TopCoder Statistics - Problem Statement

Problem Statement

Your task is to write a function that will assign airplane seats to groups of passengers.

The airplane has R rows of seats. Rows are numbered from 1 (in the front) to R (in the back).

In each row there are six seats, labelled A, B, C, D, E, F. The label of each seat is its row followed by its letter. For example, the label of seat C in row 12 is 12C.

All seats can be ordered: first by row number and then by letter alphabetically. This will be called the canonical order. The first few seats in the canonical order: 1A, 1B, 1C, 1D, 1E, 1F, 2A, 2B, ...

The 0-based index of a seat in the canonical order is its canonical number: 1A = 0, 1B = 1, ..., 2A = 6, 2B = 7, and so on.

In each row, seats A and F are called "window seats", seats C and D are called "aisle seats", and seats B and E are called "middle seats".

When seating the passengers, you must follow the following simple rules:

Whenever you have multiple equally good options where to seat a passenger, choose the one among them that is first in the canonical order.
When seating a single passenger (a group of size 1):
- If there is an available window seat, give them a window seat.
- If there is an available aisle seat, give them an aisle seat.
- And if there are only middle seats left, give them a middle seat.
When seating a group of passengers:
- If there are enough empty seats available in any row, seat all passengers in the group in the first such row. (And, as the tiebreaker implies, use the leftmost available seats.)
- Otherwise, seat each member of the group as an individual passenger.

You are given the following inputs:

the int R that specifies the number of rows in the airplane
the int[] groups with the sizes of a small number of initial groups of passengers to process
the int seed used to generate additional groups of passengers until the plane becomes full

Proceed according to the following pseudocode:


start with an empty plane
for each element g of groups, in order:
    seat a group of g passengers

state = seed
in an infinite loop:
    state = (state * 1103515245 + 12345) modulo 2^31
    g = ((state >> 10) modulo 6) + 1
    try to seat a group of g passengers
    if you failed to find room for them on the plane: terminate

For each group that you manage to seat, write down the canonical numbers of seats they received. (When seating a group into the same row, write the seat numbers in ascending order. When breaking up a group into individuals and seating each of them separately, write the seat numbers in the order in which they were assigned.)

Let S = { S[0], S[1], S[2], ... } be the sequence you have written down. Return the value sum( (i+1)*S[i] ).

Definition

Class:: OccupiedAirplane
Method:: seat
Parameters:: int, int[], int
Returns:: long
Method signature:: long seat(int R, int[] groups, int seed)
(be sure your method is public)

Notes

The reference solution does not depend on the input being pseudorandom.

Constraints

R will be between 1 and 100,000, inclusive.
groups will have between 0 and 100 elements, inclusive.
Each element of groups will be between 1 and 6, inclusive.
The sum of groups will not exceed 6*R.
seed will be between 0 and 2^31 - 1, inclusive.

Examples

1

{1, 1, 4}

47

Returns: 60

A single row of seats. The first passenger gets the seat 1A, the second passenger gets the seat 1F, and then the group of four gets the other four seats. We will write down the sequence 0, 5, 1, 2, 3, 4. The correct return value is therefore 1*0 + 2*5 + 3*1 + 4*2 + 5*3 + 6*4.
1

{2}

46

Returns: 2

The first group of two passengers gets the seats 1A and 1B. The next group (the first one generated from the seed) has six passengers. It does not fit onto the plane, so we are done. (Note that we don't seat a part of the group.) The return value is 1*0 + 2*1.
1

{1, 1, 1, 3}

46

Returns: 59

The first three passengers get seats 1A, 1F, and then 1C. The group of three gets three non-consecutive seats in row 1: 1B, 1D, and 1E.
2

{1, 1, 1, 3}

46

Returns: 519

Here, the first three passengers get seats 1A, 1F, and 2A. The group of three then gets three consecutive seats in row 1: 1B, 1C, and 1D. Finally, we have a group of six. (This group is generated as the first pseudorandom group.) There is no row into which all six would fit, so we are going to seat them as individuals. The first of them is lucky to get the last window seat (2F). The next ones get aisle seats (2C, 2D) and the last three fill in the remaining middle seats (1E, 2B, 2E). The sequence S that describes the order in which we assigned seats looks as follows: S = {0, 5, 6, 1, 2, 3, 11, 8, 9, 4, 7, 10}.
2

{1, 1, 1, 1, 1, 4}

46

Returns: 342

The first four passengers grab the four window seats. The next passenger gets the aisle seat 1C. Finally, we have a group of four to seat. They don't fit into the first row, so they'll get all the empty seats in row 2 (seats 2B, 2C, 2D, 2E).
100000

{}

47

Returns: 71979928435137299
4

{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

389820672

Returns: 3828
12

{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

415522429

Returns: 103644
11

{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

1654387811

Returns: 79827
26

{1, 1, 2, 2, 2, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 1, 2, 1, 1, 2, 2, 2, 2, 2, 1, 2, 1, 1, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 2, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 2, 1, 2, 1}

2025278040

Returns: 1193254
22

{1, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 2}

2039351502

Returns: 758537
9

{2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 2, 1, 1, 2, 2, 1, 1, 1, 1}

1095555483

Returns: 49565
18

{1, 2, 1, 1, 3, 3, 1, 2, 3, 1, 3, 2, 2, 1, 2, 2, 1, 3, 3, 3, 2, 2, 3, 2, 1, 1, 1, 2, 1, 3, 1, 3, 3, 1, 1, 3, 3, 1, 2, 2, 1, 1, 2, 3, 3, 2, 3, 2, 1, 1, 2, 3, 3, 2, 1}

1611268898

Returns: 409304
17

{2, 2, 3, 3, 2, 3, 1, 2, 2, 2, 1, 3, 2, 2, 1, 2, 1, 1, 3, 3, 3, 1, 1, 3, 1, 1, 1, 2, 2, 2, 3, 2, 3, 3, 1, 1, 3, 3, 3, 2, 3, 3, 2, 2, 3, 3, 1, 1, 1}

1929784672

Returns: 339735
10

{3, 3, 1, 1, 1, 1, 1, 3, 1, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 1, 1, 3, 3, 3, 3, 3, 1}

1517782795

Returns: 69484
30

{1, 2, 3, 4, 4, 4, 3, 4, 4, 2, 1, 4, 4, 4, 4, 3, 3, 3, 3, 4, 4, 1, 3, 2, 4, 4, 1, 1, 1, 3, 3, 2, 1, 3, 3, 2, 1, 4, 4, 3, 2, 3, 3, 3, 4, 1, 2, 2, 2, 3, 2, 4, 3, 2, 3, 1, 2, 2, 2, 3, 2, 2, 1, 3, 4, 2}

315055730

Returns: 1863047
22

{2, 2, 4, 1, 4, 3, 1, 3, 1, 2, 2, 3, 4, 1, 3, 3, 1, 4, 3, 2, 3, 3, 3, 1, 2, 3, 4, 3, 1, 2, 2, 3, 3, 3, 1, 3, 2, 1, 3, 2, 2, 4, 4, 1, 4, 1, 2, 1, 4, 3, 2, 4, 2, 1}

1578273028

Returns: 734323
23

{2, 1, 4, 3, 3, 3, 1, 1, 3, 4, 2, 1, 1, 3, 4, 2, 1, 3, 3, 4, 3, 1, 1, 3, 4, 2, 4, 3, 3, 4, 2, 3, 2, 2, 2, 2, 1, 1, 3, 3, 2, 3, 3, 2, 3, 3, 2, 2, 4, 1, 1, 4, 4, 4}

1712581354

Returns: 816589
22

{1, 4, 3, 3, 3, 2, 4, 1, 3, 5, 4, 3, 4, 3, 2, 2, 2, 3, 2, 3, 1, 2, 5, 4, 1, 3, 1, 3, 3, 5, 4, 5, 2, 4, 4, 1, 1, 2, 4, 4, 2, 2, 1, 4, 4}

1161823613

Returns: 744046
19

{1, 5, 1, 5, 4, 5, 4, 5, 2, 2, 2, 3, 3, 2, 5, 4, 5, 3, 4, 3, 3, 5, 1, 2, 3, 2, 1, 2, 2, 4, 1, 3, 5, 2, 3, 1, 3}

410819034

Returns: 469852
8

{3, 3, 2, 2, 1, 2, 1, 5, 2, 5, 5, 5, 5, 1, 3, 1}

1915640639

Returns: 33907
8

{1, 4, 3, 1, 3, 2, 5, 4, 5, 6, 2, 2, 2, 6}

578896872

Returns: 34895
30

{2, 5, 3, 3, 6, 6, 4, 1, 3, 2, 6, 1, 4, 2, 3, 6, 4, 2, 4, 1, 3, 6, 2, 4, 5, 2, 2, 2, 5, 1, 2, 3, 5, 4, 6, 3, 6, 3, 6, 1, 3, 2, 1, 5, 4, 3, 2, 3, 4, 2, 2, 5, 3}

2021170730

Returns: 1870875
12

{3, 5, 6, 1, 3, 1, 6, 1, 5, 5, 4, 5, 5, 4, 2, 4, 4, 6}

667906056

Returns: 112489
10

{2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2}

1512334379

Returns: 71980
11

{2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2}

215319891

Returns: 95810
6

{2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2}

1257565381

Returns: 15540
24

{3, 2, 2, 2, 2, 3, 2, 3, 2, 2, 3, 3, 2, 3, 2, 3, 2, 2, 3, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 2, 2, 3, 2, 3, 3, 3, 3, 3, 2, 2, 2, 2, 3, 3, 3, 3, 3, 2, 3, 3, 2, 3, 2, 3, 3, 3, 2}

2115049137

Returns: 936003
9

{2, 3, 3, 2, 3, 3, 2, 2, 2, 2, 2, 3, 2, 2, 2, 3, 3, 2, 2, 2, 3, 3}

2112593978

Returns: 47772
6

{3, 3, 2, 3, 3, 3, 3, 2, 3, 2, 2, 2, 2, 2}

691363188

Returns: 14133
18

{2, 4, 4, 4, 4, 4, 2, 4, 4, 3, 2, 4, 4, 2, 4, 2, 3, 3, 3, 2, 4, 3, 4, 4, 4, 2, 4, 4, 3, 4, 2, 3}

576202932

Returns: 394998
17

{2, 4, 2, 2, 2, 3, 2, 4, 4, 4, 2, 4, 3, 2, 3, 4, 4, 3, 4, 3, 4, 3, 4, 2, 2, 4, 3, 3, 2, 4, 2, 2, 4}

2019209101

Returns: 324652
6

{2, 3, 2, 4, 2, 4, 2, 2, 3, 3, 3, 3, 2}

153158521

Returns: 14907
24

{2, 4, 5, 2, 4, 5, 5, 3, 2, 4, 4, 5, 2, 5, 2, 5, 2, 3, 4, 3, 3, 3, 3, 5, 2, 4, 2, 5, 3, 2, 3, 4, 3, 4, 4, 3, 4, 4, 3, 3, 5}

1041383905

Returns: 939685
21

{4, 3, 5, 2, 2, 5, 3, 2, 2, 3, 2, 2, 3, 2, 3, 5, 2, 2, 5, 2, 2, 3, 4, 3, 3, 4, 3, 3, 2, 5, 3, 5, 2, 2, 3, 5, 2, 4, 3, 4}

1685904872

Returns: 636616
9

{2, 4, 2, 3, 2, 4, 4, 5, 4, 2, 4, 4, 3, 3, 3, 2}

1220698700

Returns: 50916
10

{4, 5, 5, 2, 2, 4, 6, 5, 2, 2, 6, 4, 3, 4, 4, 2}

1163884435

Returns: 69870
7

{6, 5, 5, 6, 4, 3, 4, 4, 5}

189183085

Returns: 24033
18

{3, 6, 5, 5, 3, 2, 4, 2, 3, 2, 2, 4, 3, 5, 5, 3, 6, 2, 2, 6, 4, 4, 6, 2, 4, 4, 4, 4, 3}

1922646244

Returns: 406978
26

{3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3}

221778828

Returns: 1265420
29

{3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3}

1200066851

Returns: 1755950
25

{3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3}

440965586

Returns: 1124950
11

{4, 3, 4, 3, 4, 3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 4, 4, 4}

685873561

Returns: 88223
17

{4, 3, 3, 4, 4, 4, 4, 4, 3, 3, 4, 4, 3, 4, 4, 3, 4, 3, 3, 3, 4, 4, 3, 4, 3, 4, 3, 3}

96388952

Returns: 292616
26

{3, 3, 4, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 4, 4, 4, 3, 3, 4, 4, 4, 4, 4, 3, 4, 3, 3, 4, 4, 3, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 3, 3, 4}

1473700186

Returns: 1138876
25

{5, 4, 3, 4, 4, 3, 5, 5, 4, 5, 4, 5, 5, 3, 3, 5, 3, 3, 3, 4, 5, 4, 4, 3, 3, 5, 5, 4, 3, 4, 3, 5, 3, 4, 3, 3, 4, 3}

1960597885

Returns: 987827
30

{3, 4, 3, 4, 3, 5, 5, 5, 3, 4, 5, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 3, 4, 5, 5, 4, 4, 3, 5, 3, 3, 5, 5, 3, 5, 4, 3, 4, 5, 4, 4, 4, 3, 4, 3}

1965167647

Returns: 1759387
22

{5, 3, 5, 4, 4, 5, 5, 3, 5, 5, 3, 4, 3, 3, 5, 5, 5, 5, 3, 3, 5, 3, 5, 4, 5, 3, 5, 3, 5, 3, 3, 5}

879918350

Returns: 712121
16

{3, 3, 4, 6, 5, 5, 5, 6, 6, 3, 5, 5, 5, 6, 3, 5, 5, 5, 6, 4}

1919683563

Returns: 279243
22

{3, 3, 6, 6, 5, 6, 5, 4, 3, 3, 5, 4, 5, 6, 5, 5, 5, 4, 4, 4, 4, 4, 4, 6, 5, 5, 4, 6}

169751015

Returns: 738035
21

{6, 3, 3, 6, 3, 3, 4, 6, 4, 6, 3, 3, 4, 3, 4, 3, 6, 6, 4, 4, 4, 6, 6, 3, 4, 5, 3, 6}

1769939475

Returns: 603951
12

{4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4}

1846329392

Returns: 110454
7

{4, 4, 4, 4, 4, 4, 4, 4, 4, 4}

90158906

Returns: 19060
6

{4, 4, 4, 4, 4, 4, 4, 4, 4}

1158402265

Returns: 13989
30

{5, 5, 5, 4, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 4, 4, 5, 5, 4, 4, 4, 5, 4, 5, 4, 4, 5, 5, 4, 4, 5, 5, 4, 4, 5}

989123077

Returns: 1641209
16

{5, 4, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 5, 4, 4}

1460409855

Returns: 251842
28

{4, 5, 5, 4, 5, 4, 5, 4, 5, 4, 4, 4, 4, 5, 4, 5, 5, 4, 5, 5, 4, 5, 4, 5, 5, 5, 4, 5, 5, 4, 5, 4, 4, 5, 5, 4, 5}

1348651038

Returns: 1421754
25

{6, 5, 6, 5, 6, 4, 6, 4, 6, 4, 5, 6, 6, 6, 5, 6, 4, 6, 6, 6, 4, 6, 5, 6, 6, 6, 6}

676901777

Returns: 1037169
24

{4, 4, 6, 5, 6, 5, 6, 5, 5, 5, 5, 5, 4, 4, 4, 5, 5, 6, 6, 5, 5, 5, 5, 5, 4, 5, 4, 6, 4}

2098131330

Returns: 910683
20

{5, 5, 4, 5, 6, 6, 5, 5, 4, 5, 4, 5, 4, 4, 5, 4, 6, 6, 6, 4, 6, 5, 6}

1813641495

Returns: 510064
15

{5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5}

1283320413

Returns: 227745
24

{5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5}

1379922888

Returns: 854010
28

{5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5}

1494108161

Returns: 1395865
26

{6, 6, 5, 5, 6, 6, 5, 5, 6, 5, 5, 6, 6, 6, 5, 6, 6, 5, 6, 6, 6, 5, 5, 6, 6, 5, 5, 6}

191660964

Returns: 1225133
30

{5, 5, 5, 6, 5, 5, 6, 6, 6, 5, 6, 6, 6, 6, 5, 5, 5, 5, 6, 5, 5, 6, 5, 6, 6, 6, 6, 6, 6, 6, 5, 6}

2073187810

Returns: 1812008
11

{5, 5, 6, 5, 5, 5, 5, 5, 6, 5, 6, 6}

2122512069

Returns: 83638
26

{6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6}

1216135882

Returns: 1265420
29

{6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6}

314001442

Returns: 1755950
19

{6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6}

1912739663

Returns: 493810
9

{1, 1, 1, 1, 6, 4, 1, 1, 5, 1, 5, 6, 2, 1, 1, 2, 6, 1, 1, 6}

695797067

Returns: 48052
24

{1, 1, 5, 5, 1, 1, 1, 5, 6, 6, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 3, 6, 1, 1, 6, 1, 3, 1, 3, 1, 4, 1, 5, 1, 1, 6, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 1, 1, 5, 1, 1, 1, 1, 6}

871773192

Returns: 930165
13

{1, 1, 5, 1, 6, 5, 4, 1, 4, 6, 1, 4, 2, 3, 2, 1, 3, 1, 1, 1, 4, 6, 6, 4, 1, 1, 1}

1112926868

Returns: 145623
9

{1, 1, 2, 1, 3, 1, 3, 1, 1, 4, 1, 1, 1, 3, 1, 2, 1, 3, 5, 1, 4, 1, 6, 1, 1, 3, 1}

245347176

Returns: 49138
18

{1, 1, 4, 1, 1, 6, 1, 3, 3, 1, 1, 1, 4, 1, 1, 1, 4, 5, 3, 1, 1, 1, 2, 2, 4, 5, 1, 1, 2, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 2, 1, 2, 1, 3, 1, 5, 1, 1, 4, 1, 1}

1492052662

Returns: 397989
11

{1, 4, 2, 1, 1, 1, 1, 1, 5, 3, 1, 1, 1, 1, 1, 3, 1, 4, 5, 1, 5, 6, 1, 5, 1, 1, 3, 2}

1496326047

Returns: 84106
10

{1, 1, 1, 5, 1, 1, 3, 1, 2, 1, 1, 1, 4, 5, 1, 5, 1, 1, 3, 4, 3, 1, 6, 1, 1, 3}

1307481101

Returns: 62715
13

{1, 2, 6, 6, 1, 1, 4, 1, 1, 1, 5, 6, 5, 1, 1, 1, 6, 1, 1, 1, 3, 3, 5, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1}

751603398

Returns: 150034
3

{1, 3, 4, 1, 3, 2, 1, 3}

525489464

Returns: 1831
13

{1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 5, 3, 6, 1, 4, 1, 1, 1, 1, 6, 1, 6, 1, 2, 2, 2, 2, 1, 4, 1, 1, 1, 1, 1, 3}

898361508

Returns: 141936
97567

{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

589686326

Returns: 66866706090708958
99791

{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

1723445313

Returns: 71506449991988153
96326

{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

1645491468

Returns: 64340687088199636
98498

{1, 1, 2, 2, 2, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 1, 2, 1, 1, 2, 2, 2, 2, 2, 1, 2, 1, 1, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 2, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 2, 1, 2, 1}

2085995278

Returns: 68794838982008051
96830

{1, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 2}

1318702886

Returns: 65356694998908262
95798

{2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 2, 1, 1, 2, 2, 1, 1, 1, 1}

684010265

Returns: 63287542989591104
97594

{1, 2, 1, 1, 3, 3, 1, 2, 3, 1, 3, 2, 2, 1, 2, 2, 1, 3, 3, 3, 2, 2, 3, 2, 1, 1, 1, 2, 1, 3, 1, 3, 3, 1, 1, 3, 3, 1, 2, 2, 1, 1, 2, 3, 3, 2, 3, 2, 1, 1, 2, 3, 3, 2, 1}

479474032

Returns: 66920537849717962
98647

{2, 2, 3, 3, 2, 3, 1, 2, 2, 2, 1, 3, 2, 2, 1, 2, 1, 1, 3, 3, 3, 1, 1, 3, 1, 1, 1, 2, 2, 2, 3, 2, 3, 3, 1, 1, 3, 3, 3, 2, 3, 3, 2, 2, 3, 3, 1, 1, 1}

1130412453

Returns: 69107357639784454
96255

{3, 3, 1, 1, 1, 1, 1, 3, 1, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 1, 1, 3, 3, 3, 3, 3, 1}

1137388751

Returns: 64166914964680180
97095

{1, 2, 3, 4, 4, 4, 3, 4, 4, 2, 1, 4, 4, 4, 4, 3, 3, 3, 3, 4, 4, 1, 3, 2, 4, 4, 1, 1, 1, 3, 3, 2, 1, 3, 3, 2, 1, 4, 4, 3, 2, 3, 3, 3, 4, 1, 2, 2, 2, 3, 2, 4, 3, 2, 3, 1, 2, 2, 2, 3, 2, 2, 1, 3, 4, 2}

435384246

Returns: 65881752520225728
98526

{2, 2, 4, 1, 4, 3, 1, 3, 1, 2, 2, 3, 4, 1, 3, 3, 1, 4, 3, 2, 3, 3, 3, 1, 2, 3, 4, 3, 1, 2, 2, 3, 3, 3, 1, 3, 2, 1, 3, 2, 2, 4, 4, 1, 4, 1, 2, 1, 4, 3, 2, 4, 2, 1}

1376800490

Returns: 68824579494525223
96507

{2, 1, 4, 3, 3, 3, 1, 1, 3, 4, 2, 1, 1, 3, 4, 2, 1, 3, 3, 4, 3, 1, 1, 3, 4, 2, 4, 3, 3, 4, 2, 3, 2, 2, 2, 2, 1, 1, 3, 3, 2, 3, 3, 2, 3, 3, 2, 2, 4, 1, 1, 4, 4, 4}

322959397

Returns: 64711438784376599
96899

{1, 4, 3, 3, 3, 2, 4, 1, 3, 5, 4, 3, 4, 3, 2, 2, 2, 3, 2, 3, 1, 2, 5, 4, 1, 3, 1, 3, 3, 5, 4, 5, 2, 4, 4, 1, 1, 2, 4, 4, 2, 2, 1, 4, 4}

539788335

Returns: 65488809470417145
96303

{1, 5, 1, 5, 4, 5, 4, 5, 2, 2, 2, 3, 3, 2, 5, 4, 5, 3, 4, 3, 3, 5, 1, 2, 3, 2, 1, 2, 2, 4, 1, 3, 5, 2, 3, 1, 3}

986306501

Returns: 64293278554360044
95260

{3, 3, 2, 2, 1, 2, 1, 5, 2, 5, 5, 5, 5, 1, 3, 1}

19710054

Returns: 62230860358888982
97703

{1, 4, 3, 1, 3, 2, 5, 4, 5, 6, 2, 2, 2, 6}

239459293

Returns: 67139951335375922
96060

{2, 5, 3, 3, 6, 6, 4, 1, 3, 2, 6, 1, 4, 2, 3, 6, 4, 2, 4, 1, 3, 6, 2, 4, 5, 2, 2, 2, 5, 1, 2, 3, 5, 4, 6, 3, 6, 3, 6, 1, 3, 2, 1, 5, 4, 3, 2, 3, 4, 2, 2, 5, 3}

376785669

Returns: 63799267227490808
97240

{3, 5, 6, 1, 3, 1, 6, 1, 5, 5, 4, 5, 5, 4, 2, 4, 4, 6}

133088909

Returns: 66177862945845607
95440

{2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2}

1569066461

Returns: 62571107690817345
95053

{2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2}

1147715469

Returns: 61827217212116763
97403

{2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2}

16020863

Returns: 66530237970158357
96421

{3, 2, 2, 2, 2, 3, 2, 3, 2, 2, 3, 3, 2, 3, 2, 3, 2, 2, 3, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 2, 2, 3, 2, 3, 3, 3, 3, 3, 2, 2, 2, 2, 3, 3, 3, 3, 3, 2, 3, 3, 2, 3, 2, 3, 3, 3, 2}

1972408621

Returns: 64520594866768157
96716

{2, 3, 3, 2, 3, 3, 2, 2, 2, 2, 2, 3, 2, 2, 2, 3, 3, 2, 2, 2, 3, 3}

1030530889

Returns: 65113272907295680
97586

{3, 3, 2, 3, 3, 3, 3, 2, 3, 2, 2, 2, 2, 2}

1651932104

Returns: 66899265911563197
97533

{2, 4, 4, 4, 4, 4, 2, 4, 4, 3, 2, 4, 4, 2, 4, 2, 3, 3, 3, 2, 4, 3, 4, 4, 4, 2, 4, 4, 3, 4, 2, 3}

522170821

Returns: 66780604774184852
95851

{2, 4, 2, 2, 2, 3, 2, 4, 4, 4, 2, 4, 3, 2, 3, 4, 4, 3, 4, 3, 4, 3, 4, 2, 2, 4, 3, 3, 2, 4, 2, 2, 4}

342510536

Returns: 63401419289880587
98690

{2, 3, 2, 4, 2, 4, 2, 2, 3, 3, 3, 3, 2}

50398124

Returns: 69195489686070583
96442

{2, 4, 5, 2, 4, 5, 5, 3, 2, 4, 4, 5, 2, 5, 2, 5, 2, 3, 4, 3, 3, 3, 3, 5, 2, 4, 2, 5, 3, 2, 3, 4, 3, 4, 4, 3, 4, 4, 3, 3, 5}

1258203282

Returns: 64570655571990838
96530

{4, 3, 5, 2, 2, 5, 3, 2, 2, 3, 2, 2, 3, 2, 3, 5, 2, 2, 5, 2, 2, 3, 4, 3, 3, 4, 3, 3, 2, 5, 3, 5, 2, 2, 3, 5, 2, 4, 3, 4}

362865603

Returns: 64734172387082938
99786

{2, 4, 2, 3, 2, 4, 4, 5, 4, 2, 4, 4, 3, 3, 3, 2}

1450407234

Returns: 71532847628977169
95665

{4, 5, 5, 2, 2, 4, 6, 5, 2, 2, 6, 4, 3, 4, 4, 2}

2110945802

Returns: 63008404799446243
98625

{6, 5, 5, 6, 4, 3, 4, 4, 5}

1060331720

Returns: 69059042483671771
99020

{3, 6, 5, 5, 3, 2, 4, 2, 3, 2, 2, 4, 3, 5, 5, 3, 6, 2, 2, 6, 4, 4, 6, 2, 4, 4, 4, 4, 3}

1119072951

Returns: 69877594077579436
99519

{3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3}

1377481704

Returns: 70958174174712962
97513

{3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3}

179054521

Returns: 66753925171381255
95237

{3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3}

1648035822

Returns: 62189713913075913
97640

{4, 3, 4, 3, 4, 3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 4, 4, 4}

816154815

Returns: 67006377993305872
99716

{4, 3, 3, 4, 4, 4, 4, 4, 3, 3, 4, 4, 3, 4, 4, 3, 4, 3, 3, 3, 4, 4, 3, 4, 3, 4, 3, 3}

715558246

Returns: 71355068072633578
96344

{3, 3, 4, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 4, 4, 4, 3, 3, 4, 4, 4, 4, 4, 3, 4, 3, 3, 4, 4, 3, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 3, 3, 4}

525402902

Returns: 64374228862822043
98348

{5, 4, 3, 4, 4, 3, 5, 5, 4, 5, 4, 5, 5, 3, 3, 5, 3, 3, 3, 4, 5, 4, 4, 3, 3, 5, 5, 4, 3, 4, 3, 5, 3, 4, 3, 3, 4, 3}

2087892778

Returns: 68470881440775387
96383

{3, 4, 3, 4, 3, 5, 5, 5, 3, 4, 5, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 3, 4, 5, 5, 4, 4, 3, 5, 3, 3, 5, 5, 3, 5, 4, 3, 4, 5, 4, 4, 4, 3, 4, 3}

422052075

Returns: 64455817182655978
95677

{5, 3, 5, 4, 4, 5, 5, 3, 5, 5, 3, 4, 3, 3, 5, 5, 5, 5, 3, 3, 5, 3, 5, 4, 5, 3, 5, 3, 5, 3, 3, 5}

423769718

Returns: 63045576671323981
99365

{3, 3, 4, 6, 5, 5, 5, 6, 6, 3, 5, 5, 5, 6, 3, 5, 5, 5, 6, 4}

1888517317

Returns: 70627820677016557
97845

{3, 3, 6, 6, 5, 6, 5, 4, 3, 3, 5, 4, 5, 6, 5, 5, 5, 4, 4, 4, 4, 4, 4, 6, 5, 5, 4, 6}

93958153

Returns: 67432192906110755
99293

{6, 3, 3, 6, 3, 3, 4, 6, 4, 6, 3, 3, 4, 3, 4, 3, 6, 6, 4, 4, 4, 6, 6, 3, 4, 5, 3, 6}

1206275013

Returns: 70455709398388202
99683

{4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4}

784501809

Returns: 71309237983103186
99087

{4, 4, 4, 4, 4, 4, 4, 4, 4, 4}

64025555

Returns: 70041263073240103
98777

{4, 4, 4, 4, 4, 4, 4, 4, 4}

292735094

Returns: 69377899058453584
97002

{5, 5, 5, 4, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 4, 4, 5, 5, 4, 4, 4, 5, 4, 5, 4, 4, 5, 5, 4, 4, 5, 5, 4, 4, 5}

1156729687

Returns: 65690044642660872
95920

{5, 4, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 5, 4, 4}

1570733817

Returns: 63525385636681996
97792

{4, 5, 5, 4, 5, 4, 5, 4, 5, 4, 4, 4, 4, 5, 4, 5, 5, 4, 5, 5, 4, 5, 4, 5, 5, 5, 4, 5, 5, 4, 5, 4, 4, 5, 5, 4, 5}

1238869809

Returns: 67328404732096749
98807

{6, 5, 6, 5, 6, 4, 6, 4, 6, 4, 5, 6, 6, 6, 5, 6, 4, 6, 6, 6, 4, 6, 5, 6, 6, 6, 6}

462324456

Returns: 69427991461030237
99081

{4, 4, 6, 5, 6, 5, 6, 5, 5, 5, 5, 5, 4, 4, 4, 5, 5, 6, 6, 5, 5, 5, 5, 5, 4, 5, 4, 6, 4}

1046383229

Returns: 70023134672854566
95274

{5, 5, 4, 5, 6, 6, 5, 5, 4, 5, 4, 5, 4, 4, 5, 4, 6, 6, 6, 4, 6, 5, 6}

58821394

Returns: 62256817416756239
98975

{5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5}

1878462771

Returns: 69802896085286087
95680

{5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5}

113072094

Returns: 63054187002545815
96366

{5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5}

1798333443

Returns: 64431304383532809
99599

{6, 6, 5, 5, 6, 6, 5, 5, 6, 5, 5, 6, 6, 6, 5, 6, 6, 5, 6, 6, 6, 5, 5, 6, 6, 5, 5, 6}

1245219619

Returns: 71135962937773426
95466

{5, 5, 5, 6, 5, 5, 6, 6, 6, 5, 6, 6, 6, 6, 5, 5, 5, 5, 6, 5, 5, 6, 5, 6, 6, 6, 6, 6, 6, 6, 5, 6}

1201642658

Returns: 62628697547506084
97053

{5, 5, 6, 5, 5, 5, 5, 5, 6, 5, 6, 6}

255209564

Returns: 65806595793761726
97079

{6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6}

529897286

Returns: 65867388622221716
95864

{6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6}

1174443297

Returns: 63421721514519675
98604

{6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6}

752293839

Returns: 68996597406203804
99602

{1, 1, 1, 1, 6, 4, 1, 1, 5, 1, 5, 6, 2, 1, 1, 2, 6, 1, 1, 6}

783826068

Returns: 71129638095006844
96326

{1, 1, 5, 5, 1, 1, 1, 5, 6, 6, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 3, 6, 1, 1, 6, 1, 3, 1, 3, 1, 4, 1, 5, 1, 1, 6, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 1, 1, 5, 1, 1, 1, 1, 6}

1991262463

Returns: 64338541256159952
95672

{1, 1, 5, 1, 6, 5, 4, 1, 4, 6, 1, 4, 2, 3, 2, 1, 3, 1, 1, 1, 4, 6, 6, 4, 1, 1, 1}

207579155

Returns: 63043183212612621
99170

{1, 1, 2, 1, 3, 1, 3, 1, 1, 4, 1, 1, 1, 3, 1, 2, 1, 3, 5, 1, 4, 1, 6, 1, 1, 3, 1}

1533112088

Returns: 70204046700352676
98157

{1, 1, 4, 1, 1, 6, 1, 3, 3, 1, 1, 1, 4, 1, 1, 1, 4, 5, 3, 1, 1, 1, 2, 2, 4, 5, 1, 1, 2, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 2, 1, 2, 1, 3, 1, 5, 1, 1, 4, 1, 1}

219112206

Returns: 68067048045574551
95940

{1, 4, 2, 1, 1, 1, 1, 1, 5, 3, 1, 1, 1, 1, 1, 3, 1, 4, 5, 1, 5, 6, 1, 5, 1, 1, 3, 2}

1610783972

Returns: 63556859702689428
97482

{1, 1, 1, 5, 1, 1, 3, 1, 2, 1, 1, 1, 4, 5, 1, 5, 1, 1, 3, 4, 3, 1, 6, 1, 1, 3}

2083983488

Returns: 66674829907582235
97617

{1, 2, 6, 6, 1, 1, 4, 1, 1, 1, 5, 6, 5, 1, 1, 1, 6, 1, 1, 1, 3, 3, 5, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1}

343587088

Returns: 66948160463759436
97095

{1, 3, 4, 1, 3, 2, 1, 3}

1576609312

Returns: 65899037180558208
96414

{1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 5, 3, 6, 1, 4, 1, 1, 1, 1, 6, 1, 6, 1, 2, 2, 2, 2, 1, 4, 1, 1, 1, 1, 1, 3}

384767114

Returns: 64507006933989997
100000

{6, 5, 2, 1, 3, 1, 2, 1 }

1234

Returns: 71994828992777483
100000

{2, 2, 2, 2, 3, 3, 3, 3 }

57

Returns: 71988247759924212

Statistics

Problem Statement for "OccupiedAirplane"

Problem Statement

Definition

Notes

Constraints

Examples