\def\Q{{\bf Q}}\def\Z{{\bf Z}}\def\N{{\bf N}}
\def\R{{\bf R}}\def\F{{\bf F}}
\def\calR{{\cal R}}\def\I{{\cal I}}
\def\frac#1#2{{{#1}\over{#2}}}\def\colon{:}
\def\longmapsto{\mapsto}\def\lneqq{<}
\def\hookrightarrow{\rightarrow}
\def\mid{ | }\def\lbrack{[}\def\rbrack{]}
\def\gets{\leftarrow}\def\land{\wedge}