| 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. |
|
|
|
|
