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long_comps_intel  Problem Statement
Contest: Intel Multi-Threading Competition 6
Problem: BoxPacking

Problem Statement

    You run a company that ships a lot of items to customers. The items are all rectangular and thus can be represented by their widths, heights, and depths (in inches).



You often need to ship a lot of items to a single customer, and need to figure out the best way to pack all the items into rectangular boxes. You can pack them in any way, so long as the faces of the items are parallel to the faces of the boxes. The shipping company charges you by the pound, so your primary controllable cost when packing is the cost of the cardboard used in the boxes. A box with dimensions x <= y <= z has y*z*2 + x*z*2 + x*y*4 square inches of cardboard in it (the top and bottom have two layers, while the sides have one layer). The cost to manufacture and ship such a box is proportional to the number of square inches of cardboard it uses.



You can use as many boxes as you like. However, the shipping company will not accept any boxes for which z + 2*x + 2*y is greater than maxLG (an input). Furthermore, boxes may have any amount of empty space (which will be filled with packing materials that are practically free). Finally, each second of processing time used by your solution will cost the equivalent of 1 square inch of cardboard.



Your task is to write a method pack, that takes 4 inputs. itemA[i], itemB[i], and itemC[i] give the three dimensions of item i, while maxLG is defined above. Your function should return a String[] with one element for each box. Each element should be formatted as: "boxX boxY boxZ itemIndex1 itemLX1 itemLY1 itemLZ1 itemUX1 itemUY1 itemUZ1 itemIndex2 itemLX2 ...". In other words, the string should first contain the three dimensions of the box. Next, for each item in the box, it should contain the index of the item in the input, followed by the coordinates of two of the item's opposite corners in the box, assuming the box goes from (0,0,0) to (boxX, boxY, boxZ). Thus a box with k items in it will be represented by a string with 7*k+3 single-space delimited integers.



Your score for a test case will be the percent improvement in the cost of your packing scheme (1 unit per square inch of cardboard plus 1 unit per second of processing time) over the cost of sending every item in its own box. So, if the cost of your scheme is 40, while the cost of putting each item in its own box is 60, your score would be 33.33. If your return is invalid in any way (doesn't include all the items, items go outside the box, box too big, invalid return format, etc.), you will receive 0 for that test case. Your final score will be the sum of these savings (in percentages) over all test cases.



To generate the test cases, maxLG will be chosen between 60 and 300, inclusive, with uniform probability. There will be up to 1000 items in the input, and at least 10 (again chosen uniformly). Each item will have its three dimensions chosen randomly and independently between 1 and floor(maxLG/5) with a skew towards smaller numbers. The skew will be accomplished by picking dimension = floor((floor(maxLG/5))*rand()*rand()) + 1, where rand() is a function that returns a uniform random real number between 0 and 1.



You will have a maximum of 40 seconds of execution time per test cases. The memory limit is 1024MB and the thread limit is 32 (including the main thread).
 

Definition

    
Class:BoxPacking
Method:pack
Parameters:int, int[], int[], int[]
Returns:String[]
Method signature:String[] pack(int maxLG, int[] itemA, int[] itemB, int[] itemC)
(be sure your method is public)
    
 

Notes

-In the packing scheme that you return, it does not matter which way you orient the boxes (which dimension is x, y, or z). It also doesn't matter which two corners you pick to represent for the items, as long as they are two opposite corners of the item.
-If your score for a test case would be negative (you do worse than packing into single boxes), you will be given a zero for that test case.
-The tests will be run on systems with 8 hyperthreaded cores.
-There are 40 non-example test cases.
-Processing time means wallclock time.
 

Examples

0)
    
maxLG = 163
There are 10 items:
itemA = [4 19 32 10 6 12 4 1 26 24]
itemB = [6 26 1 18 1 2 4 6 1 10]
itemC = [4 23 6 15 1 15 7 11 2 7]
If, for example, we decided to put items 1 and 2 in the same box, one way to do it would represented in the return as:

"32 23 20 1 0 0 0 26 23 19 2 32 23 20 0 17 19"

This inidcates that the items go in a box that is 32x23x20. Item 1 goes from (0,0,0) to (26,23,19), while item 2 goes from (32,23,20) to (0,17,19). One way to pack all the items into a single box is represented by the string

"23 23 50 2 0 0 0 1 6 32 1 1 0 0 20 23 26 8 20 0 0 21 2 26 9 1 0 26 8 10 50 3 8 0 26 18 15 44 5 21 0 0 23 12 15 7 20 2 0 21 8 11 6 18 0 26 22 4 33 0 18 4 26 22 8 32 4 0 6 0 1 7 6"
1)
    
maxLG = 185
There are 11 items:
itemA = [1 1 2 7 18 3 21 17 3 24 25]
itemB = [13 21 3 3 4 2 4 2 1 8 3]
itemC = [6 20 6 2 2 16 16 6 33 7 2]
2)
    
maxLG = 105
There are 12 items:
itemA = [11 1 4 2 9 8 1 2 3 5 6 1]
itemB = [7 12 8 8 8 4 18 4 1 4 2 7]
itemC = [3 4 13 3 7 1 15 2 4 10 9 9]
3)
    
maxLG = 227
There are 359 items:
itemA = [21 7 3 1 10 12 1 3 1 35 10 4 2 31 12 18 33 7 4 12 27 30 3 2 5 2 1 13 1 20 11 1 8 11 3 5 2 16 5 13 7 9 4 9 14 23 3 7 10 3 14 33 26 20 12 28 4 2 10 15 15 1 37 28 26 8 14 21 5 31 14 6 1 1 18 1 22 2 37 25 8 30 9 1 3 9 26 35 35 10 7 1 28 9 6 8 30 27 6 13 10 11 15 5 30 15 3 8 31 29 9 5 4 26 7 6 25 2 1 6 1 7 25 5 14 16 6 1 6 9 9 5 9 10 7 17 2 19 22 27 26 11 38 10 1 12 2 1 6 13 2 28 23 14 6 5 16 1 7 11 1 5 22 11 1 14 1 3 12 2 3 27 4 1 8 5 1 7 32 2 12 1 9 12 15 6 1 1 5 6 7 24 2 15 19 2 33 21 18 4 17 37 8 3 3 19 1 7 20 15 19 6 28 2 5 17 8 7 9 3 20 4 18 2 23 1 9 35 4 1 3 6 1 1 29 15 3 19 3 7 29 9 1 5 4 4 29 1 9 8 16 4 1 21 3 26 9 17 22 9 11 17 2 38 4 18 18 2 20 3 20 16 2 15 20 10 13 4 2 7 10 40 29 14 18 8 13 10 29 4 29 2 32 6 19 3 1 2 19 4 24 2 5 1 3 21 20 9 1 15 17 24 12 23 16 2 15 4 24 11 17 15 4 9 1 1 4 8 2 42 1 19 1 10 5 1 5 11 11 13 18 21 14 31 3 11 12 15 6 7 3 3 25 2 2 32 8 4 12]
itemB = [5 3 5 2 7 9 13 1 1 2 28 21 10 4 6 1 10 5 1 10 3 34 6 22 16 11 14 3 20 12 2 7 17 13 1 3 7 4 21 24 17 21 1 29 3 7 39 5 1 16 12 18 26 5 7 14 25 23 23 17 3 38 25 8 9 7 5 9 1 12 5 7 32 5 7 5 17 1 2 5 5 1 5 37 1 1 3 22 5 6 24 1 16 19 4 12 11 2 2 34 2 14 23 3 7 8 9 11 17 3 2 6 1 29 31 26 15 8 3 3 7 7 35 4 12 9 22 13 14 14 18 2 1 19 1 2 11 32 2 33 4 9 10 5 1 34 1 1 15 1 21 1 9 7 4 16 11 27 13 1 6 11 25 6 17 2 4 2 35 5 18 11 28 17 31 5 13 10 11 12 18 11 25 1 4 12 6 4 7 3 23 5 4 11 11 10 41 4 4 4 6 20 8 2 25 15 1 23 13 5 1 5 2 1 1 3 1 1 1 1 27 1 11 9 1 25 2 15 7 10 2 12 24 34 25 22 40 29 1 39 6 18 24 27 21 8 22 16 21 11 6 13 12 8 12 15 6 4 2 13 16 26 12 2 21 19 19 29 8 13 6 15 19 5 7 12 3 5 30 2 5 8 14 9 3 37 7 3 5 5 6 2 31 9 5 18 6 11 13 8 41 31 34 1 6 17 3 1 1 36 25 2 4 4 1 25 18 31 13 29 5 1 7 6 2 27 13 6 7 2 1 1 16 26 39 2 6 6 1 19 8 1 13 18 26 1 1 2 27 7 1 19 2 5 28 4 17 1 24]
itemC = [1 31 2 8 5 8 1 31 8 15 33 35 1 1 38 6 1 10 24 20 10 4 1 11 2 2 1 2 18 1 5 3 9 1 5 34 5 7 34 1 19 14 1 1 17 1 21 1 14 14 3 2 23 27 3 6 25 29 10 10 5 3 21 1 22 11 2 4 38 2 3 23 18 27 7 39 28 1 7 16 1 4 1 30 6 28 4 4 7 10 14 6 2 2 10 6 15 31 18 11 16 27 3 7 4 8 5 5 1 23 10 8 4 24 2 16 11 5 3 4 16 11 17 11 4 1 17 13 17 34 14 21 36 20 18 12 14 13 22 3 15 4 28 9 24 28 33 1 4 13 7 15 2 6 13 1 9 11 6 36 4 3 22 23 15 5 2 3 10 5 8 18 18 4 1 1 2 15 25 5 3 4 1 12 11 28 7 6 16 1 23 20 28 2 14 35 6 9 17 19 2 30 3 24 16 26 1 9 2 1 23 2 19 13 21 19 16 32 15 3 4 13 1 23 1 5 18 8 2 2 17 6 33 18 6 33 9 1 30 10 15 1 13 2 10 1 4 15 6 7 3 29 1 4 22 1 11 1 12 4 10 4 10 17 13 7 2 5 3 6 20 2 9 14 11 1 11 12 22 11 7 24 9 3 7 22 2 12 2 9 1 4 36 14 43 2 11 5 3 5 12 4 26 18 3 11 28 17 11 12 2 13 17 2 11 20 7 1 17 1 5 10 11 17 3 5 7 22 4 26 1 20 2 4 21 20 22 2 3 25 18 6 8 5 23 33 6 12 4 2 1 16 1 3 8 19 3 21 5]
4)
    
maxLG = 134
There are 602 items:
itemA = [1 13 6 4 13 1 1 7 7 3 7 4 3 1 13 23 13 3 8 6 7 20 1 15 8 12 11 2 5 9 1 11 2 6 9 6 9 4 11 13 2 14 8 7 7 1 4 14 8 6 4 5 7 1 2 1 5 4 9 1 20 2 13 4 1 1 1 1 9 3 1 2 18 3 3 7 2 8 7 7 3 18 6 9 8 17 4 9 3 17 4 8 1 3 1 23 11 7 14 15 8 1 6 13 21 14 18 1 1 3 9 12 6 14 15 3 1 3 12 5 1 15 4 3 4 2 2 1 6 8 7 15 6 23 6 1 6 6 16 14 2 4 2 11 4 3 4 14 17 1 1 4 15 13 2 2 2 1 3 10 13 9 6 13 6 2 5 3 1 9 1 1 4 3 6 7 3 7 3 1 3 1 19 3 4 14 6 1 1 21 16 7 2 1 16 11 4 4 4 2 4 9 4 2 22 9 6 10 1 2 7 9 2 18 14 5 2 6 9 15 10 9 6 7 2 11 14 1 9 13 5 3 1 7 18 2 6 14 4 5 5 15 13 2 7 13 4 14 10 23 1 2 2 4 12 5 4 5 4 1 6 4 19 2 4 2 5 10 3 4 10 12 5 7 7 7 1 11 4 5 8 16 1 8 2 6 6 1 9 3 3 1 1 7 1 1 3 15 1 2 1 5 18 15 3 6 2 1 2 6 8 7 1 1 11 8 9 2 2 18 11 8 8 1 3 12 1 8 6 7 3 8 2 1 6 3 20 8 16 4 8 5 3 9 3 15 22 17 9 7 8 1 5 1 9 5 3 7 3 1 4 2 1 2 4 3 11 4 1 5 3 13 21 6 9 2 20 23 13 9 1 6 7 7 3 13 13 1 4 4 4 17 4 16 18 14 9 4 20 2 3 11 10 1 18 3 11 4 1 3 11 1 23 4 1 2 11 2 1 7 3 13 21 7 13 1 7 4 10 9 1 8 1 16 10 6 1 6 1 2 13 2 12 2 4 4 16 12 7 5 18 2 5 3 10 11 8 4 1 5 2 2 8 6 16 5 5 4 4 16 6 2 3 8 1 6 5 5 4 8 9 7 5 2 1 1 6 1 9 6 2 1 10 6 3 4 1 15 21 11 8 17 14 3 5 1 1 15 5 11 3 3 4 1 2 22 15 3 2 2 3 2 3 6 1 22 10 3 12 13 10 6 1 1 4 7 10 1 10 4 1 1 1 2 1 10 6 17 2 18 2 11 12 7 4 2 19 4 2 18 14 18 5 3 6 25 2 14 17 1 8 2 13 1 2 5 1 3 7 2 5 23 17 17 16 8 10 1 5 5 10 3 9 14 13 4 13 14 4 4 5 3]
itemB = [1 2 7 6 8 16 15 19 1 12 4 1 8 6 6 2 2 3 19 8 5 1 2 17 3 18 10 2 4 6 2 15 4 6 16 15 6 10 21 16 10 4 4 5 1 12 2 4 10 8 2 3 2 2 1 5 2 4 3 2 1 16 15 17 1 1 1 20 4 13 24 1 1 1 3 8 1 8 6 3 7 2 10 14 6 11 5 8 24 5 2 20 1 17 1 4 15 14 1 10 23 13 2 22 12 8 1 3 6 1 1 1 2 3 3 5 6 1 3 7 5 8 1 10 20 6 1 9 2 9 15 13 18 2 11 4 2 18 6 2 7 4 14 16 12 13 11 3 3 6 5 2 11 7 7 22 2 13 5 6 5 6 1 1 5 10 4 4 13 1 9 7 2 6 14 4 23 6 13 10 2 25 7 1 6 3 10 7 15 7 10 5 22 2 1 1 9 1 7 8 3 3 8 4 5 7 25 5 3 1 2 10 8 4 1 1 10 5 3 11 6 2 5 2 1 2 1 8 16 8 2 3 8 5 7 4 1 2 9 14 6 1 8 1 16 23 2 15 8 4 4 11 15 7 6 13 9 5 9 4 2 5 13 1 2 1 4 11 6 10 11 21 8 7 5 21 13 2 9 10 15 4 7 3 6 9 4 22 4 2 5 5 2 16 13 4 2 8 5 4 13 9 2 1 9 3 4 3 2 4 15 17 1 4 1 3 6 6 1 8 1 3 8 3 3 16 6 3 17 1 2 1 4 1 10 8 8 7 7 4 13 1 12 10 10 3 1 13 17 14 1 7 4 1 13 2 1 18 3 1 18 1 2 4 1 4 16 14 15 4 4 6 12 8 6 1 1 9 14 12 6 12 2 11 16 1 12 1 8 2 11 2 12 5 7 15 1 6 1 7 6 1 1 15 8 15 9 2 2 2 3 5 6 10 4 4 2 20 9 1 4 5 12 2 3 5 17 4 8 2 1 7 4 2 3 7 1 9 6 6 10 4 3 1 19 4 2 15 5 10 20 1 1 14 3 9 2 17 2 9 1 9 1 4 2 1 2 20 3 1 9 6 2 5 16 1 8 3 2 6 6 7 8 2 3 1 21 5 4 2 1 11 3 5 6 12 5 10 6 17 7 15 2 1 3 12 8 13 4 7 2 1 10 1 11 3 2 1 16 4 23 17 4 21 1 4 5 4 7 18 4 5 11 20 4 13 12 8 11 12 14 1 1 9 1 6 11 2 7 15 2 8 3 3 3 8 3 11 2 2 1 3 2 5 3 3 10 17 4 12 2 1 23 10 1 19 2 11 22 5 1 2 1 7 1 5 1 4 7 1 3 2 12 4 2 14 2 1 7 10 1 2]
itemC = [8 6 5 2 4 13 3 23 5 1 2 10 2 9 2 3 13 3 14 23 6 13 11 5 21 17 1 2 1 19 6 7 5 2 8 10 1 15 5 5 6 9 20 9 1 4 12 13 4 1 5 1 2 3 6 5 8 4 16 7 9 13 2 2 13 2 12 9 3 6 23 9 6 24 9 2 16 1 13 10 12 4 1 5 10 1 20 8 1 21 13 4 18 1 3 3 9 14 1 1 10 5 5 3 12 4 3 7 5 3 2 11 5 18 6 5 5 16 6 2 20 18 2 1 1 8 3 3 7 3 12 6 9 1 1 6 3 6 1 7 11 13 12 7 8 12 1 1 5 5 5 5 3 11 3 3 10 5 4 4 12 12 6 7 16 14 2 4 6 11 2 13 1 9 10 16 2 6 12 17 8 2 1 4 1 5 17 6 8 8 17 12 1 3 2 11 6 9 2 3 1 3 1 6 3 1 1 21 1 3 10 2 5 3 4 3 4 8 13 1 1 1 3 17 12 7 14 6 20 15 7 12 1 21 21 2 19 15 2 9 1 2 3 10 5 2 1 3 11 7 4 18 14 10 1 4 5 9 4 21 3 20 13 6 8 16 23 8 9 3 25 1 4 2 1 5 4 2 4 1 9 3 13 4 3 1 7 1 14 15 8 14 7 1 11 4 15 14 3 11 1 11 2 6 1 6 13 18 3 21 3 1 22 8 20 7 18 9 13 8 1 5 2 8 4 3 8 4 5 3 1 3 2 7 6 3 7 1 7 11 8 3 8 15 8 1 18 1 13 9 12 2 2 11 2 17 4 1 4 1 11 3 1 18 1 15 9 15 1 1 1 16 5 5 1 1 11 6 15 2 7 7 2 1 1 2 15 4 2 1 9 2 4 1 16 5 1 21 1 6 10 1 7 5 10 9 2 7 1 2 9 1 2 11 5 1 4 2 14 10 2 1 14 1 1 12 12 8 16 3 1 7 2 2 7 3 8 8 3 16 3 1 9 1 2 1 3 6 13 1 9 18 5 15 4 8 1 7 1 9 3 2 20 4 6 5 4 1 5 2 8 1 3 2 19 7 11 11 12 20 21 20 7 11 1 11 1 3 5 4 8 14 10 5 5 8 1 1 1 6 1 2 17 4 3 9 2 12 21 3 1 1 1 11 8 8 14 5 7 13 1 13 3 12 2 2 2 1 15 5 2 6 4 2 15 1 3 13 9 2 21 1 5 4 8 2 14 13 2 14 2 12 2 3 10 18 5 10 12 2 2 11 1 3 1 3 2 1 1 2 4 16 1 12 2 6 5 9 15 8 3 1 13 3 10 9 11 2 1 6 17 8 12 9 11 5 2 1 3 21 7 16]
5)
    
maxLG = 186
There are 257 items:
itemA = [7 5 4 1 29 3 6 2 9 14 11 9 6 14 9 11 2 2 7 10 13 14 8 1 15 2 18 13 10 5 20 16 12 16 3 8 11 7 4 26 3 4 2 15 3 13 25 1 9 1 1 11 23 5 6 6 1 1 1 5 9 5 12 9 7 1 14 2 5 32 17 1 5 20 25 1 1 2 9 12 4 3 26 4 29 12 6 3 2 9 6 25 24 10 11 14 5 9 20 10 18 7 22 6 30 1 26 1 11 4 5 3 30 15 13 7 9 3 12 5 7 18 11 10 5 1 11 6 17 31 13 20 26 2 7 16 2 2 14 1 2 27 13 15 12 2 30 1 3 6 6 10 31 6 7 14 9 8 4 10 11 6 15 2 1 11 14 17 17 12 20 21 16 4 5 6 14 20 4 5 36 13 4 2 8 11 31 1 5 1 4 5 3 8 4 4 5 28 8 15 9 5 1 2 10 6 1 5 13 11 27 10 1 4 15 3 1 6 1 11 22 17 12 6 3 8 1 8 20 14 4 2 15 10 17 2 8 16 17 1 3 2 10 1 3 7 7 16 17 2 23 5 12 3 22 19 24]
itemB = [3 2 23 6 37 6 21 1 2 9 8 5 2 9 5 21 24 6 5 1 16 4 32 1 1 15 8 1 6 1 5 1 3 15 1 1 6 5 10 25 13 1 6 18 5 15 11 1 5 11 12 1 20 10 16 1 17 11 22 2 11 7 2 17 4 1 9 1 8 2 6 2 31 21 5 13 5 3 1 10 10 15 10 12 8 16 1 1 17 1 7 9 29 29 12 25 11 9 3 1 1 3 15 13 20 21 22 25 5 14 2 22 15 17 6 2 1 18 10 5 30 4 9 6 3 3 11 19 7 9 5 8 7 12 8 9 1 2 20 4 15 3 1 3 5 8 18 30 1 23 8 2 1 10 8 3 18 2 15 9 10 3 21 23 16 7 1 6 9 1 10 19 1 24 9 15 15 2 5 25 24 18 2 15 8 14 6 4 1 11 3 1 22 9 10 9 7 9 10 8 1 32 30 3 26 18 20 18 20 6 13 13 17 8 23 10 16 6 12 6 18 13 4 6 11 5 17 1 12 20 11 7 15 14 9 1 21 4 13 3 5 23 6 32 1 31 10 1 11 24 1 4 1 17 5 29 28]
itemC = [3 17 3 1 5 4 25 1 16 8 9 19 19 16 2 12 2 19 1 9 17 10 8 2 4 13 4 23 1 2 9 17 24 23 6 19 31 8 1 21 3 1 2 1 1 2 2 13 2 24 4 25 3 3 1 16 11 1 4 14 2 24 2 1 16 6 9 18 4 15 10 34 6 19 7 17 13 13 5 2 17 15 5 14 6 21 6 23 1 5 14 11 13 2 1 1 19 2 1 8 16 9 1 21 28 1 6 3 1 1 15 8 1 1 1 27 5 4 28 4 35 5 17 2 3 4 19 5 1 13 13 1 10 8 1 8 14 4 3 27 1 1 2 11 27 4 4 5 3 1 8 22 3 20 2 9 3 5 10 6 15 1 13 17 21 1 14 1 19 16 15 2 18 17 9 24 3 2 10 16 15 12 5 5 9 4 33 3 24 5 5 9 33 4 4 21 20 15 1 7 14 9 7 11 1 17 1 3 13 8 6 9 1 19 18 1 16 9 5 30 15 6 5 8 2 5 9 11 6 20 1 14 3 4 5 32 5 5 6 1 24 11 22 1 11 3 12 5 2 2 1 19 3 1 14 1 2]
6)
    
maxLG = 182
There are 689 items:
itemA = [3 32 2 2 26 13 9 9 5 11 2 2 21 12 4 16 13 8 28 12 33 23 10 15 18 1 13 9 3 3 6 28 2 21 1 8 4 4 26 14 3 6 2 32 4 2 9 11 1 4 7 21 32 3 34 1 8 15 25 26 12 1 15 6 15 16 15 2 34 6 8 20 4 4 17 14 17 6 2 8 11 1 1 5 13 8 2 20 29 4 8 15 23 7 2 5 1 1 31 3 10 5 6 18 5 11 2 2 10 11 1 12 7 2 8 4 29 28 25 4 2 20 3 28 3 14 11 21 14 6 28 6 1 10 25 12 20 13 12 1 11 25 5 8 1 5 5 23 4 12 11 6 2 23 12 1 18 28 1 13 1 22 22 4 22 12 12 5 24 8 5 1 3 2 9 15 7 2 11 6 24 1 4 4 9 17 14 1 3 1 8 5 9 1 1 4 1 24 19 1 2 11 19 1 3 10 13 1 1 24 1 7 15 5 10 1 4 14 21 10 25 14 7 18 11 19 3 1 24 17 4 31 2 26 12 10 22 12 5 14 1 2 18 7 9 1 17 6 1 6 1 4 12 1 9 4 2 8 1 2 1 2 13 2 32 21 5 12 6 5 1 13 1 28 6 13 16 4 9 10 5 3 13 16 8 1 3 9 8 1 18 10 10 12 17 2 11 10 8 2 11 8 12 24 3 1 4 11 7 6 2 9 4 33 5 9 2 6 6 11 3 1 2 5 5 11 22 3 2 2 5 1 1 3 2 4 12 2 15 3 20 27 21 4 4 4 4 13 2 30 18 10 3 1 4 7 10 11 11 1 4 3 17 3 1 5 6 4 3 2 3 3 21 4 20 1 1 2 8 1 21 4 20 16 7 15 1 5 10 10 22 21 1 6 6 8 2 10 7 16 10 3 3 2 17 12 19 12 6 4 3 1 3 12 4 22 23 8 1 21 5 7 20 9 2 1 7 9 14 11 33 6 4 10 11 10 7 10 1 5 11 3 1 4 7 9 8 28 5 5 12 5 3 10 2 12 3 5 15 20 14 6 19 6 10 15 7 26 2 7 12 1 1 1 4 18 1 7 6 10 26 5 1 22 1 31 1 6 3 28 9 8 6 2 8 31 2 8 3 2 8 2 3 11 16 3 6 2 4 2 5 1 7 1 6 17 7 7 7 2 2 16 34 3 15 5 5 16 4 4 1 19 2 8 4 5 3 1 19 9 1 14 3 9 15 5 22 17 17 2 1 2 10 2 3 1 13 4 15 3 3 12 17 4 5 14 8 12 26 31 21 1 7 1 22 6 6 1 3 3 4 5 2 10 6 11 11 28 29 34 9 14 2 6 11 20 11 2 15 3 8 11 5 2 20 19 2 5 12 4 4 14 18 6 21 9 13 17 7 4 5 1 10 11 23 14 11 3 7 21 17 2 10 1 1 1 19 1 2 1 11 2 15 3 6 3 9 11 6 4 21 2 22 2 11 4 18 16 3 11 4 18 9 4 15 1 8 4 2 1 21 1 17 9 4 10 10 10 1 11 1 16 34 9 1 2 31 5 3]
itemB = [6 25 16 9 1 2 9 8 3 8 6 19 3 2 1 10 10 2 13 1 7 4 2 21 9 33 20 1 5 5 4 11 12 10 21 3 2 17 1 8 3 4 4 15 1 32 16 11 12 2 21 5 1 7 20 8 32 11 2 2 3 6 11 5 1 18 2 14 21 5 1 1 9 9 14 9 19 4 15 9 17 5 6 19 4 9 5 8 4 5 31 1 4 11 13 5 4 8 14 22 17 3 13 16 2 17 25 21 6 5 3 4 28 31 31 8 16 10 6 6 29 3 25 26 3 11 8 17 5 4 13 9 6 3 1 2 14 2 13 4 12 9 18 1 2 2 1 2 11 1 23 8 2 16 18 11 1 17 6 1 22 5 16 23 9 28 3 21 7 22 3 4 1 1 9 13 6 4 7 18 6 17 9 24 14 9 21 15 4 6 18 7 10 15 13 26 2 29 15 2 12 23 2 1 4 10 21 14 5 3 15 21 4 19 1 23 12 2 4 4 13 6 12 1 7 1 23 31 11 6 8 1 31 5 10 6 10 1 2 21 8 7 22 9 34 4 18 18 21 21 10 8 2 9 1 6 7 9 3 8 5 1 19 16 9 1 22 1 1 5 1 2 5 10 14 7 17 8 8 6 9 11 4 4 27 27 26 2 1 1 1 5 9 18 22 4 2 5 1 1 5 13 2 2 34 27 4 12 12 2 12 9 7 23 3 21 8 13 5 15 9 15 3 10 21 6 9 13 3 2 14 17 5 12 19 1 29 1 24 12 1 1 5 5 2 8 6 10 7 14 18 3 15 6 9 24 18 4 8 2 1 2 1 1 18 12 1 14 9 9 19 2 1 7 13 16 29 12 10 8 18 9 6 9 2 9 5 1 1 4 2 1 1 15 5 25 6 1 7 2 1 7 13 13 3 21 9 23 20 4 3 9 8 2 22 2 7 1 2 1 1 14 16 1 1 1 10 7 7 13 6 4 22 7 25 17 5 12 8 4 20 2 15 3 19 12 5 14 14 8 1 13 7 5 1 3 5 12 3 15 6 4 2 10 2 21 10 1 3 7 2 3 18 1 2 4 31 10 18 21 8 9 9 19 24 1 7 3 7 5 14 14 16 23 21 1 3 22 6 16 2 3 26 7 2 11 25 3 1 20 4 4 7 13 23 4 2 7 3 1 1 23 30 10 3 7 4 2 23 7 2 7 7 29 2 14 14 11 4 4 5 29 3 5 4 27 2 21 28 2 13 18 5 11 12 1 8 24 15 30 3 2 14 3 5 22 2 10 1 1 3 5 10 1 6 2 3 1 26 3 14 6 3 2 1 12 4 2 3 13 1 2 10 2 2 21 15 5 6 3 30 5 12 9 1 2 8 7 3 4 1 3 1 20 1 9 31 36 3 9 15 30 26 11 3 7 4 2 11 2 8 1 11 7 12 3 15 18 5 2 7 1 9 4 3 2 3 1 22 1 5 5 13 1 15 14 11 3 6 3 26 3 6 8 1 8 18 25 1 1 8 4 5 6 5 9 6 1 12 15 16 17 28 9 1 3 1 2 1]
itemC = [8 16 4 5 12 9 3 18 2 18 2 1 4 13 1 2 2 3 11 20 10 9 1 1 15 6 10 17 18 19 11 6 1 5 29 10 7 21 17 18 2 12 32 2 5 3 11 13 10 16 9 3 13 10 12 13 18 5 8 2 3 26 13 6 15 9 4 15 8 1 4 7 9 4 9 4 3 1 15 3 9 10 2 8 12 1 11 2 27 8 19 3 17 15 4 14 25 3 7 12 7 19 7 8 23 5 17 1 4 9 8 7 5 31 1 22 1 26 7 29 18 7 11 5 19 5 1 1 10 18 10 3 20 2 5 6 10 13 2 25 16 12 7 18 13 3 5 23 3 2 4 2 20 26 13 1 1 1 6 4 14 17 4 2 22 5 2 5 21 1 1 11 9 1 5 29 5 12 9 4 7 13 5 6 1 1 7 1 17 11 5 5 10 3 8 3 17 8 12 5 1 5 7 4 3 6 17 20 1 1 1 25 23 8 6 16 16 18 18 2 17 3 16 30 4 4 9 1 4 7 3 3 8 19 23 8 12 4 5 2 6 22 6 25 4 8 5 14 29 23 4 19 25 14 4 1 27 10 9 4 33 5 7 3 18 28 9 21 5 3 2 15 8 22 2 2 9 2 1 7 7 1 6 20 4 10 1 10 14 4 1 9 22 21 2 3 6 3 2 23 17 2 11 2 4 9 18 3 1 1 6 11 12 1 4 9 5 2 1 10 2 16 3 2 22 1 9 18 7 14 2 15 10 15 4 8 12 3 5 13 21 18 10 9 2 2 31 6 17 17 25 4 13 2 32 3 1 8 17 21 9 2 8 1 2 1 1 1 12 1 2 9 13 1 22 3 3 6 20 16 8 2 8 6 6 4 1 6 8 1 1 15 12 1 14 16 9 18 25 22 5 16 2 11 7 12 2 1 5 10 26 6 6 25 5 13 5 4 4 2 30 8 11 9 5 17 3 17 8 26 14 1 1 4 22 32 2 1 1 23 17 21 17 6 7 1 14 6 3 2 3 10 3 29 11 1 1 18 2 2 5 9 2 1 7 2 15 29 20 1 31 9 9 7 12 3 13 1 7 14 4 12 9 17 24 12 14 25 2 15 1 22 2 2 9 3 13 9 5 25 5 15 12 10 17 2 13 8 6 4 12 1 1 14 5 25 3 2 2 30 14 26 1 33 4 7 10 10 9 5 1 6 2 2 1 9 5 13 14 1 1 7 4 11 13 24 4 14 16 13 7 3 8 2 1 1 4 7 1 23 1 10 31 20 24 18 8 4 3 14 1 2 24 5 25 14 1 7 20 11 4 16 8 10 6 8 25 19 2 11 10 11 6 2 10 11 6 20 6 6 7 10 29 7 3 20 11 4 9 3 9 9 11 11 10 22 20 6 3 9 16 28 2 11 1 15 12 25 20 22 6 5 4 10 2 4 1 2 4 6 2 12 25 2 22 13 10 17 20 25 1 10 7 9 6 2 16 13 2 4 1 7 4 2 3 1 2 7 1 9 2 22 9 26 2 5 6 6 17 15 32 20 11 18 10 20 3 3 8]
7)
    
maxLG = 132
There are 376 items:
itemA = [4 1 9 10 7 7 3 4 2 4 19 3 1 17 1 9 1 5 2 8 9 1 13 2 6 4 5 22 16 11 5 2 10 4 5 5 3 9 2 8 8 2 2 13 3 2 16 2 10 3 8 8 1 2 6 1 10 4 2 15 5 6 1 21 6 2 21 4 6 5 10 6 1 1 16 23 10 14 15 1 4 1 10 1 8 3 2 4 5 10 1 5 1 13 1 1 9 2 2 1 10 7 15 9 1 7 11 2 1 14 4 14 5 11 20 17 1 1 3 4 1 2 2 8 19 2 11 1 12 6 4 13 3 11 7 16 3 5 3 19 1 6 22 10 10 1 2 14 1 11 2 16 8 1 2 6 14 3 7 2 2 4 1 5 18 12 5 2 1 4 11 8 16 18 2 13 17 1 9 11 5 4 2 11 1 1 11 11 10 5 9 23 3 19 6 8 10 1 4 2 4 1 7 6 1 6 7 10 17 10 2 1 6 15 12 14 5 17 8 1 1 1 7 3 1 14 3 7 4 2 2 6 4 1 3 12 1 9 3 9 6 1 14 4 2 1 7 9 14 16 2 3 1 9 3 2 2 9 15 2 3 11 4 5 11 3 2 2 9 20 5 11 10 17 8 1 2 3 11 1 17 9 4 15 10 6 10 1 22 8 22 12 9 4 6 18 5 8 3 14 16 4 13 3 1 10 4 9 7 2 19 2 4 8 24 6 1 19 1 1 1 5 8 3 3 1 2 12 2 6 6 17 20 3 8 9 1 4 10 5 7 2 2 7 1 4 2 6 4 1 2 1 21 8 4 10 1 2 4 12 1 17 1 1 10 6 10 6 14 18 15 9 23 14 9 3]
itemB = [7 5 1 18 1 1 1 5 8 5 5 4 5 4 1 1 1 1 4 11 10 3 3 3 16 3 8 7 1 1 1 1 11 3 21 1 2 5 1 3 2 12 4 12 5 10 11 16 4 16 3 2 6 1 4 13 1 7 7 3 1 4 7 3 17 18 3 17 6 12 3 5 5 4 1 4 3 7 6 1 3 1 1 1 2 1 12 1 3 2 22 8 13 10 14 7 21 6 9 3 12 23 1 12 7 7 2 5 13 14 6 1 4 15 17 8 14 1 7 3 12 17 5 16 5 15 1 3 1 1 5 6 2 9 20 1 3 8 3 11 6 3 9 11 16 18 7 8 24 5 3 8 17 15 1 4 1 10 3 9 12 10 23 2 7 1 2 21 16 4 1 1 12 11 1 12 2 7 4 6 1 11 15 9 7 5 9 3 15 1 2 7 1 2 4 1 1 8 13 7 6 12 7 4 10 2 3 6 1 4 18 2 2 6 14 3 1 2 10 7 7 8 15 13 1 1 13 15 3 11 3 1 1 10 10 3 17 1 9 18 7 8 3 21 3 11 2 2 9 14 10 13 4 19 1 1 8 8 1 18 1 2 14 1 16 9 10 8 3 17 24 3 3 7 9 2 19 1 8 4 3 3 1 4 4 11 3 8 10 20 9 4 1 5 9 2 1 2 10 5 26 4 10 18 8 11 2 11 16 2 5 1 2 1 5 10 11 11 1 3 7 3 12 6 5 2 5 15 6 15 13 7 18 12 7 1 11 10 21 12 10 1 14 4 12 1 1 7 20 3 1 11 10 13 3 3 13 21 10 4 3 1 23 4 8 7 2 21 14 17 4 13 5 10 5 2]
itemC = [16 5 12 20 18 2 2 7 1 1 1 13 4 1 12 9 2 11 8 7 2 13 1 3 2 12 3 14 2 16 11 5 2 6 3 7 1 8 12 4 13 4 5 8 1 1 14 11 12 14 1 3 2 3 6 3 3 9 15 7 10 11 5 2 1 6 3 4 5 20 14 1 6 7 10 6 9 1 7 2 10 5 6 3 10 2 12 1 4 3 3 16 20 2 4 1 4 19 3 13 7 10 6 2 8 1 2 10 24 9 17 8 8 7 6 2 1 20 3 1 2 9 6 3 3 9 8 22 4 3 1 11 19 16 3 6 1 18 9 5 4 14 1 1 8 9 2 1 12 8 4 1 17 2 1 3 6 15 10 16 2 11 16 5 9 6 3 1 1 10 14 5 1 15 6 25 7 17 1 6 14 6 4 15 7 2 3 4 8 2 1 1 6 6 4 21 23 1 9 7 7 24 13 1 2 1 2 4 9 6 11 6 7 6 3 4 3 9 5 1 2 2 4 6 15 10 21 1 4 12 1 14 7 1 10 11 4 3 4 21 1 8 7 17 11 13 8 7 13 1 8 3 4 1 17 20 5 7 3 3 4 3 1 11 7 1 9 1 11 1 11 12 2 2 18 1 14 4 24 3 2 6 3 21 1 1 4 4 2 19 1 12 9 26 2 10 2 1 21 3 2 6 2 1 6 13 6 7 1 1 22 3 7 8 2 23 3 4 9 1 23 5 14 7 1 3 4 6 1 1 1 6 7 21 21 10 13 8 8 2 11 3 3 2 1 5 13 20 1 2 6 8 4 4 12 4 18 10 4 17 1 5 7 7 14 12 2 1 1 1 1 2 2 14 1 13]
8)
    
maxLG = 118
There are 665 items:
itemA = [1 2 1 9 11 9 4 1 6 10 2 1 1 17 3 9 15 2 6 5 10 7 14 2 6 5 3 1 8 1 8 1 19 1 6 9 7 4 1 14 2 4 4 1 4 4 12 1 1 11 1 1 6 6 2 5 9 17 2 12 4 2 3 1 3 6 14 3 1 7 2 1 2 2 19 6 6 2 2 4 10 1 1 1 5 7 6 2 1 3 11 1 6 18 1 1 7 3 1 6 6 1 1 14 3 5 4 10 2 7 5 4 4 16 4 5 3 1 11 4 1 1 2 4 1 1 1 1 18 6 3 1 11 1 6 15 4 6 4 7 13 4 4 1 1 8 4 5 3 5 7 19 1 1 9 11 5 4 2 10 16 6 1 18 3 14 8 7 6 1 5 4 3 3 2 15 11 11 7 5 5 19 2 7 4 7 17 2 3 6 18 8 8 1 14 14 12 8 1 1 1 12 6 10 3 7 8 1 8 20 6 12 8 6 1 2 3 18 8 1 1 3 9 1 1 1 1 2 1 7 9 12 7 5 1 2 3 11 1 6 6 6 2 3 1 4 3 4 10 1 1 1 5 18 7 2 4 2 22 2 3 3 16 8 8 6 6 13 4 9 5 1 1 2 6 5 1 5 1 10 1 5 1 12 15 5 4 3 5 2 2 14 11 5 1 5 2 5 16 7 2 7 4 12 3 5 8 8 1 13 7 1 13 5 1 5 10 3 5 6 7 2 8 1 5 4 11 5 5 3 4 1 3 8 10 5 2 1 10 1 3 1 1 4 2 2 1 1 19 2 2 16 7 1 4 13 14 4 6 5 16 17 6 7 4 3 2 3 3 4 9 6 1 6 2 8 3 5 1 5 2 11 15 4 12 13 3 23 12 1 3 1 3 1 15 9 1 7 6 4 12 5 21 5 2 1 11 8 1 1 2 13 9 3 2 11 1 9 11 9 8 3 11 7 3 6 8 2 2 3 2 18 13 5 5 8 12 2 8 3 18 10 3 4 4 12 2 14 4 5 2 1 7 2 16 1 2 3 16 6 5 2 22 1 2 3 1 12 3 1 1 1 14 1 8 1 2 2 2 14 5 1 2 5 2 12 4 7 22 11 4 9 6 6 15 1 16 5 3 5 7 5 1 2 7 10 8 5 2 16 1 18 7 1 1 6 4 15 18 3 3 5 4 1 11 1 6 11 4 9 4 1 6 10 2 12 1 20 15 5 10 3 2 2 12 5 5 1 3 18 6 1 6 5 4 1 6 2 7 3 4 3 10 2 8 1 7 2 5 3 18 1 2 11 18 9 4 3 14 18 1 2 5 8 1 8 3 8 10 1 5 3 10 3 2 1 14 12 8 14 7 21 1 2 5 1 1 10 5 8 4 11 3 4 8 20 12 8 1 2 1 1 9 5 1 1 3 7 2 14 2 2 2 5 3 3 11 8 1 5 17 12 1 9 3 8 1 1 8 1 4 2 4 2 7 1 2 11 4 8 6 17 6 6 7]
itemB = [9 1 2 1 1 6 1 7 3 13 1 9 2 2 11 1 1 3 2 3 9 8 22 18 11 17 1 1 6 6 9 1 1 4 1 8 4 2 1 3 1 15 3 13 14 9 2 6 10 2 3 6 2 7 9 1 9 19 7 9 7 1 11 10 3 9 5 19 3 4 3 3 8 1 10 4 4 2 1 1 4 6 4 9 5 1 2 8 16 7 3 5 1 1 11 16 1 9 19 5 1 15 5 3 15 1 3 7 1 7 2 8 14 1 5 3 9 1 3 2 1 9 3 5 3 1 9 10 3 1 10 3 5 9 20 4 5 17 1 4 18 19 3 8 3 15 8 2 9 16 4 8 10 2 15 6 20 1 1 3 1 16 5 2 9 6 4 15 6 1 6 7 1 8 5 2 10 2 16 5 5 3 15 18 14 16 1 3 11 9 12 7 12 4 5 17 5 2 2 8 12 1 4 1 2 1 14 1 17 3 4 1 21 13 4 2 3 1 17 1 2 10 6 11 7 5 1 3 1 6 7 9 6 1 19 15 2 2 3 1 3 2 1 5 13 5 7 15 3 8 11 1 1 1 7 4 21 4 1 8 9 1 7 16 11 1 5 8 1 11 2 2 1 9 16 5 7 18 6 3 6 5 1 5 3 19 8 3 12 4 15 9 4 5 3 8 11 11 3 11 17 1 1 5 3 10 5 6 8 9 2 18 7 4 3 3 1 2 9 10 3 2 3 6 16 6 2 11 6 5 20 7 3 5 2 2 3 16 16 8 3 8 1 1 7 1 7 6 1 9 3 5 6 4 3 5 1 1 7 6 6 4 1 16 1 18 13 11 18 15 14 4 6 1 3 1 2 13 8 9 7 1 6 7 11 2 9 2 2 5 3 1 3 4 6 6 17 12 3 1 2 2 6 8 3 11 3 2 10 14 8 17 2 1 10 15 4 2 3 10 4 16 6 1 1 1 6 2 20 2 6 1 3 6 6 1 11 5 12 3 1 20 1 3 3 6 8 4 19 8 1 2 2 2 2 4 3 5 10 13 6 16 8 4 2 11 2 11 21 2 12 5 3 4 8 4 5 5 5 1 3 5 7 13 3 20 20 3 4 11 15 1 3 16 16 10 7 6 5 6 3 1 1 1 2 1 7 2 12 1 1 15 5 7 1 7 11 11 1 1 8 11 3 6 3 1 5 12 2 12 3 3 1 4 2 3 2 7 23 2 3 15 6 3 3 10 4 9 2 10 3 5 1 5 9 16 1 1 5 5 2 13 9 3 9 16 21 1 12 16 4 21 5 8 4 12 2 1 4 1 1 1 13 1 5 16 11 13 12 10 1 10 1 13 7 19 2 13 3 2 3 3 5 1 7 1 7 12 2 2 3 3 7 1 1 9 2 3 19 4 3 1 4 1 1 1 3 2 11 10 6 6 8 4 3 6 6 10 2 8 5 14 11 3 5 1 21 1 1 9 2 13 3 3 7 4 1 2 3 2 7 1 10 4 4]
itemC = [2 1 5 4 15 5 2 3 5 13 3 17 2 4 12 3 2 7 12 8 14 8 11 5 3 2 2 12 1 10 2 13 11 13 5 3 3 1 1 4 3 1 15 15 4 10 7 5 1 3 1 1 5 2 4 6 16 4 3 1 15 1 20 12 2 2 1 7 7 3 2 3 12 10 8 13 8 14 4 7 2 4 12 16 1 2 2 1 3 17 11 1 18 1 8 1 5 19 15 7 6 7 3 3 1 15 5 3 9 2 10 10 3 3 5 6 7 5 11 4 3 2 3 22 11 6 14 1 9 2 3 3 1 4 1 2 3 6 6 5 5 13 1 3 5 23 6 2 1 6 1 8 7 10 10 4 1 1 7 11 16 9 8 10 1 2 9 4 1 15 1 1 5 14 13 5 5 6 3 2 6 2 4 4 14 1 2 10 5 9 2 6 7 5 2 6 11 1 1 2 8 6 1 11 11 3 9 1 17 1 10 1 10 1 7 7 1 8 16 2 1 13 7 2 6 4 2 11 3 3 6 3 11 8 7 4 2 10 7 1 2 1 1 6 4 4 3 2 16 9 1 12 16 4 16 7 5 8 1 4 1 5 10 1 1 4 11 14 3 4 2 3 6 3 1 1 3 5 4 4 5 16 2 12 1 13 8 1 1 8 18 2 6 5 3 8 3 3 7 6 2 1 5 6 1 1 3 6 11 3 4 1 2 7 2 1 9 13 6 13 5 5 4 5 15 4 1 2 6 7 1 19 7 13 1 8 9 12 5 11 7 2 2 7 2 7 2 10 17 4 2 1 6 4 4 1 1 10 2 10 1 1 9 14 4 20 7 22 2 6 10 4 1 2 12 5 4 3 4 15 11 8 4 2 6 3 2 1 5 15 3 2 1 3 6 6 1 15 5 7 2 3 4 2 2 14 11 20 7 3 3 7 1 2 11 11 2 7 1 2 10 13 13 16 3 9 12 13 3 10 1 2 7 9 3 2 9 3 2 4 12 7 1 1 1 1 1 2 7 3 1 6 2 7 11 6 2 6 10 5 1 1 2 4 3 1 16 5 3 16 5 4 4 1 2 10 5 7 5 9 4 3 21 4 4 4 16 6 7 7 14 12 7 12 18 5 1 3 1 1 10 6 12 5 1 5 3 1 2 21 8 6 5 6 9 13 10 11 2 1 12 9 9 11 14 2 7 4 8 11 15 1 6 19 9 9 7 9 13 9 1 4 14 7 12 1 1 6 4 9 3 20 1 16 1 11 3 1 3 4 14 2 11 4 8 2 1 3 9 7 18 6 1 8 2 1 10 3 13 1 3 11 2 11 2 3 6 6 1 8 5 8 4 3 7 11 1 9 4 2 1 1 9 8 3 9 3 19 1 5 1 3 2 5 14 3 2 3 3 2 1 16 10 3 3 11 8 5 20 9 1 6 5 5 8 6 3 3 4 13 7 11 8 12 9 4 12 1 7 7 5 2 2 19 10 2 2 2 1 4 2 7 3 6 2]
9)
    
maxLG = 94
There are 757 items:
itemA = [4 13 2 3 2 5 8 1 1 1 11 2 2 4 1 7 9 17 11 3 1 4 8 2 12 1 7 1 2 1 10 2 3 2 2 1 3 8 9 3 1 4 1 1 1 1 8 4 9 3 9 8 2 2 7 9 1 6 1 5 9 3 6 4 1 9 4 4 6 4 3 6 6 4 1 3 5 8 3 12 3 4 2 3 9 1 11 1 2 1 5 3 1 6 1 2 4 3 1 1 8 8 4 17 5 1 1 2 1 7 1 1 2 4 1 5 1 2 7 13 1 2 7 5 14 4 4 3 1 8 9 7 12 13 3 7 1 4 2 1 1 2 1 1 1 4 8 2 7 8 5 1 2 9 4 6 16 7 9 1 1 1 1 17 7 2 2 9 3 8 2 1 1 4 6 9 2 1 5 1 1 3 2 15 5 5 7 13 10 9 3 5 7 2 1 6 3 10 4 1 2 1 8 10 1 8 3 4 1 11 5 1 3 2 4 5 1 7 8 2 2 3 9 7 7 3 1 5 9 7 2 4 8 1 1 1 7 2 2 1 11 1 9 10 7 4 8 6 11 2 2 2 8 6 9 6 9 5 13 1 9 2 3 2 9 2 6 15 8 2 1 13 6 5 15 4 1 11 13 5 1 12 9 5 5 9 11 1 3 1 5 1 8 7 1 6 1 3 4 4 10 4 10 1 2 1 2 8 2 7 1 16 5 7 2 2 1 4 4 4 3 1 14 6 1 5 1 6 4 4 2 12 3 2 4 2 3 8 1 11 6 4 4 2 7 1 7 3 6 1 11 8 1 1 1 1 2 8 2 13 2 10 5 5 6 2 8 11 6 8 1 2 2 7 6 2 1 2 4 5 1 15 1 1 8 2 6 7 7 10 1 4 2 10 2 5 1 1 8 7 1 1 7 14 1 1 2 4 1 2 13 1 6 6 2 1 1 5 2 2 3 5 1 7 8 3 1 14 3 2 1 1 7 2 3 6 5 6 4 10 1 5 9 4 2 5 2 1 3 10 10 15 1 5 2 2 7 11 5 4 1 14 3 8 12 1 3 7 1 6 14 13 9 1 6 2 8 15 6 8 1 1 10 10 10 5 2 3 4 3 8 7 3 1 7 10 5 3 7 5 14 12 8 9 8 1 1 2 2 4 6 3 4 2 2 7 1 1 9 2 2 11 10 3 1 15 1 7 1 7 1 2 6 3 16 1 14 12 5 6 4 3 2 1 1 2 1 9 1 4 3 5 4 3 3 5 4 15 8 5 4 4 2 4 1 1 11 8 11 1 1 2 8 1 12 8 3 1 4 6 2 1 10 4 6 2 14 1 10 8 13 1 3 11 8 4 4 8 8 1 1 4 1 9 1 2 7 4 6 9 1 8 3 7 2 2 3 10 1 1 5 10 12 5 6 1 10 1 4 4 3 12 1 1 3 1 5 2 16 8 1 7 11 3 1 11 2 2 1 4 5 12 4 10 1 11 7 6 7 8 5 10 8 1 1 9 6 3 4 11 8 10 1 11 2 1 4 6 1 3 3 9 4 3 1 3 15 4 7 4 6 1 4 6 5 3 4 1 1 6 3 1 1 2 5 3 13 1 4 4 2 10 11 8 1 1 4 10 10 2 2 1 15 2 10 1 7 3 10 4 1 5 7 1 1 12 5 1 13 5 10 1 6 3 3 3 1 1 1 4 2 5 4 1 7 8 3]
itemB = [1 9 3 2 3 2 14 2 3 2 5 3 3 7 14 2 1 1 15 3 10 6 17 4 4 1 9 2 4 2 1 1 1 3 8 10 2 2 2 1 2 1 12 6 13 6 9 6 3 3 7 3 6 10 1 7 1 5 3 2 9 1 3 1 7 3 2 12 1 2 4 7 2 9 4 5 1 13 11 2 3 1 7 1 10 6 4 3 15 2 13 9 2 2 1 9 3 13 1 6 1 6 4 15 1 1 1 11 1 7 1 4 4 6 3 3 1 6 9 9 1 5 3 1 9 10 6 13 6 3 1 4 6 1 1 3 1 2 5 3 7 7 5 6 2 3 11 6 1 2 1 5 5 1 1 2 12 7 6 4 5 1 6 7 10 7 4 4 5 2 3 3 5 13 2 6 5 7 5 2 4 2 13 1 7 4 1 10 15 2 2 1 7 12 2 2 9 5 13 3 1 1 1 12 1 2 5 15 1 8 1 2 1 12 3 6 13 2 6 3 1 9 16 1 2 18 5 3 8 1 2 6 6 4 2 1 1 1 5 2 5 1 2 2 5 2 3 8 13 4 4 2 8 12 3 2 5 1 3 2 8 1 14 15 5 1 2 2 1 11 4 2 6 8 1 3 1 3 14 3 3 3 2 10 1 1 6 2 5 11 1 1 1 2 13 1 4 14 1 3 3 2 1 3 1 11 12 5 3 3 1 3 1 12 15 2 4 1 4 1 9 9 9 1 5 1 4 1 1 2 5 1 6 3 4 3 7 9 7 4 10 1 3 6 2 2 7 5 13 2 10 4 2 5 2 7 17 3 2 1 1 4 13 3 7 1 8 10 5 2 2 5 2 9 5 1 1 1 4 2 10 1 1 7 4 6 8 4 12 1 9 11 15 1 1 2 6 2 4 10 3 2 3 8 6 1 18 6 2 5 3 9 2 5 5 6 6 5 8 1 1 5 11 2 3 4 5 2 6 1 2 1 2 13 7 2 1 2 3 1 3 2 1 6 3 8 3 2 9 7 3 4 6 1 1 5 3 3 1 3 7 14 1 3 7 3 9 2 8 1 6 11 8 7 13 1 1 1 12 1 5 6 9 10 9 1 4 6 2 1 6 8 1 4 1 1 3 8 2 3 7 5 4 1 1 2 5 1 1 9 5 6 3 4 12 11 1 10 7 5 9 5 1 3 10 8 9 10 1 6 13 4 1 6 3 15 8 2 4 4 1 2 9 1 1 1 2 2 1 5 9 1 6 3 1 17 3 2 7 2 1 3 7 3 6 9 1 10 3 1 3 11 1 3 7 1 4 7 2 15 2 3 14 4 6 2 5 2 3 2 7 2 2 7 5 14 5 10 2 8 3 5 2 2 8 4 5 2 6 1 4 4 3 8 10 4 3 12 1 1 13 2 1 7 5 2 5 8 11 4 3 4 3 5 1 4 4 3 18 4 4 15 11 1 10 1 4 14 8 4 8 4 1 4 12 3 3 7 1 2 2 1 3 1 6 3 9 1 14 8 17 12 1 2 1 9 6 5 9 4 5 3 12 7 2 7 1 1 7 6 5 14 11 2 8 6 8 5 1 6 1 2 4 4 11 7 12 5 6 1 1 5 1 5 5 9 7 4 9 15 2 10 3 4 14 2 2 7 1 11 8 13 1 13 3 2 1 7 2 1 11 5 18 2 11 5 9 2 2 2 4 2 9 4 6 5 1]
itemC = [5 4 3 3 2 4 6 17 3 2 1 14 4 11 9 2 11 11 13 4 10 6 8 3 1 1 11 7 1 3 4 9 4 3 8 1 6 10 4 2 13 1 7 2 12 6 6 8 7 1 2 5 9 1 10 9 3 8 6 9 4 1 3 6 14 5 1 7 5 2 13 7 1 2 5 8 1 2 2 3 2 2 4 4 5 2 1 1 12 4 10 7 6 1 2 16 2 5 2 6 2 16 5 3 9 1 11 1 4 5 11 4 4 4 1 6 4 8 5 4 2 6 12 3 2 2 7 6 2 3 9 7 3 1 9 15 1 1 9 2 9 6 1 8 3 4 1 16 2 1 9 8 1 1 15 1 3 9 5 13 9 4 8 2 2 15 1 3 2 1 12 1 2 3 7 8 15 3 1 13 2 1 11 4 6 7 1 15 1 1 8 9 1 1 6 3 2 6 1 2 10 13 5 1 15 8 8 3 16 3 1 3 5 5 1 9 1 4 5 2 2 7 6 2 7 1 6 1 4 2 2 11 1 2 2 1 7 1 3 4 15 1 1 3 2 13 6 4 1 9 17 1 6 7 4 9 8 10 2 12 3 2 15 15 9 5 1 4 2 4 1 13 2 13 4 9 4 1 14 1 8 9 6 2 2 14 4 3 4 11 5 9 1 1 7 10 8 1 6 2 10 1 4 2 3 1 1 5 7 6 2 8 1 3 12 12 8 1 3 1 5 7 5 4 14 3 2 4 1 5 3 1 14 3 8 9 9 13 5 7 14 5 1 4 1 3 1 6 12 7 4 1 3 7 7 7 1 6 2 1 1 1 8 5 1 6 8 4 8 9 5 12 4 7 2 4 1 7 1 6 12 5 5 2 3 9 1 11 4 6 4 4 1 2 4 6 3 5 8 2 1 4 7 2 4 1 4 3 14 9 1 2 9 2 5 7 2 1 1 2 10 1 9 4 5 1 5 1 2 1 3 1 1 2 1 10 15 1 1 9 8 5 7 1 3 4 1 2 2 7 15 2 6 5 2 8 18 6 7 1 3 3 6 1 10 15 13 15 5 1 4 6 14 16 5 6 8 2 2 2 7 12 1 3 7 13 7 3 7 13 7 6 16 8 1 4 1 9 13 1 6 3 10 2 5 14 1 2 10 8 7 13 1 10 6 3 1 5 4 8 8 1 1 1 10 6 3 3 2 7 7 2 1 4 6 9 4 6 1 2 2 1 7 1 5 4 8 8 4 7 2 1 4 14 2 9 8 3 3 1 6 9 1 2 16 1 11 4 1 3 11 6 3 3 6 3 17 2 8 17 16 3 4 13 5 1 5 4 15 4 7 3 3 10 4 1 6 1 2 1 1 1 6 5 4 5 8 2 7 12 11 12 2 8 1 10 8 2 5 7 5 2 6 7 2 1 6 2 2 3 14 7 1 13 1 2 1 9 2 13 1 3 11 1 4 1 2 12 1 3 2 7 4 1 2 4 11 6 15 3 1 6 3 2 10 2 15 2 1 16 4 2 1 2 4 3 3 10 1 4 2 1 1 4 18 5 6 7 1 8 1 2 5 2 5 7 1 1 3 1 10 1 2 4 1 3 2 6 8 8 7 10 8 1 6 2 5 1 1 14 1 10 5 6 1 1 2 1 3 2 1 1 1 1 4 4 5 2 4 4 8 4 8 6 4 11 2 2 3 2 1 1 1 3 7 11 1]

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