function [Y,Xt] = maxyhat(P,m,n)
yy = [];
XXt = {};
F = zeros(m^n,1);
for t=1:n
  dimx = repmat([m],[1 t]);
  for xi = 1:m^t
    Xt = ind2coord(xi,dimx);
    [fv,xhat,K] = boundYxhat(P,Xt,m,n);
    yy(end+1) = fv;
    XXt{end+1} = Xt;
  end
end
[Y,yind] = max(yy);
Xt = XXt{yind};
return



function [fv,xhat,K] = boundYxhat(P,Xt,m,n)
yy = [];
KK = {};
F = zeros(m^n,1);
for xhat = 1:m
  [fv0,K] = condexphat(P,F,Xt,m,n,xhat);
  KK{xhat} = K;
  [phi,fv] = maxphi(K);
  yy(xhat) = fv;
end
[fv,xhat] = max(abs(yy));
K = KK{xhat};
return