Time Limit: 10 Seconds
Memory Limit: 32768 KB
Once upon a time, there lived Catherine Ironfist, the Queen of Enroth. One
day, she received the news of her father's death. So she sailed for Erathia
to attend her father's funeral. Fearing the worst, she assembled a military
fleet as her escort. On reaching the coast of Erathia, Catherine found an allied
wizard's tower, devastated from battle and abandoned. There she learned that
a black-hearted knight poisoned her father using a goblet of wine, and Erathia
was falling to the enemies. And then, she mustered local armies, and marched
to Erathia's castle, restoring lost land along the way.
During the battles, she found that the equipments for the soldiers were in urgent
need. And she knew clearly that the best equipments were made by the battle
dwarf's workshop in the world. The workshop's equipments were well known for
the firmness and top-quality. "Cloak of the Undead King", "Armor
of the Damned", "Angelic Helm" are the nonesuch ones. But unfortunately,
the workshop was seated at the Erathia's castle, the territory under the enemy's
control. So she sent a brave volunteer to come into the castle and asked for
the workshop's help.
"It's our pleasure to help the righteous heroine." Rion, the leader
of the workshop sent the message to Catherine, " We haven't enough resources
to build the nonesuch equipments. So we'll try to offer the ordinary equipments
as more as possible. Still, those ones are much better the equipments made by
other workshops. But we have faced a difficult problem. The castle is in a state
of siege. The guards prohibited the equipments to be carried away from the castle.
We have to ask for the trade caravans' help. As you know, each trade caravan's
capability of carrying equipments is limited. If they had carried a little more,
they would be detected by the guards, which would lead them into the prison.
So you have to arrange how to carry these equipments."
The workshop would offer helms, armors and boots. These three ones had different
defend capabilities. Also, their weight and size were different from each other.
What's more, Rion had told Catherine that if armed with those three ones together,
they would form a set of equipments, which might provide much more defend capability.
As far as the trade caravan was concerned, each one had its special weight limitation
and size limitation. Catherine had to make the decision on how to arrange the
transportation plan to provide her soldiers as more defend capabilities as possible.
Could you help her to finish the plan?
The input describes several test cases. The first line of input for each test
case contains a single integer n, the number of trade caravans (0 <= n <= 100).
The following four lines describe the information of those equipments. The first
line contains three integers w1, s1 and d1, indicating the weight, size and
defend capabilities of the helm. The integers w2, s2 and d2 in the second line
represent the weight, size and defend capabilities of the armor. Also, in the
third line, w3, s3 and d3 are the weight, size and defend capabilities of the
boot. The fourth line contains four integers c1, c2, c3 and d4. Among those
integers, c1, c2, c3 are the number of helms, armors and boots in a set of equipments,
d4 is the capability of this set.
In the test case, following those data are n lines, describing the carrying
capabilities of the trade caravans. Each line contains two integers, xi and
yi, indicating the weight limit and size limit of a trade caravan.
The input is terminated by a description starting with n = 0. This description
should not be processed.
Note: Because of the trade caravans' carrying capabilities, you may assume the
quantities of the helms, armors and boots will not exceed 500 respectively.
Your program must compute the defend capability of the best carrying plan. That
is, after having performed the carrying plan, the defend capability of the equipments
which have been carried away from the castle should be the largest. For each
test case in the input file, print the case number and a colon, and then the
defend capability of those equipments.
Print a blank line between test cases.
1 1 3
5 6 10
2 1 2
1 1 1 50
Output for the Sample Input
Case 1: 50
Source: Asia 2001, Shanghai (Mainland China)