| Some pies are sweet, full of fruit and jam and sugar. | |
| Some pies are savory, full of meat and potatoes and spices. | |
| Some pies are in fact not pies at all but tarts or galettes. This probably | |
| won't stop you from eating them. | |
| Every single day for **N** days, you're determined to eat a pie for dinner. | |
| Every morning, you'll take a trip to your local pie shop, and buy 0 or more of | |
| their pies. Every night, you'll eat one pie that you've bought. Pies never go | |
| bad, so you don't need to eat a pie on the same day that you bought it. You | |
| may instead eat one that you purchased on an earlier day. | |
| On the _i_th day, the shop has **M** pies for sale, with the _j_th of these | |
| pies costing **Ci,j** dollars. You can choose to buy any (possibly empty) | |
| subset of them. However, this shop has measures in place to protect itself | |
| against crazy pie fanatics buying out its products too quickly. In particular, | |
| if you buy **p** pies on a single day, you must pay an additional tax of | |
| **p**2 dollars. | |
| ### Input | |
| Input begins with an integer **T**, the number of times you go on a pie-eating | |
| spree. For each case, there is first a line containing two space-separated | |
| integers, **N** and **M**. Then, **N** lines follow, each containing **M** | |
| space-separated integers. The _j_th integer on the _i_th line is **Ci,j**. | |
| ### Output | |
| For the _i_th case, print a line containing "Case #**i**: " followed by the | |
| minimum you need to pay to eat a pie every day. | |
| ### Constraints | |
| 1 ≤ **T** ≤ 100 | |
| 1 ≤ **N**, **M** ≤ 300 | |
| 1 ≤ **Ci,j** ≤ 1,000,000 | |
| ### Explanation of Sample | |
| In the first case, you should buy both pies on the first day, for a total cost | |
| of 1 + 1 + 22 = 6. On the second day you should buy one pie for 100 + 12 = | |
| 101. On the third day you can eat one of the spare pies you bought on the | |
| first day. | |
| In the third case, you should buy and eat the cheapest pie every day, for a | |
| daily cost of 1 + 12 = 2, and a total cost of 10. | |
| In the fourth case, one possible solution is to buy two pies on the first day | |
| (1 + 1 + 22 = 6), two pies on the second day (2 + 2 + 22 = 8), and one pie on | |
| the third day (3 + 12 = 4) for a total cost of 18. On the fourth and fifth | |
| days you can eat your two spare pies from the first and second days. | |