| What day is it today? Wasn't there something you were supposed to remember? | |
| Eh, it was probably nothing... | |
| ... | |
| Wait! Oh no! It's your anniversary today! And you don't have a gift for your | |
| spouse! | |
| Only one thing can save you now: online shopping. Logging onto your favourite | |
| shopping site, the top automated suggestion looks perfect (or at least | |
| passable) — a graph. Your spouse probably loves graphs, right? More | |
| importantly, it can be delivered directly to your house within half an hour. | |
| The graph comes with **N** nodes, the _i_th of which is labelled with a non- | |
| zero integer **Li**. Unfortunately, no edges are included by default — you | |
| have to pay extra for those. You'd better purchase one or more edges so that | |
| it looks like you put extensive thought into your gift. Purchasing an | |
| undirected edge between two different nodes _i_ and _j_ costs **Li** * **Lj** | |
| dollars (note that this cost may be negative, in which case you actually | |
| receive money for "purchasing" that edge). You won't purchase more than one | |
| edge between any unordered pair of nodes, and you won't purchase any self- | |
| loops (edges connecting a node directly to itself). | |
| In order to make the graph appealing to your spouse, you've decided that it | |
| should have the following two properties: | |
| 1. Each node should be adjacent to at least one other node. | |
| 2. Each node with a positive label should be adjacent to at most one node with a negative label. | |
| Any such graph should make a fine gift, so... you might as well go with the | |
| cheapest option, right? You'd like to determine the minimum possible total | |
| cost of edges to purchase which result in a graph with both properties | |
| described above. Note that this total "cost" may be negative. | |
| ### Input | |
| Input begins with an integer **T**, the number of test cases. For each test | |
| case, there is first a line containing the integer **N**. Then one more line | |
| follows containing the **N** space-separated integers **L1** through **LN**. | |
| ### Output | |
| For the _i_th test case, output a line containing "Case #_i_: " followed by | |
| the minimum cost (in dollars) required to complete the graph gift. | |
| ### Constraints | |
| 1 ≤ **T** ≤ 40 | |
| 2 ≤ **N** ≤ 30,000 | |
| -10,000,000 ≤ **Li** ≤ 10,000,000 | |
| **Li** ≠0 | |
| ### Explanation of Sample | |
| In the first case, you should purchase an edge between the two nodes for a | |
| cost of (-1)*(-1) = 1. | |
| In the second case, you should purchase an edge from the third node to each of | |
| the other nodes, for a cost of (-3)*(-1) + (-3)*2 + (-3)*4 = -15. | |