concat([],L,L).
concat([A|G],L,[A|R]):-concat(G,L,R).

genere(0,[]):-!.
genere(N,[N|L]):-M is N-1, genere(M,L).

perm([],[]).
perm([X|L],Z):-perm(L,W),insertion(X,W,Z).

insertion(X,L,[X|L]).
insertion(X,[Y|L],[Y|G]):-insertion(X,L,G).

nombremagique(N,M):-M is (N*(N*N+1))//2.


nth([H|_],1,H).
nth([_|L],N,R):-N>0,P is N-1, nth(L,P,R).

accumuler(_,_,_,0,0).
accumuler(L,N,M,P,R):-P>0, S is P-1, nth(L,N,X), 
Next is N+M, accumuler(L,Next,M,S,T), R is T+X.

sommeligne(L,N,I,R):- Init is N*(I-1)+1,accumuler(L, Init, 1, N, R).

sommecolonne(L,N,I,R):-  accumuler(L, I, N, N, R).

testlignes(L,N,V):-auxlignes(L,N,V,1).
auxlignes(_,N,_,K):-K=:=N+1,!.
auxlignes(L,N,V,K):-sommeligne(L,N,K,V), S is K+1,auxlignes(L,N,V,S).


testcolonnes(L,N,V):-auxcolonnes(L,N,V,1).
auxcolonnes(_,N,_,K):-K=:=N+1,!.
auxcolonnes(L,N,V,K):-sommecolonne(L,N,K,V), S is K+1,auxcolonnes(L,N,V,S).

diago(L,N,R):-S is N+1, accumuler(L,1,S,N,R).

adiago(L,N,R):-S is N-1, accumuler(L,N,S,N,R).

carremagique(N,L1):-P is N*N, nombremagique(N,M),genere(P,L),perm(L,L1),
testlignes(L1,N,M),testcolonnes(L1,N,M),diago(L1,N,M),adiago(L1,N,M).