function phi = extremizf(phi,m,n)
global nstate
nstate = m;

y = zeros(1,n);
dims = repmat([m],[1 n]);

xx = list_all_ind(repmat([m],[1 n-1]));

global FN
FN{n} = phi;

%r = rand;
r = 1;
for i=1:n
  r = rand;
  %r=0;
  %r = mod(i,2);
  for xind = 1:size(xx,1)
    xl = xx(xind,1:i-1);
    xr = xx(xind,i:n-1);
    fv = [];
    for xj = 1:m
      x = [xl xj xr];
      fv(end+1) = F(x);
    end
    [a,mind] = min(fv);
    [A,Mind] = max(fv);
    if A-a > 1-1e-7
      for xj = 1:m
        x = [xl xj xr];
        xind = coord2ind(x,dims);
        fv = F(x);
        if 0 % these are arbitrary
          if abs(fv-a)<1e-8
            phi(xind) = a;
          elseif abs(fv-A)<1e-8
            phi(xind) = A;
          else
            %  phi(xind) = a;
            %  if 1
            r = rand;
            if r<.5
              phi(xind) = a;
            else
              phi(xind) = A;
            end
            %phi(xind) = r*a + (1-r)*A;
            %end
          end
        else
          % not arbitrary
          if abs(fv-a) < abs(fv-A)
            % closer to min
            phi(xind) = a;
          else
            % closer to max
            phi(xind) = A;
          end
        end
      end
      %break;
    else
      %
    end
    FN{n} = phi;
  end
end
return




function r = F(x)
global nstate
lenseq = length(x);
global FN
FF = FN{lenseq};
ind = coord2ind(x,(repmat(nstate,1,lenseq)));
r = FF(ind);
return