python3 - <<'EOF'
A=[2,3,4,5,7,9,11,13,16,17,19,23,25,29,31,36,37,41,43,47,49]
N=21
T={}
for i in range(N):
 for j in range(i+1,N):
  d=A[j]-A[i]
  T.setdefault(d*d,[]).append(((1<<i)|(1<<j),i,j))
M={}
p=n=s=q=0
for x in range(1<<N):
 y=x^(x>>1)
 z=y^p
 if z:
  b=(z&-z).bit_length()-1
  v=A[b]
  if y>>b& 1:
   n+=1
   s+=v
   q+=v*v
  else:
   n-=1
   s-=v
   q-=v*v
  p=y
 if n>2:
  u=4*(n*q-s*s)
  d=n*n
  if u%d==0 and u//d in T:
   for pm,i,j in T[u//d]:
    if y&pm==pm and (i,j) not in M:
     M[(i,j)]=(y,n,s,q)
L=sorted(M)
print(len(L))
print(L[:20])
i,j=(2,13)
i,j=A.index(2),A.index(13)
y,n,s,q=M[(i,j)]
X=[A[k] for k in range(N) if y>>k& 1]
print(X,Dval:=(4*(n*q-s*s), n*n))
EOF