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Based on http://www.coinheist.com/rubik/a_regular_crossword/grid.pdf
 
(ND|ET|IN)[^X]*
[CHMNOR]*I[CHMNOR]*
P+(..)\1.*
(E|CR|MN)*
([^MC]|MM|CC)*
[AM]*CM(RC)*R?
.*
.*H.*H.*
.*PRR.*DDC.*
(DI|NS|TH|OM)*
(HHX|[^HX])*
F.*[AO].*[AO].*
([^EMC]|EM)*
(O|RHH|MM)*
.*OXR.*
.*
.*LR.*RL.*
C*MC(CCC|MM)*
.*SE.*UE.*
[^C]*[^R]*III.*
(...?)\1*
(S|MM|HHH)*
([^X]|XCC)*
[^M]*M[^M]*
(RR|HHH)*.?
(RX|[^R])*
N.*X.X.X.*E
[CEIMU]*OH[AEMOR]*
R*D*M*
.*(.)C\1X\1.*
.(C|HH)*
[^C]*MMM[^C]*
.*G.*V.*H.*
[CR]*
.*XEXM*
.*DD.*CCM.*
.*XHCR.*X.*
.*(.)(.)(.)(.)\4\3\2\1.*
.*(IN|SE|HI)