipped with a |
| state-of-the-art warp drive capable of attaining warp factor 11 and revising |
| the Enterprise's space-time coordinates almost at will (even sending the ship |
| back in time), not much can stand in the explorers' way. Though, they _are_ |
| low on medical supplies, so they will need to first stock up on neurozine gas |
| for anesthetic purposes. |
|
|
| The Enterprise is heading to the Alpha Omicron solar system, which consists of |
| **N** planets, numbered from 1 to **N**. It also features **M** space |
| conduits, the _i_th of which allows the Enterprise to travel in either |
| direction between two different planets **Ai** and **Bi**. No two conduits |
| directly link the same unordered pair of planets, and **each planet is |
| reachable from each other planet** by following a sequence of conduits. |
|
|
| There's a geyser capable of emitting neurozine located on each planet, though |
| all **N** geysers are initially inactive. A sequence of **K** events will then |
| take place, one per hour. The event at hour _i_ is described by integers |
| **Ei** and **Vi**, with **Ei** indicating the event's type, which is one of |
| the following: |
|
|
| * **Ei** = 1: The **Vi**th conduit (1 ≤ **Vi** ≤ **M**) collapses, and can no longer be used from that moment onwards. Each conduit collapses at most once. |
| * **Ei** = 2: The geyser on planet **Vi** (1 ≤ **Vi** ≤ **N**) activates, and begins emitting neurozine. Each geyser is activated at most once. |
| * **Ei** = 3: The geyser on planet **Vi** (1 ≤ **Vi** ≤ **N**) deactivates, and no longer emits neurozine from that moment onwards. Each geyser is deactivated at most once, and is guaranteed to not be deactivated before it has been activated. |
|
|
| The Enterprise will arrive in the Alpha Omicron system at some planet _x_ and |
| just before some hour _y_. When the starship is currently at a certain planet |
| (and a certain time), Captain Picard may issue any of the following commands |
| to his crew: |
|
|
| * Remain at that planet and wait until any future time. |
| * Travel through an uncollapsed space conduit directly from that planet to another one. Thanks to warp technology, this may be done instantly. |
| * Collect neurozine from that planet's geyser, if it's currently active. This may be done instantly. |
| * Remain at that planet while travelling backwards to any past time which is **at most 24 hours earlier than the Enterprise's original arrival time in the solar system** (in other words, the Enterprise may end up just before hour (_y_ \- 24), but no earlier). However, **this may only be done at most once**. The Enterprise retains any neurozine that it had collected before this "temporal revision". |
|
|
| Picard wants his crew to collect neurozine from as many _different_ geysers as |
| possible; there's no additional value in collecting neurozine from any given |
| geyser multiple times, including both before and after travelling back in |
| time. However, Picard hasn't yet decided where and when the Enterprise should |
| arrive in the Alpha Omicron system. He has **S** such possible starting |
| situations in mind, the _i_th of which would have the Enterprise arrive at |
| planet **Xi** just before hour **Yi**. For each hypothetical starting |
| situation, please help Picard determine the maximum number of different |
| geysers from which the Enterprise could then proceed to collect neurozine! |
|
|
| Letting **ansi** be the answer for the _i_th starting situation, you must |
| output the sum of **ans1..S** in order to minimize the size of the output. |
| Please note that this sum may not fit within a 32-bit integer. |
|
|
| The starting situations must be considered one after another. In order to |
| enforce this, rather than being given **X1..S** and **Y1..S** explicitly, you |
| must compute them based on given values **X'1..S** and **Y'1..S**. For the |
| first starting situation, **X1** = **X'1** and **Y1** = **Y'1**, while for |
| each subsequent starting situation _i_ (2 ≤ _i_ ≤ **S**), **Xi** = **X'i** xor |
| **ansi-1** and **Yi** = **Y'i** xor **ansi-1** (where "xor" is the bitwise xor |
| operator, "^" in most programming languages). |
|
|
| ### Input |
|
|
| Input begins with an integer **T**, the number of missions. |
| For each mission, there is first a line containing the space-separated |
| integers **N**, **M**, **K** and **S**. |
| Then, **M** lines follow, the _i_th of which contains the space-separated |
| integers **Ai** and **Bi**. |
| Then, **K** lines follow, the _i_th of which contains the space-separated |
| integers **Ei** and **Vi**. |
| Then, **S** lines follow, the _i_th of which contains the space-separated |
| integers **X'i** and **Y'i**. |
|
|
| ### Output |
|
|
| For the _i_th mission, print a line containing "Case #_i_: " followed by one |
| integer, the sum of the answers for the **S** starting situations. |
|
|
| ### Constraints |
|
|
| 1 ≤ **T** ≤ 100 |
| 2 ≤ **N** ≤ 800,000 |
| 1 ≤ **M**, **K**, **S** ≤ 800,000 |
| 1 ≤ **Ai**, **Bi** ≤ **N** |
| 1 ≤ **Ei** ≤ 3 |
| 1 ≤ **Xi** ≤ **N** |
| 1 ≤ **Yi** ≤ **K** |
| 0 ≤ **X'i**, **Y'i** ≤ 1,000,000,000 |
|
|
| The sum of **N** across all **T** test cases is no greater than 2,000,000. |
| The sum of **M** across all **T** test cases is no greater than 2,000,000. |
| The sum of **K** across all **T** test cases is no greater than 2,000,000. |
| The sum of **S** across all **T** test cases is no greater than 2,000,000. |
|
|
| ### Explanation of Sample |
|
|
| In the first case, if the Enterprise arrives at planet 1 just before hour 3, |
| Picard could issue the following sequence of orders to help his crew collect |
| neurozine from both planets' geysers: |
|
|
| 1. Travel through the 1st space conduit to planet 2. |
| 2. Wait until after hour 3. |
| 3. Collect neurozine from planet 2's now-active geyser. |
| 4. Travel back in time to just before hour 2. |
| 5. Travel through the 1st space conduit to planet 1. |
| 6. Collected neurozine from planet 1's active geyser. |
|
|
| In the second case, the starting situations and corresponding answers are as |
| follows: |
|
|
| i | Xi | Yi | ansi |
| ------------------ |
| 1 | 2 | 1 | 3 |
| 2 | 1 | 6 | 2 |
| 3 | 3 | 5 | 3 |
| |
| For the first starting situation, the Enterprise could remain on planet 2 |
| until its geyser activates at hour 6, collect its neurozine, travel back in |
| time to just before hour 2, travel to planet 1 and collect its neurozine, |
| travel to planet 2 and then to planet 3, and remain there to collect its |
| neurozine after hour 5. On the other hand, for the second starting situation, |
| neurozine from all 3 geysers cannot be collected. |
|
|
| In the third case, the starting situations and corresponding answers are as |
| follows: |
|
|
| i | Xi | Yi | ansi |
| ------------------ |
| 1 | 1 | 4 | 4 |
| 2 | 5 | 8 | 3 |
| 3 | 2 | 9 | 3 |
| 4 | 3 | 6 | 4 |
| |
| In the fourth case, the starting situations and corresponding answers are as |
| follows: |
|
|
| i | Xi | Yi | ansi |
| ------------------ |
| 1 | 6 | 16 | 7 |
| 2 | 4 | 6 | 8 |
| 3 | 10 | 22 | 7 |
| 4 | 3 | 13 | 7 |
| 5 | 6 | 11 | 8 |
| 6 | 5 | 17 | 6 |
| 7 | 2 | 21 | 7 |
| |
| In the fifth case, the first 5 starting situations and corresponding answers |
| are as follows: |
|
|
| i | Xi | Yi | ansi |
| ------------------ |
| 1 | 20 | 47 | 2 |
| 2 | 4 | 49 | 7 |
| 3 | 24 | 47 | 1 |
| 4 | 20 | 9 | 13 |
| 5 | 3 | 38 | 9 |
| |
|
|
