/*

  Problem 11
  """
  In the 2020 grid below, four numbers along a diagonal line have been marked in red.

  08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
  49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
  81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
  52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
  22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
  24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
  32 98 81 28 64 23 67 10|26|38 40 67 59 54 70 66 18 38 64 70
  67 26 20 68 02 62 12 20 95|63|94 39 63 08 40 91 66 49 94 21
  24 55 58 05 66 73 99 26 97 17|78|78 96 83 14 88 34 89 63 72
  21 36 23 09 75 00 76 44 20 45 35|14|00 61 33 97 34 31 33 95
  78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
  16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
  86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
  19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
  04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
  88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
  04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
  20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
  20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
  01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48

  The product of these numbers is 26 x 63 x 78 x 14 = 1788696.

  What is the greatest product of four adjacent numbers in any direction 
  (up, down, left, right, or diagonally) in the 20 x 20 grid?
  """

  This Pop-11 program was created by Hakan Kjellerstrand (hakank@gmail.com).
  See also my Pop-11 / Poplog page: http://www.hakank.org/poplog/


*/
compile('/home/hakank/Poplib/init.p');

;;; note the \ at the end of line (is "\n")
vars p11_matrix = 
'08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08\
49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00\
81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65\
52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91\
22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80\
24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50\
32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70\
67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21\
24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72\
21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95\
78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92\
16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57\
86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58\
19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40\
04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66\
88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69\
04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36\
20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16\
20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54\
01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48';

define productlist(list) -> res;
   applist(1, list, nonop * ) -> res;
enddefine;


define problem11();

    ;;; convert to matrix aa (and print it)
    lvars i,j, x, aa;
    [%split_with(p11_matrix,'\n')%] -> x;
    newarray([1 20 1 20]) -> aa;
    for i from 1 to 20 do 
        for j from 1 to 20 do 
            strnumber([%x(i).split%](j)) -> aa(i,j);
        endfor;
    endfor;
    npr('');

    lvars across, col, row, a;
    ;;; npr('across');
    [%for col from 1 to 20 do
        for a from 1 to 17 do
            productlist([%
            for row from a to a + 3 do
                aa(col, row)
            endfor;
            %])
        endfor;
    endfor%] -> across;
    ;;; across=>
            
    lvars updown;
    ;;; npr('updown');
    [%for row from 1 to 20 do
        for a from 1 to 17 do
            productlist([%
            for col from a to a + 3 do
                aa(col, row)
            endfor;
            %])
        endfor;
    endfor%] -> updown;
    ;;; updown=>
            

    lvars diag_down;
    ;;; npr('diag_down');
    [%for j from 1 to 17 do
        for i from 1 to 17 do
            productlist([%
            for a from 0 to 3 do
                aa(a + i, a+j)
            endfor;
            %])
        endfor;
    endfor%] -> diag_down;
    ;;; diag_down=>
            

    lvars diag_up;
    ;;; npr('diag_up');
    [%for j from 1 to 17 do
        for i from 4 to 20 do
            productlist([%
            for a from 0 to 3 do
                aa(i - a, j + a)
            endfor;
            %])
        endfor;
    endfor%] -> diag_up;
    ;;; diag_up=>
            
    last(sort([^^across ^^updown ^^diag_down ^^diag_up]))=>;

enddefine;


'problem11()'=>
problem11();