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DJ357.pl
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DJ357.pl
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/* <DJ357 and name of the Daniel Jenkyn>
THIS WORK IS ENTIRELY MY OWN.
The program does not produce multiple answers.
I have not used built-ins.
1. 1747 elements in the list binding Q after executing s1(Q,100)
- Generates a list of Quadruples containing [X,Y,S,P].
- It then sorts the list by ascending product.
- Finally removes all unique products.
2. 145 elements in the list binding Q after executing s2(Q,100)
- Performs S1.
- Sorts the S1 by ascending Sum.
- Generates a new list of Quadruples containing [X,Y,S,P].
- It then sorts the new list by ascending product.
- Then remove duplicate products from this list.
- Sorts the list by ascending Sum.
- Gets the list of sums to some of the unique products
- Remove list of Sums To Some Unique Products
- Finally sorts the list by ascending product.
3. 86 elements in the list binding Q after executing s3(Q,100)
- Performs S2.
- Then remove duplicate products from this list.
- Sorts the list by ascending Sum.
4. - Performs S3.
- Then remove duplicate sums from this list.
5. 1 of elements in the list binding Q after executing s4(Q,500)
s4(Q,500) uses 9,897,933 inferences. */
/* <BODY OF THE PROGRAM> */
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
% Generate a list of Quadruples [X,Y,S,P]
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
s0(X,Y,Max,[[X,Y,S,P]|T]) :-
X + Y =< Max,!,
S is X + Y,
P is X * Y,
Y2 is Y + 1,
s0(X,Y2,Max,T).
s0(X,_,Max,T) :-
X + X =< Max,!,
X2 is X + 1,
Y2 is X2 + 1,
s0(X2,Y2,Max,T).
s0(_,_,_,[]) :- !.
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
% Merge Sort by Product
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
mergeP([],[]).
mergeP([A],[A]).
mergeP([A,B|R],S) :-
split([A,B|R],L1,L2),
mergeP(L1,S1),
mergeP(L2,S2),
mergeSplits(S1,S2,S),!.
split([],[],[]).
split([A],[A],[]).
split([A,B|R],[A|Ra],[B|Rb]) :-
split(R,Ra,Rb),!.
mergeSplits(A,[],A).
mergeSplits([],B,B):-
B\=[],!.
mergeSplits([[X,Y,Sum1,A]|Ra],[[X2,Y2,Sum2,B]|Rb],[[X,Y,Sum1,A]|M]) :-
A =< B,
mergeSplits(Ra,[[X2,Y2,Sum2,B]|Rb],M).
mergeSplits([[X,Y,Sum1,A]|Ra],[[X2,Y2,Sum2,B]|Rb],[[X2,Y2,Sum2,B]|M]) :-
A > B,
mergeSplits([[X,Y,Sum1,A]|Ra],Rb,M),!.
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
% Merge Sort by Sum
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
mergeS([],[]).
mergeS([A],[A]).
mergeS([A,B|R],S) :-
split([A,B|R],L1,L2),
mergeS(L1,S1),
mergeS(L2,S2),
mergeSplitsS(S1,S2,S),!.
mergeSplitsS(A,[],A).
mergeSplitsS([],B,B):-
B\=[],!.
mergeSplitsS([[X,Y,Sum1,A]|Ra],[[X2,Y2,Sum2,B]|Rb],[[X,Y,Sum1,A]|M]) :-
Sum1 =< Sum2,
mergeSplitsS(Ra,[[X2,Y2,Sum2,B]|Rb],M).
mergeSplitsS([[X,Y,Sum1,A]|Ra],[[X2,Y2,Sum2,B]|Rb],[[X2,Y2,Sum2,B]|M]) :-
Sum1 > Sum2,
mergeSplitsS([[X,Y,Sum1,A]|Ra],Rb,M),!.
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
% Remove unique Products
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
removeUniqueP([],[],[]).
removeUniqueP([A],[A],[]).
removeUniqueP([[X,Y,S,P],[X2,Y2,S2,P]],[],[[X,Y,S,P],[X2,Y2,S2,P]]).
removeUniqueP([[X,Y,S,P],[X2,Y2,S2,P],[X3,Y3,S3,P]|T1],L,[[X,Y,S,P]|T2]) :-
removeUniqueP([[X2,Y2,S2,P],[X3,Y3,S3,P]|T1],L,T2),!.
removeUniqueP([[X,Y,S1,P],[X2,Y2,S2,P],H|T1],L,[[X,Y,S1,P],[X2,Y2,S2,P]|T2]) :-
removeUniqueP([H|T1],L,T2),!.
removeUniqueP([A,B|T1],[A|T2],L) :-
removeUniqueP([B|T1],T2,L),!.
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
% Remove duplicate Products
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
removePDupes([],Result,Result).
removePDupes([[_,_,_,P],[X2,Y2,S2,P],[X3,Y3,S3,P]|T],L,Result) :-
removePDupes([[X2,Y2,S2,P],[X3,Y3,S3,P]|T],L,Result),!.
removePDupes([[_,_,_,P],[_,_,_,P],[X3,Y3,S3,P3]|T],L,Result) :-
P\=P3,
removePDupes([[X3,Y3,S3,P3]|T], L,Result),!.
removePDupes([[X,Y,S,P],[X2,Y2,S2,P2],[X3,Y3,S3,P3]|T],L,Result) :-
P\=P2,P2\=P3,P\=P3,
removePDupes([[X3,Y3,S3,P3]|T],[[X,Y,S,P],[X2,Y2,S2,P2]|L],Result),!.
removePDupes([[X,Y,S,P],[X2,Y2,S2,P2],[X3,Y3,S3,P2]|T],L,Result) :-
P\=P2,
removePDupes([[X2,Y2,S2,P2],[X3,Y3,S3,P2]|T],[[X,Y,S,P]|L],Result),!.
removePDupes([[_,_,_,P],[_,_,_,P]|T],L,Result) :-
removePDupes(T,L,Result),!.
removePDupes([[X,Y,S,P],[X2,Y2,S2,P2]|T],L,Result) :-
P\=P2,
removePDupes([[X2,Y2,S2,P2]|T],[[X,Y,S,P]|L], Result),!.
removePDupes([[X,Y,S,P]|T],L,Result) :-
removePDupes(T,[[X,Y,S,P]|L],Result),!.
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
% Removes first input list (SumsToSomeUniqueProducts) from second Input list
%(Unique sums)
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
removeSumsToSomeUniqueProducts([],_,[]) :- !.
removeSumsToSomeUniqueProducts([[X,Y,S,P]|Q],[Sum|St],[[X,Y,S,P]|Result]) :-
S < Sum,!,
removeSumsToSomeUniqueProducts(Q,[Sum|St],Result).
removeSumsToSomeUniqueProducts([[X,Y,S,P]|Q],[Sum|St],Result) :-
S > Sum,!,
removeSumsToSomeUniqueProducts([[X,Y,S,P]|Q],St,Result).
removeSumsToSomeUniqueProducts([[_,_,S,_],[_,_,S,_],[_,_,S,_], [_,_,S,_],
[_,_,S,_]|Q],[S|St],Result) :-
removeSumsToSomeUniqueProducts(Q, [S | St], Result).
removeSumsToSomeUniqueProducts([[_,_,S,_],[_,_,S,_], [_,_,S,_], [_,_,S,_]|Q],
[S|St],Result) :-
removeSumsToSomeUniqueProducts(Q,[S|St],Result).
removeSumsToSomeUniqueProducts([[_,_,S,_],[_,_,S,_],[_,_,S,_]|Q], [S|St],
Result) :-
removeSumsToSomeUniqueProducts(Q,[S|St],Result).
removeSumsToSomeUniqueProducts([[_,_,S,_],[_,_,S,_]|Q],[S|St],
Result) :-
removeSumsToSomeUniqueProducts(Q,[S|St],Result).
removeSumsToSomeUniqueProducts([[_,_,S,_]|Q],[S|St],Result) :-
removeSumsToSomeUniqueProducts(Q,[S|St],Result).
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
% Remove duplicate Sums
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
removeSDupes([],Result,Result).
removeSDupes([[_,_,S,_],[X2,Y2,S,P2],[X3,Y3,S,P3]|T],L,Result) :-
removeSDupes([[X2,Y2,S,P2],[X3,Y3,S,P3]|T],L,Result),!.
removeSDupes([[_,_,S,_],[_,_,S,_],[X3,Y3,S3,P3]|T],L,Result) :-
S\=S3,
removeSDupes([[X3,Y3,S3,P3]|T], L,Result),!.
removeSDupes([[X,Y,S,P],[X2,Y2,S2,P2],[X3,Y3,S3,P3]|T],L,Result) :-
S\=S2,S2\=S3,S\=S3,
removeSDupes([[X3,Y3,S3,P3]|T],[[X,Y,S,P],[X2,Y2,S2,P2]|L],Result),!.
removeSDupes([[X,Y,S,P],[X2,Y2,S2,P2],[X3,Y3,S3,P2]|T],L,Result) :-
S\=S2,
removeSDupes([[X2,Y2,S2,P2],[X3,Y3,S3,P2]|T],[[X,Y,S,P]|L],Result),!.
removeSDupes([[_,_,S,_],[_,_,S,_]|T],L,Result) :-
removeSDupes(T,L,Result),!.
removeSDupes([[X,Y,S,P],[X2,Y2,S2,P2]|T],L,Result) :-
S\=S2,
removeSDupes([[X2,Y2,S2,P2]|T],[[X,Y,S,P]|L], Result),!.
removeSDupes([[X,Y,S,P]|T],L,Result) :-
removeSDupes(T,[[X,Y,S,P]|L],Result),!.
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
% Make a list of all unique sums
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
getSumsToSomeUniqueProducts([],[]).
getSumsToSomeUniqueProducts([[_,_,S,_]|T],[S|RT]) :-
getSumsToSomeUniqueProducts(T,RT),!.
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
% Parts 1-4 to solve Impossible Puzzle where X and Y are two integers with
% 1 < X < Y and X + Y ≤ 100.
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
s1(Q, Max) :-
s0(2,3,Max,S0),
mergeP(S0,S0Sorted),
removeUniqueP(S0Sorted,_,Q),!.
s2(Q,Max) :-
s1(S1,Max),
mergeS(S1,S1Sorted),
s0(2,3, Max,S0),
mergeP(S0,S0Sorted),
removePDupes(S0Sorted,[],NoPDupes),
mergeS(NoPDupes,NoPDupesSorted),
getSumsToSomeUniqueProducts(NoPDupesSorted,UniqueS),
removeSumsToSomeUniqueProducts(S1Sorted,UniqueS,S2),
mergeP(S2,Q),!.
s3(Q,Max) :-
s2(S2,Max),
removePDupes(S2,[],S2NoPDupes),
mergeS(S2NoPDupes,Q),!.
s4(Q,Max) :-
s3(S3,Max),
removeSDupes(S3,[],Q),!.
/* <END OF THE PROGRAM> */
/* <PROGRAM OUTPUT>
?- consult('DJ357.pl').
true.
?- time(s1(Q,100)).
% 93,780 inferences, 0.094 CPU in 0.107 seconds (88% CPU, 1000320 Lips)
Q =
[[3,4,7,12],[2,6,8,12],[3,6,9,18],[2,9,11,18],[4,5,9,20],[2,10,12,20],[3,8,11,24
],[2,12,14,24],[4,6,10,24],[4,7,11,28],[2,14,16,28],[2,15,17,30],[5,6,11,30],[3,
10,13,30],[4,8,12,32],[2,16,18,32],[3,12,15,36],[4,9,13,36],[2,18,20,36],[5,8,13
,40],[2,20,22,40],[4,10,14,40],[6,7,13,42],[2,21,23,42],[3,14,17,42],[4,11,15,44
],[2,22,24,44],[5,9,14,45],[3,15,18,45],[3,16,19,48],[4,12,16,48],[2,24,26,48],[
6,8,14,48],[2,25,27,50],[5,10,15,50],[4,13,17,52],[2,26,28,52],[2,27,29,54],[6,9
,15,54],[3,18,21,54],[7,8,15,56],[2,28,30,56],[4,14,18,56],[5,12,17,60],[3,20,23
,60],[4,15,19,60],[2,30,32,60],[6,10,16,60],[3,21,24,63],[7,9,16,63],[4,16,20,64
],[2,32,34,64],[6,11,17,66],[3,22,25,66],[2,33,35,66],[4,17,21,68],[2,34,36,68],
[2,35,37,70],[5,14,19,70],[7,10,17,70],[3,24,27,72],[8,9,17,72],[2,36,38,72],[6,
12,18,72],[4,18,22,72],[3,25,28,75],[5,15,20,75],[4,19,23,76],[2,38,40,76],[2,39
,41,78],[6,13,19,78],[3,26,29,78],[5,16,21,80],[2,40,42,80],[4,20,24,80],[8,10,1
8,80],[7,12,19,84],[3,28,31,84],[4,21,25,84],[6,14,20,84],[2,42,44,84],[8,11,19,
88],[2,44,46,88],[4,22,26,88],[6,15,21,90],[2,45,47,90],[3,30,33,90],[5,18,23,90
],[9,10,19,90],[4,23,27,92],[2,46,48,92],[3,32,35,96],[4,24,28,96],[8,12,20,96],
[2,48,50,96],[6,16,22,96],[7,14,21,98],[2,49,51,98],[3,33,36,99],[9,11,20,99],[5
,20,25,100],[4,25,29,100],[2,50,52,100],[2,51,53,102],[3,34,37,102],[6,17,23,102
],[8,13,21,104],[2,52,54,104],[4,26,30,104],[5,21,26,105],[7,15,22,105],[3,35,38
,105],[3,36,39,108],[9,12,21,108],[4,27,31,108],[2,54,56,108],[6,18,24,108],[10,
11,21,110],[2,55,57,110],[5,22,27,110],[7,16,23,112],[4,28,32,112],[2,56,58,112]
,[8,14,22,112],[6,19,25,114],[3,38,41,114],[2,57,59,114],[4,29,33,116],[2,58,60,
116],[9,13,22,117],[3,39,42,117],[8,15,23,120],[3,40,43,120],[5,24,29,120],[6,20
,26,120],[10,12,22,120],[2,60,62,120],[4,30,34,120],[4,31,35,124],[2,62,64,124],
[2,63,65,126],[6,21,27,126],[9,14,23,126],[3,42,45,126],[7,18,25,126],[8,16,24,1
28],[4,32,36,128],[2,64,66,128],[10,13,23,130],[5,26,31,130],[2,65,67,130],[3,44
,47,132],[11,12,23,132],[4,33,37,132],[6,22,28,132],[2,66,68,132],[3,45,48,135],
[9,15,24,135],[5,27,32,135],[8,17,25,136],[2,68,70,136],[4,34,38,136],[6,23,29,1
38],[2,69,71,138],[3,46,49,138],[5,28,33,140],[7,20,27,140],[4,35,39,140],[2,70,
72,140],[10,14,24,140],[3,48,51,144],[9,16,25,144],[6,24,30,144],[2,72,74,144],[
4,36,40,144],[8,18,26,144],[7,21,28,147],[3,49,52,147],[4,37,41,148],[2,74,76,14
8],[2,75,77,150],[10,15,25,150],[5,30,35,150],[6,25,31,150],[3,50,53,150],[8,19,
27,152],[2,76,78,152],[4,38,42,152],[9,17,26,153],[3,51,54,153],[2,77,79,154],[1
1,14,25,154],[7,22,29,154],[4,39,43,156],[3,52,55,156],[12,13,25,156],[2,78,80,1
56],[6,26,32,156],[5,32,37,160],[4,40,44,160],[2,80,82,160],[10,16,26,160],[8,20
,28,160],[6,27,33,162],[3,54,57,162],[2,81,83,162],[9,18,27,162],[4,41,45,164],[
2,82,84,164],[5,33,38,165],[3,55,58,165],[11,15,26,165],[3,56,59,168],[7,24,31,1
68],[8,21,29,168],[2,84,86,168],[6,28,34,168],[4,42,46,168],[12,14,26,168],[2,85
,87,170],[5,34,39,170],[10,17,27,170],[3,57,60,171],[9,19,28,171],[4,43,47,172],
[2,86,88,172],[2,87,89,174],[6,29,35,174],[3,58,61,174],[7,25,32,175],[5,35,40,1
75],[11,16,27,176],[4,44,48,176],[2,88,90,176],[8,22,30,176],[9,20,29,180],[12,1
5,27,180],[3,60,63,180],[5,36,41,180],[4,45,49,180],[6,30,36,180],[2,90,92,180],
[10,18,28,180],[2,91,93,182],[13,14,27,182],[7,26,33,182],[8,23,31,184],[2,92,94
,184],[4,46,50,184],[6,31,37,186],[3,62,65,186],[2,93,95,186],[4,47,51,188],[2,9
4,96,188],[9,21,30,189],[3,63,66,189],[7,27,34,189],[10,19,29,190],[2,95,97,190]
,[5,38,43,190],[3,64,67,192],[8,24,32,192],[12,16,28,192],[4,48,52,192],[6,32,38
,192],[2,96,98,192],[3,65,68,195],[13,15,28,195],[5,39,44,195],[7,28,35,196],[4,
49,53,196],[2,98,100,196],[9,22,31,198],[6,33,39,198],[11,18,29,198],[3,66,69,19
8],[5,40,45,200],[8,25,33,200],[10,20,30,200],[4,50,54,200],[3,68,71,204],[4,51,
55,204],[12,17,29,204],[6,34,40,204],[3,69,72,207],[9,23,32,207],[13,16,29,208],
[4,52,56,208],[8,26,34,208],[6,35,41,210],[14,15,29,210],[3,70,73,210],[7,30,37,
210],[10,21,31,210],[5,42,47,210],[9,24,33,216],[3,72,75,216],[8,27,35,216],[6,3
6,42,216],[12,18,30,216],[4,54,58,216],[5,44,49,220],[11,20,31,220],[4,55,59,220
],[10,22,32,220],[6,37,43,222],[3,74,77,222],[7,32,39,224],[4,56,60,224],[8,28,3
6,224],[14,16,30,224],[5,45,50,225],[9,25,34,225],[3,75,78,225],[3,76,79,228],[1
2,19,31,228],[4,57,61,228],[6,38,44,228],[10,23,33,230],[5,46,51,230],[11,21,32,
231],[3,77,80,231],[7,33,40,231],[8,29,37,232],[4,58,62,232],[6,39,45,234],[3,78
,81,234],[9,26,35,234],[13,18,31,234],[7,34,41,238],[14,17,31,238],[15,16,31,240
],[5,48,53,240],[3,80,83,240],[6,40,46,240],[10,24,34,240],[4,60,64,240],[12,20,
32,240],[8,30,38,240],[3,81,84,243],[9,27,36,243],[5,49,54,245],[7,35,42,245],[6
,41,47,246],[3,82,85,246],[8,31,39,248],[4,62,66,248],[5,50,55,250],[10,25,35,25
0],[3,84,87,252],[9,28,37,252],[7,36,43,252],[4,63,67,252],[12,21,33,252],[6,42,
48,252],[14,18,32,252],[3,85,88,255],[15,17,32,255],[5,51,56,255],[8,32,40,256],
[4,64,68,256],[6,43,49,258],[3,86,89,258],[5,52,57,260],[13,20,33,260],[4,65,69,
260],[10,26,36,260],[9,29,38,261],[3,87,90,261],[11,24,35,264],[3,88,91,264],[8,
33,41,264],[6,44,50,264],[4,66,70,264],[12,22,34,264],[14,19,33,266],[7,38,45,26
6],[10,27,37,270],[9,30,39,270],[5,54,59,270],[6,45,51,270],[15,18,33,270],[3,90
,93,270],[16,17,33,272],[4,68,72,272],[8,34,42,272],[13,21,34,273],[7,39,46,273]
,[3,91,94,273],[11,25,36,275],[5,55,60,275],[12,23,35,276],[3,92,95,276],[4,69,7
3,276],[6,46,52,276],[3,93,96,279],[9,31,40,279],[5,56,61,280],[7,40,47,280],[8,
35,43,280],[14,20,34,280],[10,28,38,280],[4,70,74,280],[6,47,53,282],[3,94,97,28
2],[5,57,62,285],[3,95,98,285],[15,19,34,285],[13,22,35,286],[11,26,37,286],[9,3
2,41,288],[3,96,99,288],[4,72,76,288],[12,24,36,288],[6,48,54,288],[8,36,44,288]
,[16,18,34,288],[10,29,39,290],[5,58,63,290],[14,21,35,294],[7,42,49,294],[6,49,
55,294],[8,37,45,296],[4,74,78,296],[9,33,42,297],[11,27,38,297],[5,60,65,300],[
15,20,35,300],[4,75,79,300],[12,25,37,300],[10,30,40,300],[6,50,56,300],[16,19,3
5,304],[4,76,80,304],[8,38,46,304],[6,51,57,306],[9,34,43,306],[17,18,35,306],[7
,44,51,308],[11,28,39,308],[4,77,81,308],[14,22,36,308],[10,31,41,310],[5,62,67,
310],[8,39,47,312],[13,24,37,312],[6,52,58,312],[12,26,38,312],[4,78,82,312],[7,
45,52,315],[15,21,36,315],[5,63,68,315],[9,35,44,315],[5,64,69,320],[8,40,48,320
],[4,80,84,320],[16,20,36,320],[10,32,42,320],[14,23,37,322],[7,46,53,322],[9,36
,45,324],[12,27,39,324],[4,81,85,324],[6,54,60,324],[5,65,70,325],[13,25,38,325]
,[8,41,49,328],[4,82,86,328],[6,55,61,330],[15,22,37,330],[11,30,41,330],[5,66,7
1,330],[10,33,43,330],[7,48,55,336],[16,21,37,336],[14,24,38,336],[6,56,62,336],
[12,28,40,336],[4,84,88,336],[8,42,50,336],[17,20,37,340],[5,68,73,340],[4,85,89
,340],[10,34,44,340],[18,19,37,342],[9,38,47,342],[6,57,63,342],[8,43,51,344],[4
,86,90,344],[5,69,74,345],[15,23,38,345],[4,87,91,348],[12,29,41,348],[6,58,64,3
48],[10,35,45,350],[5,70,75,350],[14,25,39,350],[7,50,57,350],[9,39,48,351],[13,
27,40,351],[11,32,43,352],[4,88,92,352],[8,44,52,352],[16,22,38,352],[17,21,38,3
57],[7,51,58,357],[9,40,49,360],[15,24,39,360],[5,72,77,360],[8,45,53,360],[10,3
6,46,360],[18,20,38,360],[6,60,66,360],[4,90,94,360],[12,30,42,360],[13,28,41,36
4],[7,52,59,364],[4,91,95,364],[14,26,40,364],[16,23,39,368],[4,92,96,368],[8,46
,54,368],[10,37,47,370],[5,74,79,370],[12,31,43,372],[4,93,97,372],[6,62,68,372]
,[17,22,39,374],[11,34,45,374],[15,25,40,375],[5,75,80,375],[8,47,55,376],[4,94,
98,376],[14,27,41,378],[6,63,69,378],[18,21,39,378],[7,54,61,378],[9,42,51,378],
[5,76,81,380],[19,20,39,380],[4,95,99,380],[10,38,48,380],[16,24,40,384],[8,48,5
6,384],[4,96,100,384],[12,32,44,384],[6,64,70,384],[5,77,82,385],[7,55,62,385],[
11,35,46,385],[10,39,49,390],[13,30,43,390],[5,78,83,390],[15,26,41,390],[6,65,7
1,390],[7,56,63,392],[8,49,57,392],[14,28,42,392],[11,36,47,396],[9,44,53,396],[
12,33,45,396],[18,22,40,396],[6,66,72,396],[19,21,40,399],[7,57,64,399],[5,80,85
,400],[16,25,41,400],[10,40,50,400],[8,50,58,400],[9,45,54,405],[5,81,86,405],[1
5,27,42,405],[14,29,43,406],[7,58,65,406],[17,24,41,408],[8,51,59,408],[6,68,74,
408],[12,34,46,408],[5,82,87,410],[10,41,51,410],[18,23,41,414],[6,69,75,414],[9
,46,55,414],[13,32,45,416],[8,52,60,416],[16,26,42,416],[19,22,41,418],[11,38,49
,418],[7,60,67,420],[15,28,43,420],[5,84,89,420],[12,35,47,420],[20,21,41,420],[
6,70,76,420],[14,30,44,420],[10,42,52,420],[5,85,90,425],[17,25,42,425],[13,33,4
6,429],[11,39,50,429],[10,43,53,430],[5,86,91,430],[16,27,43,432],[9,48,57,432],
[18,24,42,432],[6,72,78,432],[12,36,48,432],[8,54,62,432],[14,31,45,434],[7,62,6
9,434],[15,29,44,435],[5,87,92,435],[8,55,63,440],[11,40,51,440],[5,88,93,440],[
10,44,54,440],[20,22,42,440],[9,49,58,441],[7,63,70,441],[13,34,47,442],[17,26,4
3,442],[12,37,49,444],[6,74,80,444],[7,64,71,448],[8,56,64,448],[16,28,44,448],[
14,32,46,448],[6,75,81,450],[15,30,45,450],[10,45,55,450],[18,25,43,450],[5,90,9
5,450],[9,50,59,450],[7,65,72,455],[13,35,48,455],[5,91,96,455],[19,24,43,456],[
8,57,65,456],[6,76,82,456],[12,38,50,456],[17,27,44,459],[9,51,60,459],[20,23,43
,460],[5,92,97,460],[10,46,56,460],[21,22,43,462],[6,77,83,462],[7,66,73,462],[1
1,42,53,462],[14,33,47,462],[16,29,45,464],[8,58,66,464],[5,93,98,465],[15,31,46
,465],[12,39,51,468],[9,52,61,468],[13,36,49,468],[6,78,84,468],[18,26,44,468],[
10,47,57,470],[5,94,99,470],[19,25,44,475],[5,95,100,475],[7,68,75,476],[17,28,4
5,476],[14,34,48,476],[15,32,47,480],[12,40,52,480],[20,24,44,480],[8,60,68,480]
,[10,48,58,480],[6,80,86,480],[16,30,46,480],[7,69,76,483],[21,23,44,483],[18,27
,45,486],[9,54,63,486],[6,81,87,486],[14,35,49,490],[7,70,77,490],[10,49,59,490]
,[12,41,53,492],[6,82,88,492],[13,38,51,494],[19,26,45,494],[11,45,56,495],[15,3
3,48,495],[9,55,64,495],[16,31,47,496],[8,62,70,496],[20,25,45,500],[10,50,60,50
0],[8,63,71,504],[9,56,65,504],[7,72,79,504],[21,24,45,504],[6,84,90,504],[14,36
,50,504],[18,28,46,504],[12,42,54,504],[22,23,45,506],[11,46,57,506],[10,51,61,5
10],[6,85,91,510],[17,30,47,510],[15,34,49,510],[16,32,48,512],[8,64,72,512],[9,
57,66,513],[19,27,46,513],[12,43,55,516],[6,86,92,516],[14,37,51,518],[7,74,81,5
18],[13,40,53,520],[8,65,73,520],[10,52,62,520],[20,26,46,520],[6,87,93,522],[18
,29,47,522],[9,58,67,522],[21,25,46,525],[15,35,50,525],[7,75,82,525],[11,48,59,
528],[16,33,49,528],[22,24,46,528],[12,44,56,528],[6,88,94,528],[8,66,74,528],[7
,76,83,532],[19,28,47,532],[14,38,52,532],[7,77,84,539],[11,49,60,539],[9,60,69,
540],[15,36,51,540],[20,27,47,540],[12,45,57,540],[10,54,64,540],[18,30,48,540],
[6,90,96,540],[17,32,49,544],[8,68,76,544],[16,34,50,544],[6,91,97,546],[14,39,5
3,546],[7,78,85,546],[21,26,47,546],[13,42,55,546],[10,55,65,550],[22,25,47,550]
,[11,50,61,550],[23,24,47,552],[8,69,77,552],[6,92,98,552],[12,46,58,552],[18,31
,49,558],[6,93,99,558],[9,62,71,558],[7,80,87,560],[16,35,51,560],[14,40,54,560]
,[20,28,48,560],[10,56,66,560],[8,70,78,560],[17,33,50,561],[11,51,62,561],[12,4
7,59,564],[6,94,100,564],[7,81,88,567],[9,63,72,567],[21,27,48,567],[15,38,53,57
0],[19,30,49,570],[10,57,67,570],[11,52,63,572],[13,44,57,572],[22,26,48,572],[1
4,41,55,574],[7,82,89,574],[9,64,73,576],[8,72,80,576],[12,48,60,576],[18,32,50,
576],[16,36,52,576],[20,29,49,580],[10,58,68,580],[13,45,58,585],[9,65,74,585],[
15,39,54,585],[21,28,49,588],[7,84,91,588],[12,49,61,588],[14,42,56,588],[16,37,
53,592],[8,74,82,592],[22,27,49,594],[11,54,65,594],[9,66,75,594],[18,33,51,594]
,[7,85,92,595],[17,35,52,595],[13,46,59,598],[23,26,49,598],[8,75,83,600],[15,40
,55,600],[24,25,49,600],[10,60,70,600],[12,50,62,600],[20,30,50,600],[14,43,57,6
02],[7,86,93,602],[19,32,51,608],[8,76,84,608],[16,38,54,608],[21,29,50,609],[7,
87,94,609],[17,36,53,612],[9,68,77,612],[12,51,63,612],[18,34,52,612],[11,56,67,
616],[7,88,95,616],[8,77,85,616],[22,28,50,616],[14,44,58,616],[20,31,51,620],[1
0,62,72,620],[9,69,78,621],[23,27,50,621],[16,39,55,624],[13,48,61,624],[12,52,6
4,624],[24,26,50,624],[8,78,86,624],[11,57,68,627],[19,33,52,627],[18,35,53,630]
,[10,63,73,630],[21,30,51,630],[9,70,79,630],[14,45,59,630],[7,90,97,630],[15,42
,57,630],[13,49,62,637],[7,91,98,637],[22,29,51,638],[11,58,69,638],[16,40,56,64
0],[8,80,88,640],[20,32,52,640],[10,64,74,640],[23,28,51,644],[7,92,99,644],[14,
46,60,644],[17,38,55,646],[19,34,53,646],[9,72,81,648],[24,27,51,648],[8,81,89,6
48],[18,36,54,648],[12,54,66,648],[25,26,51,650],[13,50,63,650],[10,65,75,650],[
7,93,100,651],[21,31,52,651],[16,41,57,656],[8,82,90,656],[15,44,59,660],[12,55,
67,660],[11,60,71,660],[20,33,53,660],[22,30,52,660],[10,66,76,660],[17,39,56,66
3],[13,51,64,663],[18,37,55,666],[9,74,83,666],[21,32,53,672],[12,56,68,672],[24
,28,52,672],[8,84,92,672],[14,48,62,672],[16,42,58,672],[15,45,60,675],[25,27,52
,675],[9,75,84,675],[17,40,57,680],[8,85,93,680],[10,68,78,680],[20,34,54,680],[
22,31,53,682],[11,62,73,682],[19,36,55,684],[9,76,85,684],[12,57,69,684],[18,38,
56,684],[16,43,59,688],[8,86,94,688],[10,69,79,690],[23,30,53,690],[15,46,61,690
],[9,77,86,693],[21,33,54,693],[11,63,74,693],[8,87,95,696],[24,29,53,696],[12,5
8,70,696],[25,28,53,700],[20,35,55,700],[10,70,80,700],[14,50,64,700],[26,27,53,
702],[18,39,57,702],[13,54,67,702],[9,78,87,702],[11,64,75,704],[8,88,96,704],[1
6,44,60,704],[22,32,54,704],[14,51,65,714],[17,42,59,714],[21,34,55,714],[11,65,
76,715],[13,55,68,715],[15,48,63,720],[9,80,89,720],[16,45,61,720],[10,72,82,720
],[18,40,58,720],[12,60,72,720],[20,36,56,720],[8,90,98,720],[24,30,54,720],[22,
33,55,726],[11,66,77,726],[8,91,99,728],[13,56,69,728],[14,52,66,728],[26,28,54,
728],[15,49,64,735],[21,35,56,735],[23,32,55,736],[8,92,100,736],[16,46,62,736],
[18,41,59,738],[9,82,91,738],[20,37,57,740],[10,74,84,740],[13,57,70,741],[19,39
,58,741],[24,31,55,744],[12,62,74,744],[11,68,79,748],[17,44,61,748],[22,34,56,7
48],[10,75,85,750],[25,30,55,750],[15,50,65,750],[26,29,55,754],[13,58,71,754],[
9,84,93,756],[27,28,55,756],[12,63,75,756],[21,36,57,756],[14,54,68,756],[18,42,
60,756],[11,69,80,759],[23,33,56,759],[19,40,59,760],[10,76,86,760],[20,38,58,76
0],[9,85,94,765],[17,45,62,765],[15,51,66,765],[16,48,64,768],[12,64,76,768],[24
,32,56,768],[22,35,57,770],[14,55,69,770],[11,70,81,770],[10,77,87,770],[18,43,6
1,774],[9,86,95,774],[20,39,59,780],[13,60,73,780],[15,52,67,780],[12,65,77,780]
,[10,78,88,780],[26,30,56,780],[17,46,63,782],[23,34,57,782],[27,29,56,783],[9,8
7,96,783],[16,49,65,784],[14,56,70,784],[9,88,97,792],[11,72,83,792],[24,33,57,7
92],[22,36,58,792],[18,44,62,792],[12,66,78,792],[21,38,59,798],[14,57,71,798],[
19,42,61,798],[25,32,57,800],[20,40,60,800],[10,80,90,800],[16,50,66,800],[26,31
,57,806],[13,62,75,806],[27,30,57,810],[18,45,63,810],[15,54,69,810],[9,90,99,81
0],[10,81,91,810],[28,29,57,812],[14,58,72,812],[22,37,59,814],[11,74,85,814],[1
6,51,67,816],[17,48,65,816],[12,68,80,816],[24,34,58,816],[13,63,76,819],[21,39,
60,819],[9,91,100,819],[20,41,61,820],[10,82,92,820],[25,33,58,825],[15,55,70,82
5],[11,75,86,825],[23,36,59,828],[12,69,81,828],[18,46,64,828],[13,64,77,832],[1
6,52,68,832],[26,32,58,832],[19,44,63,836],[11,76,87,836],[22,38,60,836],[15,56,
71,840],[21,40,61,840],[24,35,59,840],[10,84,94,840],[14,60,74,840],[20,42,62,84
0],[28,30,58,840],[12,70,82,840],[10,85,95,850],[25,34,59,850],[17,50,67,850],[1
9,45,64,855],[15,57,72,855],[22,39,61,858],[11,78,89,858],[13,66,79,858],[26,33,
59,858],[20,43,63,860],[10,86,96,860],[27,32,59,864],[12,72,84,864],[18,48,66,86
4],[24,36,60,864],[16,54,70,864],[28,31,59,868],[14,62,76,868],[10,87,97,870],[2
9,30,59,870],[15,58,73,870],[23,38,61,874],[19,46,65,874],[16,55,71,880],[11,80,
91,880],[20,44,64,880],[22,40,62,880],[10,88,98,880],[14,63,77,882],[18,49,67,88
2],[21,42,63,882],[17,52,69,884],[13,68,81,884],[26,34,60,884],[24,37,61,888],[1
2,74,86,888],[27,33,60,891],[11,81,92,891],[16,56,72,896],[28,32,60,896],[14,64,
78,896],[13,69,82,897],[23,39,62,897],[25,36,61,900],[15,60,75,900],[12,75,87,90
0],[20,45,65,900],[10,90,100,900],[18,50,68,900],[22,41,63,902],[11,82,93,902],[
26,35,61,910],[13,70,83,910],[14,65,79,910],[19,48,67,912],[16,57,73,912],[12,76
,88,912],[24,38,62,912],[18,51,69,918],[17,54,71,918],[27,34,61,918],[23,40,63,9
20],[20,46,66,920],[11,84,95,924],[21,44,65,924],[28,33,61,924],[12,77,89,924],[
22,42,64,924],[14,66,80,924],[29,32,61,928],[16,58,74,928],[30,31,61,930],[15,62
,77,930],[11,85,96,935],[17,55,72,935],[24,39,63,936],[13,72,85,936],[26,36,62,9
36],[18,52,70,936],[12,78,90,936],[21,45,66,945],[15,63,78,945],[27,35,62,945],[
22,43,65,946],[11,86,97,946],[25,38,63,950],[19,50,69,950],[17,56,73,952],[14,68
,82,952],[28,34,62,952],[29,33,62,957],[11,87,98,957],[15,64,79,960],[24,40,64,9
60],[20,48,68,960],[12,80,92,960],[16,60,76,960],[30,32,62,960],[26,37,63,962],[
13,74,87,962],[21,46,67,966],[14,69,83,966],[23,42,65,966],[11,88,99,968],[22,44
,66,968],[17,57,74,969],[19,51,70,969],[27,36,63,972],[12,81,93,972],[18,54,72,9
72],[15,65,80,975],[25,39,64,975],[13,75,88,975],[28,35,63,980],[20,49,69,980],[
14,70,84,980],[24,41,65,984],[12,82,94,984],[29,34,63,986],[17,58,75,986],[19,52
,71,988],[13,76,89,988],[26,38,64,988],[18,55,73,990],[22,45,67,990],[15,66,81,9
90],[30,33,63,990],[31,32,63,992],[16,62,78,992],[25,40,65,1000],[20,50,70,1000]
,[16,63,79,1008],[21,48,69,1008],[14,72,86,1008],[18,56,74,1008],[12,84,96,1008]
,[28,36,64,1008],[24,42,66,1008],[23,44,67,1012],[22,46,68,1012],[26,39,65,1014]
,[13,78,91,1014],[15,68,83,1020],[17,60,77,1020],[20,51,71,1020],[12,85,97,1020]
,[30,34,64,1020],[27,38,65,1026],[19,54,73,1026],[18,57,75,1026],[24,43,67,1032]
,[12,86,98,1032],[23,45,68,1035],[15,69,84,1035],[28,37,65,1036],[14,74,88,1036]
,[13,80,93,1040],[16,65,81,1040],[26,40,66,1040],[20,52,72,1040],[12,87,99,1044]
,[29,36,65,1044],[18,58,76,1044],[30,35,65,1050],[14,75,89,1050],[15,70,85,1050]
,[21,50,71,1050],[25,42,67,1050],[13,81,94,1053],[27,39,66,1053],[17,62,79,1054]
,[31,34,65,1054],[32,33,65,1056],[12,88,100,1056],[24,44,68,1056],[22,48,70,1056
],[16,66,82,1056],[19,56,75,1064],[14,76,90,1064],[28,38,66,1064],[26,41,67,1066
],[13,82,95,1066],[17,63,80,1071],[21,51,72,1071],[14,77,91,1078],[22,49,71,1078
],[27,40,67,1080],[15,72,87,1080],[24,45,69,1080],[30,36,66,1080],[18,60,78,1080
],[20,54,74,1080],[17,64,81,1088],[16,68,84,1088],[32,34,66,1088],[28,39,67,1092
],[21,52,73,1092],[13,84,97,1092],[14,78,92,1092],[26,42,68,1092],[20,55,75,1100
],[25,44,69,1100],[22,50,72,1100],[29,38,67,1102],[19,58,77,1102],[23,48,71,1104
],[16,69,85,1104],[24,46,70,1104],[13,85,98,1105],[17,65,82,1105],[30,37,67,1110
],[15,74,89,1110],[31,36,67,1116],[18,62,80,1116],[26,43,69,1118],[13,86,99,1118
],[32,35,67,1120],[28,40,68,1120],[20,56,76,1120],[14,80,94,1120],[16,70,86,1120
],[22,51,73,1122],[17,66,83,1122],[33,34,67,1122],[25,45,70,1125],[15,75,90,1125
],[29,39,68,1131],[13,87,100,1131],[18,63,81,1134],[21,54,75,1134],[27,42,69,113
4],[14,81,95,1134],[15,76,91,1140],[19,60,79,1140],[20,57,77,1140],[30,38,68,114
0],[22,52,74,1144],[26,44,70,1144],[28,41,69,1148],[14,82,96,1148],[25,46,71,115
0],[23,50,73,1150],[16,72,88,1152],[24,48,72,1152],[32,36,68,1152],[18,64,82,115
2],[15,77,92,1155],[21,55,76,1155],[33,35,68,1155],[29,40,69,1160],[20,58,78,116
0],[30,39,69,1170],[15,78,93,1170],[26,45,71,1170],[18,65,83,1170],[17,69,86,117
3],[23,51,74,1173],[21,56,77,1176],[24,49,73,1176],[14,84,98,1176],[28,42,70,117
6],[31,38,69,1178],[19,62,81,1178],[32,37,69,1184],[16,74,90,1184],[33,36,69,118
8],[27,44,71,1188],[22,54,76,1188],[18,66,84,1188],[34,35,69,1190],[17,70,87,119
0],[14,85,99,1190],[23,52,75,1196],[26,46,72,1196],[21,57,78,1197],[19,63,82,119
7],[15,80,95,1200],[16,75,91,1200],[25,48,73,1200],[30,40,70,1200],[20,60,80,120
0],[24,50,74,1200],[28,43,71,1204],[14,86,100,1204],[27,45,72,1215],[15,81,96,12
15],[19,64,83,1216],[16,76,92,1216],[32,38,70,1216],[29,42,71,1218],[21,58,79,12
18],[17,72,89,1224],[24,51,75,1224],[18,68,86,1224],[34,36,70,1224],[15,82,97,12
30],[30,41,71,1230],[16,77,93,1232],[28,44,72,1232],[22,56,78,1232],[31,40,71,12
40],[20,62,82,1240],[18,69,87,1242],[27,46,73,1242],[23,54,77,1242],[32,39,71,12
48],[24,52,76,1248],[26,48,74,1248],[16,78,94,1248],[33,38,71,1254],[22,57,79,12
54],[19,66,85,1254],[34,37,71,1258],[17,74,91,1258],[35,36,71,1260],[21,60,81,12
60],[15,84,99,1260],[20,63,83,1260],[28,45,73,1260],[18,70,88,1260],[30,42,72,12
60],[15,85,100,1275],[17,75,92,1275],[25,51,76,1275],[29,44,73,1276],[22,58,80,1
276],[32,40,72,1280],[16,80,96,1280],[20,64,84,1280],[23,56,79,1288],[28,46,74,1
288],[19,68,87,1292],[17,76,93,1292],[34,38,72,1292],[27,48,75,1296],[16,81,97,1
296],[18,72,90,1296],[24,54,78,1296],[25,52,77,1300],[20,65,85,1300],[26,50,76,1
300],[21,62,83,1302],[31,42,73,1302],[19,69,88,1311],[23,57,80,1311],[32,41,73,1
312],[16,82,98,1312],[24,55,79,1320],[33,40,73,1320],[22,60,82,1320],[30,44,74,1
320],[20,66,86,1320],[27,49,76,1323],[21,63,84,1323],[26,51,77,1326],[34,39,73,1
326],[17,78,95,1326],[19,70,89,1330],[35,38,73,1330],[36,37,73,1332],[18,74,92,1
332],[29,46,75,1334],[23,58,81,1334],[21,64,85,1344],[24,56,80,1344],[28,48,76,1
344],[16,84,100,1344],[32,42,74,1344],[18,75,93,1350],[25,54,79,1350],[30,45,75,
1350],[27,50,77,1350],[17,80,97,1360],[34,40,74,1360],[20,68,88,1360],[31,44,75,
1364],[22,62,84,1364],[21,65,86,1365],[35,39,74,1365],[19,72,91,1368],[24,57,81,
1368],[18,76,94,1368],[36,38,74,1368],[17,81,98,1377],[27,51,78,1377],[23,60,83,
1380],[20,69,89,1380],[30,46,76,1380],[22,63,85,1386],[18,77,95,1386],[33,42,75,
1386],[21,66,87,1386],[29,48,77,1392],[24,58,82,1392],[34,41,75,1394],[17,82,99,
1394],[35,40,75,1400],[25,56,81,1400],[28,50,78,1400],[20,70,90,1400],[27,52,79,
1404],[36,39,75,1404],[26,54,80,1404],[18,78,96,1404],[37,38,75,1406],[19,74,93,
1406],[32,44,76,1408],[22,64,86,1408],[25,57,82,1425],[19,75,94,1425],[31,46,77,
1426],[23,62,85,1426],[21,68,89,1428],[28,51,79,1428],[34,42,76,1428],[26,55,81,
1430],[22,65,87,1430],[32,45,77,1440],[20,72,92,1440],[36,40,76,1440],[24,60,84,
1440],[18,80,98,1440],[30,48,78,1440],[21,69,90,1449],[23,63,86,1449],[25,58,83,
1450],[29,50,79,1450],[33,44,77,1452],[22,66,88,1452],[26,56,82,1456],[28,52,80,
1456],[27,54,81,1458],[18,81,99,1458],[21,70,91,1470],[35,42,77,1470],[30,49,79,
1470],[23,64,87,1472],[32,46,78,1472],[36,41,77,1476],[18,82,100,1476],[37,40,77
,1480],[20,74,94,1480],[38,39,77,1482],[19,78,97,1482],[26,57,83,1482],[33,45,78
,1485],[27,55,82,1485],[31,48,79,1488],[24,62,86,1488],[22,68,90,1496],[34,44,78
,1496],[25,60,85,1500],[20,75,95,1500],[30,50,80,1500],[29,52,81,1508],[26,58,84
,1508],[24,63,87,1512],[27,56,83,1512],[21,72,93,1512],[36,42,78,1512],[28,54,82
,1512],[22,69,91,1518],[33,46,79,1518],[23,66,89,1518],[19,80,99,1520],[20,76,96
,1520],[38,40,78,1520],[30,51,81,1530],[34,45,79,1530],[32,48,80,1536],[24,64,88
,1536],[27,57,84,1539],[19,81,100,1539],[28,55,83,1540],[35,44,79,1540],[20,77,9
7,1540],[22,70,92,1540],[25,62,87,1550],[31,50,81,1550],[37,42,79,1554],[21,74,9
5,1554],[39,40,79,1560],[24,65,89,1560],[30,52,82,1560],[26,60,86,1560],[20,78,9
8,1560],[23,68,91,1564],[34,46,80,1564],[29,54,83,1566],[27,58,85,1566],[32,49,8
1,1568],[28,56,84,1568],[35,45,80,1575],[25,63,88,1575],[21,75,96,1575],[33,48,8
1,1584],[36,44,80,1584],[22,72,94,1584],[24,66,90,1584],[21,76,97,1596],[28,57,8
5,1596],[38,42,80,1596],[25,64,89,1600],[20,80,100,1600],[32,50,82,1600],[35,46,
81,1610],[23,70,93,1610],[31,52,83,1612],[26,62,88,1612],[21,77,98,1617],[33,49,
82,1617],[27,60,87,1620],[36,45,81,1620],[30,54,84,1620],[29,56,85,1624],[28,58,
86,1624],[37,44,81,1628],[22,74,96,1628],[32,51,83,1632],[34,48,82,1632],[24,68,
92,1632],[26,63,89,1638],[21,78,99,1638],[39,42,81,1638],[22,75,97,1650],[30,55,
85,1650],[33,50,83,1650],[25,66,91,1650],[23,72,95,1656],[24,69,93,1656],[36,46,
82,1656],[32,52,84,1664],[26,64,90,1664],[38,44,82,1672],[22,76,98,1672],[31,54,
85,1674],[27,62,89,1674],[35,48,83,1680],[30,56,86,1680],[28,60,88,1680],[40,42,
82,1680],[24,70,94,1680],[25,68,93,1700],[34,50,84,1700],[37,46,83,1702],[23,74,
97,1702],[38,45,83,1710],[30,57,87,1710],[33,52,85,1716],[39,44,83,1716],[22,78,
100,1716],[26,66,92,1716],[25,69,94,1725],[23,75,98,1725],[27,64,91,1728],[24,72
,96,1728],[36,48,84,1728],[32,54,86,1728],[31,56,87,1736],[28,62,90,1736],[29,60
,89,1740],[30,58,88,1740],[23,76,99,1748],[38,46,84,1748],[25,70,95,1750],[35,50
,85,1750],[39,45,84,1755],[27,65,92,1755],[32,55,87,1760],[40,44,84,1760],[28,63
,91,1764],[36,49,85,1764],[26,68,94,1768],[34,52,86,1768],[37,48,85,1776],[24,74
,98,1776],[33,54,87,1782],[27,66,93,1782],[32,56,88,1792],[28,64,92,1792],[26,69
,95,1794],[39,46,85,1794],[29,62,91,1798],[31,58,89,1798],[24,75,99,1800],[25,72
,97,1800],[40,45,85,1800],[30,60,90,1800],[36,50,86,1800],[35,52,87,1820],[28,65
,93,1820],[26,70,96,1820],[32,57,89,1824],[24,76,100,1824],[38,48,86,1824],[27,6
8,95,1836],[36,51,87,1836],[34,54,88,1836],[33,56,89,1848],[42,44,86,1848],[28,6
6,94,1848],[37,50,87,1850],[25,74,99,1850],[29,64,93,1856],[32,58,90,1856],[31,6
0,91,1860],[30,62,92,1860],[39,48,87,1872],[26,72,98,1872],[36,52,88,1872],[30,6
3,93,1890],[35,54,89,1890],[27,70,97,1890],[42,45,87,1890],[34,56,90,1904],[28,6
8,96,1904],[29,66,95,1914],[33,58,91,1914],[40,48,88,1920],[32,60,92,1920],[30,6
4,94,1920],[37,52,89,1924],[26,74,100,1924],[28,69,97,1932],[42,46,88,1932],[38,
51,89,1938],[34,57,91,1938],[27,72,99,1944],[36,54,90,1944],[39,50,89,1950],[30,
65,95,1950],[35,56,91,1960],[40,49,89,1960],[28,70,98,1960],[29,68,97,1972],[34,
58,92,1972],[36,55,91,1980],[33,60,93,1980],[44,45,89,1980],[30,66,96,1980],[31,
64,95,1984],[32,62,94,1984],[32,63,95,2016],[28,72,100,2016],[36,56,92,2016],[42
,48,90,2016],[29,70,99,2030],[35,58,93,2030],[40,51,91,2040],[30,68,98,2040],[34
,60,94,2040],[33,62,95,2046],[31,66,97,2046],[36,57,93,2052],[38,54,92,2052],[45
,46,91,2070],[30,69,99,2070],[32,65,97,2080],[40,52,92,2080],[35,60,95,2100],[30
,70,100,2100],[42,50,92,2100],[31,68,99,2108],[34,62,96,2108],[33,64,97,2112],[4
4,48,92,2112],[32,66,98,2112],[42,51,93,2142],[34,63,97,2142],[33,65,98,2145],[3
9,55,94,2145],[45,48,93,2160],[36,60,96,2160],[40,54,94,2160],[34,64,98,2176],[3
2,68,100,2176],[39,56,95,2184],[42,52,94,2184],[40,55,95,2200],[44,50,94,2200],[
45,49,94,2205],[35,63,98,2205],[35,64,99,2240],[40,56,96,2240],[44,51,95,2244],[
34,66,100,2244],[36,63,99,2268],[42,54,96,2268],[40,57,97,2280],[38,60,98,2280],
[39,60,99,2340],[45,52,97,2340],[48,49,97,2352],[42,56,98,2352],[40,60,100,2400]
,[48,50,98,2400]].
?- time(s2(Q,100)).
% 272,349 inferences, 0.250 CPU in 0.258 seconds (97% CPU, 1089396 Lips)
Q =
[[2,9,11,18],[3,8,11,24],[4,7,11,28],[5,6,11,30],[2,15,17,30],[3,14,17,42],[2,21
,23,42],[2,25,27,50],[4,13,17,52],[2,27,29,54],[3,20,23,60],[5,12,17,60],[2,33,3
5,66],[6,11,17,66],[2,35,37,70],[7,10,17,70],[8,9,17,72],[3,24,27,72],[4,19,23,7
6],[3,26,29,78],[2,39,41,78],[2,45,47,90],[5,18,23,90],[4,23,27,92],[3,32,35,96]
,[4,25,29,100],[6,17,23,102],[2,51,53,102],[3,34,37,102],[5,22,27,110],[7,16,23,
112],[3,38,41,114],[8,15,23,120],[5,24,29,120],[4,31,35,124],[6,21,27,126],[9,14
,23,126],[10,13,23,130],[4,33,37,132],[3,44,47,132],[11,12,23,132],[6,23,29,138]
,[7,20,27,140],[4,37,41,148],[5,30,35,150],[3,50,53,150],[8,19,27,152],[7,22,29,
154],[5,32,37,160],[9,18,27,162],[8,21,29,168],[10,17,27,170],[4,43,47,172],[6,2
9,35,174],[11,16,27,176],[5,36,41,180],[9,20,29,180],[12,15,27,180],[13,14,27,18
2],[6,31,37,186],[10,19,29,190],[4,49,53,196],[7,28,35,196],[11,18,29,198],[12,1
7,29,204],[13,16,29,208],[7,30,37,210],[14,15,29,210],[6,35,41,210],[5,42,47,210
],[8,27,35,216],[8,29,37,232],[9,26,35,234],[7,34,41,238],[5,48,53,240],[6,41,47
,246],[10,25,35,250],[9,28,37,252],[11,24,35,264],[8,33,41,264],[10,27,37,270],[
12,23,35,276],[7,40,47,280],[6,47,53,282],[11,26,37,286],[13,22,35,286],[9,32,41
,288],[14,21,35,294],[12,25,37,300],[15,20,35,300],[16,19,35,304],[17,18,35,306]
,[10,31,41,310],[8,39,47,312],[13,24,37,312],[14,23,37,322],[7,46,53,322],[11,30
,41,330],[15,22,37,330],[16,21,37,336],[17,20,37,340],[18,19,37,342],[9,38,47,34
2],[12,29,41,348],[8,45,53,360],[13,28,41,364],[10,37,47,370],[14,27,41,378],[15
,26,41,390],[9,44,53,396],[11,36,47,396],[16,25,41,400],[17,24,41,408],[18,23,41
,414],[19,22,41,418],[12,35,47,420],[20,21,41,420],[10,43,53,430],[13,34,47,442]
,[14,33,47,462],[11,42,53,462],[15,32,47,480],[12,41,53,492],[16,31,47,496],[17,
30,47,510],[13,40,53,520],[18,29,47,522],[19,28,47,532],[20,27,47,540],[14,39,53
,546],[21,26,47,546],[22,25,47,550],[23,24,47,552],[15,38,53,570],[16,37,53,592]
,[17,36,53,612],[18,35,53,630],[19,34,53,646],[20,33,53,660],[21,32,53,672],[22,
31,53,682],[23,30,53,690],[24,29,53,696],[25,28,53,700],[26,27,53,702]].
?- time(s3(Q,100)).
% 274,347 inferences, 0.266 CPU in 0.261 seconds (102% CPU, 1032836 Lips)
Q =
[[2,9,11,18],[3,8,11,24],[4,7,11,28],[4,13,17,52],[7,16,23,112],[10,13,23,130],[
4,19,23,76],[8,19,27,152],[5,22,27,110],[7,20,27,140],[9,18,27,162],[2,25,27,50]
,[13,14,27,182],[4,23,27,92],[11,16,27,176],[10,17,27,170],[2,27,29,54],[10,19,2
9,190],[4,25,29,100],[11,18,29,198],[8,21,29,168],[6,23,29,138],[13,16,29,208],[
7,22,29,154],[12,17,29,204],[4,31,35,124],[14,21,35,294],[12,23,35,276],[17,18,3
5,306],[3,32,35,96],[9,26,35,234],[16,19,35,304],[10,25,35,250],[6,29,35,174],[8
,27,35,216],[5,32,37,160],[8,29,37,232],[16,21,37,336],[6,31,37,186],[9,28,37,25
2],[17,20,37,340],[10,27,37,270],[12,29,41,348],[18,23,41,414],[4,37,41,148],[10
,31,41,310],[14,27,41,378],[7,34,41,238],[16,25,41,400],[13,28,41,364],[3,38,41,
114],[19,22,41,418],[15,26,41,390],[17,24,41,408],[9,32,41,288],[6,41,47,246],[1
5,32,47,480],[22,25,47,550],[4,43,47,172],[16,31,47,496],[19,28,47,532],[18,29,4
7,522],[7,40,47,280],[23,24,47,552],[17,30,47,510],[13,34,47,442],[20,27,47,540]
,[10,37,47,370],[26,27,53,702],[13,40,53,520],[17,36,53,612],[21,32,53,672],[23,
30,53,690],[15,38,53,570],[6,47,53,282],[19,34,53,646],[10,43,53,430],[25,28,53,
700],[8,45,53,360],[18,35,53,630],[22,31,53,682],[12,41,53,492],[24,29,53,696],[
16,37,53,592],[20,33,53,660],[5,48,53,240]].
?- time(s4(Q,100)).
% 274,437 inferences, 0.266 CPU in 0.276 seconds (96% CPU, 1033175 Lips)
Q = [[4,13,17,52]].
?- time(s4(Q,500)).
% 9,897,933 inferences, 10.516 CPU in 10.727 seconds (98% CPU, 941260 Lips)
Q = [[4,13,17,52]].
<END OF PROGRAM OUTPUT>
*/