\let\a=\alpha
\let\b=\beta
\let\g=\gamma
\let\d=\delta
\let\e=\varepsilon
\let\z=\zeta
\let\h=\eta
\let\th=\theta
\let\k=\kappa
\let\l=\lambda
\let\m=\mu
\let\n=\nu
\let\x=\xi
\let\p=\pi
\let\r=\rho
\let\s=\sigma
\let\t=\tau
\let\f=\varphi
\let\ph=\varphi
\let\c=\chi
\let\ps=\psi
\let\y=\upsilon
\let\o=\omega
\let\si=\varsigma
\let\G=\Gamma
\let\D=\Delta
\let\Th=\Theta
\let\L=\Lambda
\let\X=\Xi
\let\P=\Pi
\let\Si=\Sigma
\let\F=\Phi
\let\Ps=\Psi
\let\O=\Omega
\let\Y=\Upsilon

\def\AAA{\mathcal A}
\def\XXX{\mathcal X}
\def\PPP{\mathcal P}
\def\HHH{\mathcal H}
\def\BBB{\mathcal B}
\def\III{\mathcal I}
\def\EE{\mathcal E}
\def\MM{\mathcal M}
\def\VV{\mathcal V}
\def\CC{\mathcal C}
\def\FF{\mathcal F}
\def\WW{\mathcal W}
\def\TT{\mathcal T}
\def\NN{\mathcal N}
\def\RR{\mathcal R}
\def\LL{\mathcal L}
\def\JJ{\mathcal J}
\def\OO{\mathcal O}
\def\DD{\mathcal D}
\def\GG{\mathcal G}
\def\SS{\mathcal S}
\def\KK{\mathcal K}
\def\UU{\mathcal U}
\def\QQ{\mathcal Q}

\def\aaa{\mathbf a}
\def\bbb{\mathbf b}
\def\hhh{\mathbf h}
\def\hh{\mathbf h}
\def\HH{\mathbf H}
\def\AA{\mathbf A}
\def\qq{\mathbf q}
\def\BB{\mathbf B}
\def\YY{\mathbf Y}
\def\XX{\mathbf X}
\def\PP{\mathbf P}
\def\pp{\mathbf p}
\def\vv{\mathbf v}
\def\xx{\mathbf x}
\def\yy{\mathbf y}
\def\zz{\mathbf z}
\def\II{\mathbf I}
\def\ii{\mathbf i}
\def\jj{\mathbf j}
\def\kk{\mathbf k}
\def\bS{\mathbf S}
\def\mm{\mathbf m}
\def\Vn{\mathbf n}

\def\ch{\chi}
\def\Exp{\mathrm exp}
\def\Log{\mathrm log}
\def\Ft{\varphi}
\def\E{H}

\def\RRR{\mathbb R}
\def\ZZZ{\mathbb Z}

\def\ss{\underline{\sigma}}

\let\==\equiv
\let\io=\infty 
\let\0=\noindent
\def\media#1{\left<#1\right>}
\let\dpr=\partial
\def\sign{\mathrm{sign}}
\def\const{\mathrm{const}}
\def\wt{\widetilde}
\def\wh{\widehat}
\def\Val{\mathrm{Val}}
\let\ul=\underline
\def\lis{\overline}
\let\V=\mathbf
\def\be{\begin{equation}}
\def\ee{\end{equation}}
\def\bea{\begin{eqnarray}}
\def\eea{\end{eqnarray}}
\def\nn{\nonumber}

\def\supp{\mathrm{supp}}
\def\dist{\mathrm{dist}}
\def\Ext{\mathrm{Ext}}
\def\Int{\mathrm{Int}}
\def\diam{\mathrm{diam}}