### IOI '99 - Antalya-Belek, Turkey

## Little Shop of Flowers

You want to arrange the window of your flower shop in a most
pleasant way. You have *F *bunches of flowers, each being of a different kind, and at
least as many vases ordered in a row. The vases are glued onto the shelf and are numbered
consecutively 1 through *V*, where *V* is the number of vases, from left to
right so that the vase 1 is the leftmost, and the vase *V* is the rightmost vase. The
bunches are moveable and are uniquely identified by integers between 1 and *F*. These
id-numbers have a significance: They determine the required order of appearance of the
flower bunches in the row of vases so that the bunch *i* must be in a vase to the
left of the vase containing bunch *j* whenever *i* < *j*. Suppose, for
example, you have bunch of azaleas (id-number=1), a bunch of begonias (id-number=2) and a
bunch of carnations (id-number=3). Now, all the bunches must be put into the vases keeping
their id-numbers in order. The bunch of azaleas must be in a vase to the left of begonias,
and the bunch of begonias must be in a vase to the left of carnations. If there are more
vases than bunches of flowers then the excess will be left empty. A vase can hold only one
bunch of flowers.

Each vase has a distinct characteristic (just like flowers do). Hence, putting a bunch of flowers in a vase results in a certain aesthetic value, expressed by an integer. The aesthetic values are presented in a table as shown below. Leaving a vase empty has an aesthetic value of 0.

V A S E S |
||||||

1 |
2 |
3 |
4 |
5 |
||

Bunches |
1 (azaleas) |
7 | 23 | -5 | -24 | 16 |

2 (begonias) |
5 | 21 | -4 | 10 | 23 | |

3 (carnations) |
-21 | 5 | -4 | -20 | 20 |

According to the table, azaleas, for example, would look great in vase 2, but they would look awful in vase 4.

To achieve the most pleasant effect you have to maximize the sum of aesthetic values for the arrangement while keeping the required ordering of the flowers. If more than one arrangement has the maximal sum value, any one of them will be acceptable. You have to produce exactly one arrangement.

### Input

- The first line contains two numbers: the number of bunches of flowers
*F*(1 ≤*F*≤ 100) and the number of vases*V*(*F*≤*V*≤ 100). - The following
*F*lines: Each of these lines contains*V*integers, so that*A*_{ij}(-50 ≤*A*_{ij}≤ 50) is given as the*j*number on the (^{th}*i*+1)^{th}line of the input file.

### Output

The output should consist of two lines:- The first line will contain the sum of aesthetic values for your arrangement.
- The second line must present the arrangement as a list of
*F*numbers, so that the*k*th number on this line identifies the vase in which the bunch*k*is put.

### Sample Input

3 5 7 23 -5 -24 16 5 21 -4 10 23 -21 5 -4 -20 20

### Sample Output

53 2 4 5

All Submissions

Best Solutions

**Point Value:** 10

**Time Limit:** 2.00s

**Memory Limit:** 16M

**Added:** Aug 20, 2009

**Languages Allowed:**

C++03, PAS, C, HASK, ASM, RUBY, PYTH2, JAVA, PHP, SCM, CAML, PERL, C#, C++11, PYTH3

## Comments (Search)

asdstevenon Mar 04, 2014 - 6:45:56 am UTC more than one answer for test case #63 5 20 28 30 31 32 34 35 37 39 40 45 46 50 52 53 54 55 57 58 61 62 63 65 69 71 73 74 75

It is considered wrong answer by the judge

fifimanon Jan 29, 2015 - 7:02:35 pm UTC Re: more than one answer for test case #6manolismion May 18, 2015 - 8:52:06 am UTC Re: more than one answer for test case #6Prefer lexicographicly smaller solution.

jargonon May 20, 2015 - 4:00:19 am UTC Re: more than one answer for test case #6