\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}