Scheduling Lectures

Time Limit: 10 Seconds
Memory Limit: 32768 KB

You are teaching a course and must cover n (1 <= n <= 1000) topics. The
length of each lecture is L (1 <= L <= 500) minutes. The topics require
t1, t2, ..., tn (1 <= ti <= L) minutes each. For each topic, you must decide
in which lecture it should be covered. There are two scheduling restrictions:

1. Each topic must be covered in a single lecture. It cannot be divided into
two lectures. This reduces discontinuity between lectures.

2. Topic i must be covered before topic i + 1 for all 1 <= i < n. Otherwise,
students may not have the prerequisites to understand topic i + 1.

With the above restrictions, it is sometimes necessary to have free time at
the end of a lecture. If the amount of free time is at most 10 minutes, the
students will be happy to leave early. However, if the amount of free time is
more, they would feel that their tuition fees are wasted. Therefore, we will
model the dissatisfaction index (DI) of a lecture by the formula:

where C is a positive integer, and t is the amount of free time at the end
of a lecture. The total dissatisfaction index is the sum of the DI for each
lecture.

For this problem, you must find the minimum number of lectures that is needed
to satisfy the above constraints. If there are multiple lecture schedules with
the minimum number of lectures, also minimize the total dissatisfaction index.

**This problem contains multiple test cases!**

The first line of a multiple input is an integer N, then a blank line followed
by N input blocks. Each input block is in the format indicated in the problem
description. There is a blank line between input blocks.

The output format consists of N output blocks. There is a blank line between
output blocks.

Input

The input consists of a number of cases. The first line of each case contains
the integer n, or 0 if there are no more cases. The next line contains the integers
L and C. These are followed by n integers t1, t2, ..., tn.

**Output**

For each case, print the case number, the minimum number of lectures used, and
the total dissatisfaction index for the corresponding lecture schedule on three
separate lines. Output a blank line between cases.

** Sample Input **

1

6

30 15

10

10

10

10

10

10

10

120 10

80

80

10

50

30

20

40

30

120

100

0

**Sample Output**

Case 1:

Minimum number of lectures: 2

Total dissatisfaction index: 0

Case 2:

Minimum number of lectures: 6

Total dissatisfaction index: 2700

Source:

**East Central North America 1998**
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