function phi1 = collapsefperm(K,phi,m,n,perm)
global Ainl Binl Ain1 Bin1
dims = repmat([m],[1 n]);
dims1 = repmat([m],[1 n-1]);

phi1 = zeros(1,m^(n-1));

% init phi1 to be plain-vanilla mean
for xind2n = 1:m^(n-1)
  x2n = ind2coord(xind2n,dims1);
  ff = [];
  ww = [];
  for x1 = 1:m
    xind = coord2ind([x1 x2n],dims);
    ff(end+1) = phi(xind);
  end
  phi1(xind2n) = mean(ff);
end

%for xind2n = 1:m^(n-1)
%rp = randperm(m^(n-1));
for xind2n = perm
  x2n = ind2coord(xind2n,dims1);
  ks = 0;
  ff = [];
  for x1 = 1:m
    xind = coord2ind([x1 x2n],dims);
    ks = ks + K(xind);
    ff(end+1) = phi(xind);
  end
  Y = allrho1(x2n,m);
  Yind = coord2ind(Y,dims1);
  ymax = max(phi1(Yind));
  ymin = min(phi1(Yind));
  d = ymax-ymin;
  if ks > 0
    phi1(xind2n) = min(ymax + 1 - d,n-1);
    %phi1(xind2n) = max(ff);
  else
    phi1(xind2n) = max(ymin - 1 + d,0);
    %phi1(xind2n) = floor(phi1(xind2n));
    %phi1(xind2n) = min(ff);
  end
  %if max(abs(Ain1*phi1'))>1+1e-9
  %  % not lip, back to boring
  %  phi1(xind2n) = mean(ff);
  %end
end

return