function [gam,fval] = gamlpconj(A)
% exploring |Ag|
% a conjecture
global nstate
nstate=size(A,1);
m = nstate;
h = strict(A);
C = 1+h;

adim = 0;
gdim = m^2;
xdim = gdim;


rind=0;
Aeq = zeros(0,xdim);
Beq = zeros(0,1);

% gamma sum constraint
for i=1:m
  for s=[-1 1]
    rind = rind+1;
    for j=1:m
      cind = coord2ind([i j],[m m]);
      Aing(rind,cind) = s;
    end
    Bing(rind,1) = C;
  end
end

% gamma Lip constraint:
d=1;
for j=1:m
  for i1=1:m
    for i2=i1+1:m
      ind1 = coord2ind([i1 j],[m m]);
      ind2 = coord2ind([i2 j],[m m]);
      for s=[-1 1]
        rind = rind+1;
        Aing(rind,ind1) =  s;
        Aing(rind,ind2) = -s;
        Bing(rind,1) = 2*d;
        %Bing(rind,1) = d*h;
      end
    end
  end
end


% gamma Lip+sum constraint:
for j=1:m
  for i1=1:m
    for i2=i1+1:m
      ind1 = coord2ind([i1 j],[m m]);
      ind2 = coord2ind([i2 j],[m m]);
      for s=[-1 1]
        for is=1:m
          for ss=[-1 1]
            rind = rind+1;
            for js=1:m
              cind = coord2ind([is js],[m m]);
              Aing(rind,cind) = ss;
              Aing(rind,ind1) =  s;
              Aing(rind,ind2) = -s;
              Bing(rind,1) = m*d;
            end
          end
        end
      end
    end
  end
end


Ain = assembleblock({Aing});
Bin = [Bing];

f = A(:);


[xp,fvalp] = linprog( f,Ain,Bin,Aeq,Beq);
[xn,fvaln] = linprog(-f,Ain,Bin,Aeq,Beq);
if abs(fvalp)>abs(fvaln)
  x = xp;
  fval = fvalp;
else
  x = xn;
  fval = fvaln;
end

gam = reshape(x,[m m]);

return