| You know what a finshake is, right? It's just like a handshake. Except | |
| performed by fish rather than humans. | |
| There are **N** pools of water in a row, numbered from 1 to **N** in order. | |
| Pool _i_'s water level is at an elevation of **Hi** metres. There are **N** \- | |
| 1 equally-tall walls, one between each pair of adjacent pools, with the top of | |
| each wall at an elevation of **W** metres. All of the water levels are lower | |
| than the tops of the walls (in other words, **Hi** < **W** for each _i_). | |
| There are also **M** fish throughout the pools. The _i_th fish initially lives | |
| in pool **Pi**, and has a jumping height of **Ji** metres. It can jump over a | |
| wall from any given pool **a** to an adjacent pool **b** (such that |**a** \- | |
| **b**| = 1) if and only if **Ji** > **W** \- **Ha**. Multiple fish may live in | |
| the same pool. | |
| Each of the **M** fish will spend some time jumping over walls amongst the | |
| pools, before each choosing a final pool to settle in. After all of the fish | |
| have settled down, for each unique unordered pair of fish who have ended up in | |
| the same pool as one another, they will give each other a finshake. Assuming | |
| the fish all work together, what's the maximum number of finshakes which can | |
| occur once they've all settled down in their chosen pools? | |
| ### Input | |
| Input begins with an integer **T**, the number of rows of pools. For each row | |
| of pools, there is first a line containing the space-separated integers **N**, | |
| **M**, and **W**. Then follows a line containing the **N** space-separated | |
| integers **H1** through **HN**. Then **M** lines follow, the _i_th of which | |
| contains the space-separated integers **Pi** and **Ji**. | |
| ### Output | |
| For the _i_th row of pools, output a line containing "Case #_i_: " followed by | |
| the maximum number of finshakes which can occur. | |
| ### Constraints | |
| 1 ≤ **T** ≤ 50 | |
| 1 ≤ **N** ≤ 500 | |
| 1 ≤ **M** ≤ 50 | |
| 2 ≤ **W** ≤ 1,000,000 | |
| 1 ≤ **Hi** < **W** | |
| 1 ≤ **Pi** ≤ **N** | |
| 1 ≤ **Ji** ≤ 1,000,000 | |
| ### Explanation of Sample | |
| In the first case, neither fish has a sufficient jumping height to jump over | |
| the wall from its own pool to the other pool. As such, each fish must remain | |
| isolated in its own pool, resulting in 0 finshakes being exchanged. | |
| In the second case, the second fish has sufficient jumping strength to go back | |
| and forth over the wall. It should choose to settle in the first pool. With | |
| both fish ending up in the same pool, they'll exchange 1 finshake. | |
| In the third case, the first fish is unable to leave the first pool. The | |
| fourth fish could decide to choose to stay in the first pool as well, and give | |
| the first fish a finshake. However, it's better for the last 3 fish to all | |
| congregate in the second pool instead, as this will result in a total of 3 | |
| finshakes being exchanged amongst them. | |