version 1.24, 2010/11/06 16:12:39
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version 1.31, 2010/11/10 22:41:29
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Line 33 use Apache::lonlocal;
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Line 33 use Apache::lonlocal;
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use Apache::lonnet; |
use Apache::lonnet; |
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BEGIN { |
BEGIN { |
&Apache::lonxml::register('Apache::functionplotresponse',('functionplotresponse','backgroundplot','spline','splinerule')); |
&Apache::lonxml::register('Apache::functionplotresponse',('functionplotresponse','backgroundplot','spline','functionplotrule')); |
} |
} |
|
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# |
# |
Line 339 sub end_backgroundplot {
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Line 339 sub end_backgroundplot {
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} |
} |
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# |
# |
# <splinerule ... /> |
# <functionplotrule ... /> |
# |
# |
sub start_splinerule { |
sub start_functionplotrule { |
my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_; |
my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_; |
my $result=''; |
my $result=''; |
my $label=&Apache::lonxml::get_param('index',$parstack,$safeeval); |
my $label=&Apache::lonxml::get_param('index',$parstack,$safeeval); |
$Apache::functionplotresponse::counter++; |
$Apache::functionplotresponse::counter++; |
if ($label=~/\W/) { |
if ($label=~/\W/) { |
&Apache::lonxml::warning(&mt('Spline Rule indices should only contain alphanumeric characters.')); |
&Apache::lonxml::warning(&mt('Rule indices should only contain alphanumeric characters.')); |
} |
} |
$label=~s/\W//gs; |
$label=~s/\W//gs; |
unless ($label) { |
unless ($label) { |
Line 356 sub start_splinerule {
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Line 356 sub start_splinerule {
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$label='R'.$label; |
$label='R'.$label; |
} |
} |
if ($Apache::functionplotresponse::splineorder{$label}) { |
if ($Apache::functionplotresponse::splineorder{$label}) { |
&Apache::lonxml::error(&mt('Spline Rule indices must be unique.')); |
&Apache::lonxml::error(&mt('Rule indices must be unique.')); |
} |
} |
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if ($target eq 'grade') { |
if ($target eq 'grade') { |
# Simply remember - in order - for later |
# Simply remember - in order - for later |
my $beginninglabel=&Apache::lonxml::get_param('beginninglabel',$parstack,$safeeval); |
my $beginninglabel=&Apache::lonxml::get_param('xinitiallabel',$parstack,$safeeval); |
my $endinglabel=&Apache::lonxml::get_param('endinglabel',$parstack,$safeeval); |
my $endinglabel=&Apache::lonxml::get_param('xfinallabel',$parstack,$safeeval); |
if (($beginninglabel=~/\W/) || ($endinglabel=~/W/)) { |
if (($beginninglabel=~/\W/) || ($endinglabel=~/W/)) { |
&Apache::lonxml::warning(&mt('Spline Rule labels must be alphanumeric.')); |
&Apache::lonxml::warning(&mt('Rule labels must be alphanumeric.')); |
} |
} |
$beginninglabel=~s/\W//gs; |
$beginninglabel=~s/\W//gs; |
$endinglabel=~s/\W//gs; |
$endinglabel=~s/\W//gs; |
Line 373 sub start_splinerule {
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Line 373 sub start_splinerule {
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$relationship=~s/\W//gs; |
$relationship=~s/\W//gs; |
$relationship=lc($relationship); |
$relationship=lc($relationship); |
unless ($relationship=~/^(eq|ge|gt|le|lt|ne)$/) { |
unless ($relationship=~/^(eq|ge|gt|le|lt|ne)$/) { |
&Apache::lonxml::warning(&mt('Spline Rule relationship not defined.')); |
&Apache::lonxml::warning(&mt('Rule relationship not defined.')); |
$relationship='eq'; |
$relationship='eq'; |
} |
} |
my $derivative=&Apache::lonxml::get_param('derivative',$parstack,$safeeval); |
my $derivative=&Apache::lonxml::get_param('derivative',$parstack,$safeeval); |
unless (($derivative==0) || ($derivative==1) || ($derivative==2)) { |
unless (($derivative==0) || ($derivative==1) || ($derivative==2)) { |
&Apache::lonxml::warning(&mt('Spline Rule derivative not defined.')); |
&Apache::lonxml::warning(&mt('Rule derivative not defined.')); |
$derivative=0; |
$derivative=0; |
} |
} |
push(@Apache::functionplotresponse::splinerules,join(':',( |
push(@Apache::functionplotresponse::functionplotrules,join(':',( |
$label, |
$label, |
$derivative, |
$derivative, |
&Apache::lonxml::get_param('beginningvalue',$parstack,$safeeval), |
&Apache::lonxml::get_param('xinitial',$parstack,$safeeval), |
$beginninglabel, |
$beginninglabel, |
&Apache::lonxml::get_param('endingvalue',$parstack,$safeeval), |
&Apache::lonxml::get_param('xfinal',$parstack,$safeeval), |
$endinglabel, |
$endinglabel, |
$relationship, |
$relationship, |
&Apache::lonxml::get_param('value',$parstack,$safeeval) |
&Apache::lonxml::get_param('value',$parstack,$safeeval) |
))); |
))); |
} elsif ($target eq 'edit') { |
} elsif ($target eq 'edit') { |
$result=&Apache::edit::tag_start($target,$token,'Spline Evaluation Rule'). |
$result=&Apache::edit::tag_start($target,$token,'Function Plot Evaluation Rule'). |
&Apache::edit::end_row(); |
&Apache::edit::text_arg('Index:','index', |
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$token,'4').' '. |
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&Apache::edit::select_arg(&mt('Function:'),'derivative', |
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[['0','Function itself'], |
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['1','First derivative'], |
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['2','Second derivative']],$token).' '. |
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&Apache::edit::text_arg('(Initial) x-value:','xinitial', |
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$token,'4'). |
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&Apache::edit::select_or_text_arg('(Initial) x-value label:','xinitiallabel', |
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[['start','Start of Plot']],$token,'8').' '. |
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&Apache::edit::text_arg('Optional final x-value for ranges:','xfinal', |
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$token,'4'). |
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&Apache::edit::select_or_text_arg('Optional final x-value label:','xfinallabel', |
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[['end','End of Plot']],$token,'8').' '. |
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&Apache::edit::select_arg(&mt('Relationship:'),'relationship', |
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[['eq','equal'], |
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['ne','not equal'], |
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['ge','greater than or equal'], |
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['gt','greater than'], |
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['lt','less than'], |
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['le','less than or equal']],$token). |
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$result.= &Apache::edit::select_or_text_arg('Value:','value', |
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[['undef','not defined']],$token,'4'). |
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&Apache::edit::text_arg('Percent error:','percenterror', |
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$token,'4'). |
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&Apache::edit::end_row(); |
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} elsif ($target eq 'modified') { |
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my $constructtag=&Apache::edit::get_new_args($token,$parstack, |
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$safeeval,'index','derivative','xinitial','xinitiallabel','xfinal','xfinallabel','relationship', |
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'value','percenterror'); |
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if ($constructtag) { $result=&Apache::edit::rebuild_tag($token); } |
} |
} |
return $result; |
return $result; |
} |
} |
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sub end_splinerule { |
sub end_functionplotrule { |
my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_; |
my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_; |
my $result=''; |
my $result=''; |
if ($target eq 'edit') { |
if ($target eq 'edit') { |
Line 553 sub d2dt2_cubic_hermite {
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Line 586 sub d2dt2_cubic_hermite {
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# |
# |
sub array_index { |
sub array_index { |
my ($xmin,$xmax,$x)=@_; |
my ($xmin,$xmax,$x)=@_; |
return int(($x-$xmin)/($xmax-$xmin)*200.+0.5); |
return int(($x-$xmin)/($xmax-$xmin)*400.+0.5); |
} |
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# |
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# Actual x-value of array index |
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# |
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sub index_x { |
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my ($xmin,$xmax,$i)=@_; |
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return $i*($xmax-$xmin)/200.+$xmin; |
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} |
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# |
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# Assume function to be linear between array points |
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# Return the two indices and the scale factor |
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# |
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sub indices_scale { |
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my ($xmin,$xmax,$x)=@_; |
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my $i=&array_index($xmin,$xmax,$x); |
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my $xr=&index_x($xmin,$xmax,$i); |
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if ($xr<$x) { |
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# Desired x is right of array index |
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if ($i>=200) { return (200,200,0); } |
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return($i,$i+1,200.*($x-$xr)/($xmax-$xmin)); |
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} elsif ($xr>$x) { |
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# Desired x is left of array index |
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if ($i<=0) { return (0,0,0); } |
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return($i-1,$i,1.-200.*($xr-$x)/($xmax-$xmin)); |
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} else { |
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# Desired x is at array index (unlikely, but ...) |
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if ($i>=200) { return (200,200,0); } |
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if ($i<=0) { return (0,0,0); } |
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return ($i,$i,0); |
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} |
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} |
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# |
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# Function value |
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# |
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sub func_val { |
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my ($xmin,$xmax,$x)=@_; |
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my ($il,$ih,$factor)=&indices_scale($xmin,$xmax,$x); |
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my $fl=$Apache::functionplotresponse::func[$il]; |
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my $fh=$Apache::functionplotresponse::func[$ih]; |
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unless (defined($fl) || defined($fh)) { return undef; } |
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unless (defined($fl)) { return $fh; } |
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unless (defined($fh)) { return $fl; } |
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return $fl+$factor*($fh-$fl); |
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} |
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# |
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# First derivative |
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# |
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sub dfuncdx_val { |
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my ($xmin,$xmax,$x)=@_; |
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my ($il,$ih,$factor)=&indices_scale($xmin,$xmax,$x); |
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my $fl=$Apache::functionplotresponse::dfuncdx[$il]; |
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my $fh=$Apache::functionplotresponse::dfuncdx[$ih]; |
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unless (defined($fl) || defined($fh)) { return undef; } |
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unless (defined($fl)) { return $fh; } |
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unless (defined($fh)) { return $fl; } |
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return $fl+$factor*($fh-$fl); |
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} |
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# |
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# Second derivative |
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# |
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sub d2funcdx2_val { |
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my ($xmin,$xmax,$x)=@_; |
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my ($il,$ih,$factor)=&indices_scale($xmin,$xmax,$x); |
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my $fl=$Apache::functionplotresponse::d2funcdx2[$il]; |
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my $fh=$Apache::functionplotresponse::d2funcdx2[$ih]; |
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unless (defined($fl) || defined($fh)) { return undef; } |
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unless (defined($fl)) { return $fh; } |
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unless (defined($fh)) { return $fl; } |
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return $fl+$factor*($fh-$fl); |
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} |
} |
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# |
# |
Line 641 sub d2funcdx2_val {
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Line 595 sub d2funcdx2_val {
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sub populate_arrays { |
sub populate_arrays { |
my ($id,$xmin,$xmax)=@_; |
my ($id,$xmin,$xmax)=@_; |
for (my $i=0; $i<=200; $i++) { |
for (my $i=0; $i<=400; $i++) { |
$Apache::functionplotresponse::func[$i]=undef; |
$Apache::functionplotresponse::func[$i]=undef; |
$Apache::functionplotresponse::dfuncdx[$i]=undef; |
$Apache::functionplotresponse::dfuncdx[$i]=undef; |
$Apache::functionplotresponse::d2funcd2x[$i]=undef; |
$Apache::functionplotresponse::d2funcd2x[$i]=undef; |
Line 662 sub populate_arrays {
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Line 616 sub populate_arrays {
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$env{'form.HWVAL_'.$id.'_'.$label.'P'.$ni.'_y'}, |
$env{'form.HWVAL_'.$id.'_'.$label.'P'.$ni.'_y'}, |
$env{'form.HWVAL_'.$id.'_'.$label.'S'.$ni.'_y'}); |
$env{'form.HWVAL_'.$id.'_'.$label.'S'.$ni.'_y'}); |
# Run in small steps over spline parameter |
# Run in small steps over spline parameter |
for (my $t=0; $t<=1; $t+=0.00025) { |
for (my $t=0; $t<=1; $t+=0.0001) { |
my $xi=&array_index($xmin,$xmax,&cubic_hermite($t,@xparms)); |
my $xi=&array_index($xmin,$xmax,&cubic_hermite($t,@xparms)); |
if ($xi<$xiold) { return 'no_func'; } |
if ($xi<$xiold) { return 'no_func'; } |
if (($xi>$xiold) && ($xi>=0) && ($xi<=200)) { |
if (($xi>$xiold) && ($xi>=0) && ($xi<=400)) { |
if (defined($Apache::functionplotresponse::func[$xi])) { return 'no_func'; } |
if (defined($Apache::functionplotresponse::func[$xi])) { return 'no_func'; } |
$xiold=$xi; |
$xiold=$xi; |
# Function value |
# Function value |
$Apache::functionplotresponse::func[$xi]=&cubic_hermite($t,@yparms); |
my $funcval=&cubic_hermite($t,@yparms); |
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$Apache::functionplotresponse::func[$xi]=$funcval; |
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if (defined($funcval)) { |
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if ($xi<$Apache::functionplotresponse::functionplotrulelabels{'start'}) { |
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$Apache::functionplotresponse::functionplotrulelabels{'start'}=$xi; |
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} |
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if ($xi>$Apache::functionplotresponse::functionplotrulelabels{'end'}) { |
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$Apache::functionplotresponse::functionplotrulelabels{'end'}=$xi; |
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} |
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} |
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# Chain rule |
# dy/dx=dy/dt/(dx/dt) |
# dy/dx=dy/dt/(dx/dt) |
my $dxdt=&ddt_cubic_hermite($t,@xparms); |
my $dxdt=&ddt_cubic_hermite($t,@xparms); |
if ($dxdt) { |
if ($dxdt) { |
$Apache::functionplotresponse::dfuncdx[$xi]=&ddt_cubic_hermite($t,@yparms)/$dxdt; |
$Apache::functionplotresponse::dfuncdx[$xi]=&ddt_cubic_hermite($t,@yparms)/$dxdt; |
} |
} |
# d^2y/dx^2 |
# Faa di Bruno |
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# d^2y/dx^2=(d^2y/dt^2)/(dx/dt)^2+(dy/dt)/(d^2x/dt^2) |
my $d2xdt2=&d2dt2_cubic_hermite($t,@xparms); |
my $d2xdt2=&d2dt2_cubic_hermite($t,@xparms); |
if ($d2xdt2) { |
if (($dxdt) && ($d2xdt2)) { |
$Apache::functionplotresponse::d2funcd2x[$xi]=&d2dt2_cubic_hermite($t,@yparms)/$d2xdt2; |
$Apache::functionplotresponse::d2funcdx2[$xi]= |
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&d2dt2_cubic_hermite($t,@yparms)/($dxdt*$dxdt) |
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+&ddt_cubic_hermite($t,@yparms)/$d2xdt2; |
} |
} |
} |
} |
} |
} |
Line 704 sub start_functionplotresponse {
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Line 671 sub start_functionplotresponse {
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$Apache::functionplotresponse::inputfields=''; |
$Apache::functionplotresponse::inputfields=''; |
$Apache::functionplotresponse::counter=0; |
$Apache::functionplotresponse::counter=0; |
# Remember rules |
# Remember rules |
undef @Apache::functionplotresponse::splinerules; |
undef @Apache::functionplotresponse::functionplotrules; |
# Part and ID |
# Part and ID |
my $partid=$Apache::inputtags::part; |
my $partid=$Apache::inputtags::part; |
my $id=&Apache::response::start_response($parstack,$safeeval); |
my $id=&Apache::response::start_response($parstack,$safeeval); |
Line 722 sub start_functionplotresponse {
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Line 689 sub start_functionplotresponse {
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$ymin=(defined($ymin)?$ymin:-10); |
$ymin=(defined($ymin)?$ymin:-10); |
my $ymax=&Apache::lonxml::get_param('ymax',$parstack,$safeeval); |
my $ymax=&Apache::lonxml::get_param('ymax',$parstack,$safeeval); |
$ymax=(defined($ymax)?$ymax:10); |
$ymax=(defined($ymax)?$ymax:10); |
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if ($xmax<=$xmin) { |
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&Apache::lonxml::warning('Maximum x-value needs to be larger than minimum value.'); |
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$xmax=$xmin+20; |
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} |
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if ($ymax<=$ymin) { |
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&Apache::lonxml::warning('Maximum y-value needs to be larger than minimum value.'); |
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$ymax=$ymin+20; |
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} |
my $xaxisvisible=(&Apache::lonxml::get_param('xaxisvisible',$parstack,$safeeval)=~/on|true|yes|1/i?'true':'false'); |
my $xaxisvisible=(&Apache::lonxml::get_param('xaxisvisible',$parstack,$safeeval)=~/on|true|yes|1/i?'true':'false'); |
my $yaxisvisible=(&Apache::lonxml::get_param('yaxisvisible',$parstack,$safeeval)=~/on|true|yes|1/i?'true':'false'); |
my $yaxisvisible=(&Apache::lonxml::get_param('yaxisvisible',$parstack,$safeeval)=~/on|true|yes|1/i?'true':'false'); |
my $gridvisible=(&Apache::lonxml::get_param('gridvisible',$parstack,$safeeval)=~/on|true|yes|1/i?'true':'false'); |
my $gridvisible=(&Apache::lonxml::get_param('gridvisible',$parstack,$safeeval)=~/on|true|yes|1/i?'true':'false'); |
Line 777 sub start_functionplotresponse {
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Line 752 sub start_functionplotresponse {
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return $result; |
return $result; |
} |
} |
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sub splinerulecheck { |
sub compare_rel { |
my ($rule)=@_; |
my ($relationship,$value,$realval,$tol)=@_; |
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# is the real value defined? |
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unless (defined($realval)) { |
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if ($relationship eq 'eq') { |
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if ($value eq 'undef') { |
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return 1; |
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} else { |
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return 0; |
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} |
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} elsif ($relationship eq 'ne') { |
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if ($value eq 'undef') { |
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return 0; |
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} else { |
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return 1; |
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} |
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} else { |
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return 0; |
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} |
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} |
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# it is defined. |
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if ($relationship eq 'gt') { |
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return ($realval>$value); |
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} elsif ($relationship eq 'ge') { |
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return ($realval>$value-$tol); |
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} elsif ($relationship eq 'lt') { |
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return ($realval<$value); |
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} elsif ($relationship eq 'le') { |
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return ($realval<$value+$tol); |
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} elsif ($relationship eq 'ne') { |
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return (abs($value-$realval)>$tol); |
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} else { |
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return (abs($value-$realval)<$tol); |
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} |
return 0; |
return 0; |
} |
} |
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sub functionplotrulecheck { |
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my ($rule,$xmin,$xmax,$tolfunc,$toldfdx,$told2fdx2)=@_; |
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&Apache::lonnet::logthis("Rule $rule TolFunc $tolfunc TolDfDx $toldfdx TolD2fDx2 $told2fdx2"); |
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my ($label,$derivative,$xinitial,$xinitiallabel,$xfinal,$xfinallabel,$relationship,$value) |
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=split(/\:/,$rule); |
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my $li=0; |
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my $lh=400; |
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# Special case: the upper boundary was not defined |
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# and needs to be set to the value where |
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# the condition is not true anymore => set flag |
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my $findupper=0; |
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if (($xfinal eq '') |
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&& (!defined($Apache::functionplotresponse::functionplotrulelabels{$xfinallabel})) |
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&& ($xfinallabel)) { |
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$findupper=1; |
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} |
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# if a hard value is set for the boundaries, it overrides the label |
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if (($xinitial ne '') && ($xinitiallabel ne '') && ($xinitiallabel ne 'start')) { |
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$li=&array_index($xmin,$xmax,$xinitial); |
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$Apache::functionplotresponse::functionplotrulelabels{$xinitiallabel}=$li; |
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} |
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if (($xfinal ne '') && ($xfinallabel ne '') && ($xfinallabel ne 'end')) { |
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$lh=&array_index($xmin,$xmax,$xfinal); |
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$Apache::functionplotresponse::functionplotrulelabels{$xfinallabel}=$lh; |
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} |
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# if the label is defined, use it |
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if (defined($Apache::functionplotresponse::functionplotrulelabels{$xinitiallabel})) { |
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$li=$Apache::functionplotresponse::functionplotrulelabels{$xinitiallabel}; |
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} else { |
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$li=&array_index($xmin,$xmax,$xinitial); |
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} |
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unless ($findupper) { |
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if (defined($Apache::functionplotresponse::functionplotrulelabels{$xfinallabel})) { |
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$lh=$Apache::functionplotresponse::functionplotrulelabels{$xfinallabel}; |
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} else { |
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$lh=&array_index($xmin,$xmax,$xfinal); |
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} |
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} |
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# Basic sanity checks |
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if ($li<0) { $li=0; } |
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if ($lh>400) { $lh=400; } |
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if ($li>$lh) { |
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$lh=$li; |
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} |
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&Apache::lonnet::logthis("Init $xinitial=$li Final $xfinal=$lh Findupper: $findupper"); |
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my $tol=$tolfunc; |
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if ($derivative==2) { |
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$tol=$told2fdx2; |
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} elsif ($derivative==1) { |
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$tol=$toldfdx; |
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} |
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for (my $i=$li; $i<=$lh; $i++) { |
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my $val; |
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if ($derivative==2) { |
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$val=$Apache::functionplotresponse::d2funcdx2[$i]; |
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} elsif ($derivative==1) { |
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$val=$Apache::functionplotresponse::dfuncdx[$i]; |
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} else { |
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$val=$Apache::functionplotresponse::func[$i]; |
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} |
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unless (&compare_rel($relationship,$value,$val,$tol)) { |
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&Apache::lonnet::logthis("Condition false $findupper at $i with $val"); |
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if (($findupper) && ($i>$li)) { |
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$Apache::functionplotresponse::functionplotrulelabels{$xfinallabel}=$i; |
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&Apache::lonnet::logthis("Setting $xfinallabel to $i"); |
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return 1; |
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} else { |
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return 0; |
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} |
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} |
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} |
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return 1; |
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} |
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sub end_functionplotresponse { |
sub end_functionplotresponse { |
my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_; |
my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_; |
Line 797 sub end_functionplotresponse {
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Line 883 sub end_functionplotresponse {
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&& &Apache::response::submitted() |
&& &Apache::response::submitted() |
&& $Apache::lonhomework::type eq 'exam') { |
&& $Apache::lonhomework::type eq 'exam') { |
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#&Apache::response::scored_response($partid,$id); |
&Apache::response::scored_response($partid,$id); |
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} elsif ($target eq 'grade' |
} elsif ($target eq 'grade' |
&& &Apache::response::submitted() |
&& &Apache::response::submitted() |
Line 812 sub end_functionplotresponse {
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Line 898 sub end_functionplotresponse {
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$xmin=(defined($xmin)?$xmin:-10); |
$xmin=(defined($xmin)?$xmin:-10); |
my $xmax=&Apache::lonxml::get_param('xmax',$parstack,$safeeval); |
my $xmax=&Apache::lonxml::get_param('xmax',$parstack,$safeeval); |
$xmax=(defined($xmax)?$xmax:10); |
$xmax=(defined($xmax)?$xmax:10); |
|
my $ymin=&Apache::lonxml::get_param('ymin',$parstack,$safeeval); |
|
$ymin=(defined($ymin)?$ymin:-10); |
|
my $ymax=&Apache::lonxml::get_param('ymax',$parstack,$safeeval); |
|
$ymax=(defined($ymax)?$ymax:10); |
|
|
|
my $percent=&Apache::lonxml::get_param('percenterror',$parstack,$safeeval); |
|
$percent=(defined($percent)?$percent:5); |
|
|
|
my $tolfunc=$percent*($ymax-$ymin)/100.; |
|
my $toldfdx=1; |
|
my $told2fdx2=1; |
|
if ($xmax>$xmin) { |
|
$toldfdx=$tolfunc/($xmax-$xmin); |
|
$told2fdx2=$toldfdx/($xmax-$xmin); |
|
} |
|
|
my $ad=''; |
my $ad=''; |
|
undef %Apache::functionplotresponse::functionplotrulelabels; |
|
$Apache::functionplotresponse::functionplotrulelabels{'start'}=400; |
|
$Apache::functionplotresponse::functionplotrulelabels{'end'}=0; |
if (&populate_arrays($internalid,$xmin,$xmax) eq 'no_func') { |
if (&populate_arrays($internalid,$xmin,$xmax) eq 'no_func') { |
$ad='NOT_FUNCTION'; |
$ad='NOT_FUNCTION'; |
} else { |
} else { |
# We have a function that we can actually grade, go through the spline rules. |
# We have a function that we can actually grade, go through the spline rules. |
undef %Apache::functionplotresponse::splinerulelabels; |
foreach my $rule (@Apache::functionplotresponse::functionplotrules) { |
foreach my $rule (@Apache::functionplotresponse::splinerules) { |
unless (&functionplotrulecheck($rule,$xmin,$xmax,$tolfunc,$toldfdx,$told2fdx2)) { |
unless (&splinerulecheck($rule)) { |
|
$ad='INCORRECT'; |
$ad='INCORRECT'; |
last; |
last; |
} |
} |