Обсуждение: Regexp_replace bug / does not terminate on long strings
'one,one,one,two,two,three', -- input string
'([^,]+)(,\1)*($|,)', -- pattern
'\1\3', -- replacement
'g' -- apply globally (all matches)
);
Verizon Deutschland GmbH - Sebrathweg 20, 44149 Dortmund, Germany - Amtsgericht Dortmund, HRB 14952 - Geschäftsführer: Detlef Eppig - Vorsitzender des Aufsichtsrats: Francesco de Maio
"Markhof, Ingolf" <ingolf.markhof@de.verizon.com> writes: > BRIEF: > regexp_replace(source,pattern,replacement,flags) needs very (!) long to > complete or does not complete at all (?!) for big input strings (a few k > characters). (Oracle SQL completes the same in a few ms) Regexps containing backrefs are inherently hard --- every engine has strengths and weaknesses. I doubt it'd be hard to find cases where our engine is orders of magnitude faster than Oracle's; but you've hit on a case where the opposite is true. The core of the problem is that it's hard to tell how much of the string could be matched by the (,\1)* subpattern. In principle, *all* of the remaining string could be, if it were N repetitions of the initial word. Or it could be N-1 repetitions followed by one other word, and so on. The difficulty is that since our engine guarantees to find the longest feasible match, it tries these options from longest to shortest. Usually the actual match (if any) will be pretty short, so that you have O(N) wasted work per word, making the runtime at least O(N^2). I think your best bet is to not try to eliminate multiple duplicates at a time. Get rid of one dup at a time, say by str := regexp_replace(str, '([^,]+)(,\1)?($|,)', '\1\3', 'g'); and repeat till the string doesn't get any shorter. I did come across a performance bug [1] while poking at this, but alas fixing it doesn't move the needle very much for this example. regards, tom lane [1] https://www.postgresql.org/message-id/1808998.1629412269%40sss.pgh.pa.us
select string_agg( value, ',' ) As final_result from(
select
value,
min( row_num ) as min_row_num
from(
select
sub.value,
row_number() over () as row_num
from
( select unnest( string_to_array( '1/1,1/1,1/1,1/1,1/1,1/1,1/1,1/1,1/1,1/1,1/1,2/1,2/1,2/1,2/1,2/2,2/1,2/1,2/2,2/2,2/1,2/1,2/2,2/2,2/1,2/2,2/1,2/1,2/2,2/1,2/1,2/2,3/1,3/1,3/2,3/1,3/1,3/1,3/1,3/1,3/1,3/3,3/1,3/1,3/1,3/3,3/1,3/1,3/2,3/1,3/1,3/1,3/3,3/3,3/1,3/1,4/1,4/1,4/1,4/1,4/1,4/1,5/2,5/5,5/1,5/5,5/5,5/2,5/1,5/1,5/5,5/1,6/1,6/1,6/1,6/1,6/3,6/6,6/1,6/1,6/1,6/3,6/1,6/1,6/1,6/1,6/1,6/1,6/6,6/1,7/1,7/3,7/1,7/1,7/1,7/5,7/1,7/1,7/1,7/1,7/1,7/1,7/1,7/5,7/1,7/3,7/1,8/1,8/1,8/2,8/2,8/1,8/6,8/1,8/1,8/1,8/1,8/6,8/1,8/1,8/1,9/2,9/1,9/1,9/2,10/4,10/2,10/2,10/2,10/2,10/1,10/4,10/10,10/10,10/2,10/1,10/1,10/2,10/1,10/8,10/1,10/3,10/2,10/5,10/10,10/2,10/10,10/2,10/3,10/1,10/1,10/1,10/1,10/8,10/5,12/5,12/3,12/5,12/5,12/1,12/5,12/1,12/3,12/1,12/1,12/5,12/2,12/1,12/0.768,12/1,12/2,12/2,12/2,12/2,12/2,12/1,12/1,14/3,15/1,15/10,15/1,15/2,15/3,15/2,15/1,15/15,15/1,15/2,15/4,15/15,15/5,15/1,15/2,15/15,15/1,15/5,15/1,15/3,15/5,15/5,15/1,15/10,15/4,15/2,15/2,15/15,15/3,15/2,15/2,15/3,15/3,16/3,16/3,18/4,18/3,18/1,18/2,18/2,18/2,18/4,18/2,18/2,18/1,18/3,20/20,20/5,20/0.896,20/5,20/1,20/2,20/1,20/3,20/4,20/5,20/10,20/20,20/10,20/5,20/1,20/1,20/4,20/2,20/1,20/1,20/3,20/4,20/20,20/2,20/20,20/2,20/20,20/20,24/3,24/4,24/2,24/4,24/3,24/3,24/3,24/3,25/3,25/4,25/10,25/25,25/6,25/1,25/7,25/2,25/5,25/2,25/2,25/25,25/3,25/25,25/25,25/10,25/3,25/10,25/25,25/6,25/4,25/25,25/5,25/5,25/3,25/1,25/5,25/10,25/25,25/7,25/14,25/5,25/5,25/5,25/3,25/5,25/14,25/2,30/2,30/7,30/3,30/8,30/15,30/1,30/4,30/7,30/2,30/5,30/30,30/8,30/5,30/5,30/5,30/8,30/8,30/1,30/10,30/3,30/30,30/10,30/4,30/30,30/30,30/3,30/1,30/15,30/3,30/5,30/3,35/5,35/12,35/5,35/10,35/3,35/3,35/4,35/10,35/12,35/5,35/5,35/4,40/15,40/4,40/40,40/2,40/10,40/10,40/5,40/3,40/3,40/40,40/4,40/15,40/10,40/2,40/5,45/6,45/6,45/6,45/6,45/6,50/8,50/4,50/50,50/8,50/15,50/7,50/3,50/20,50/25,50/50,50/5,50/50,50/12,50/7,50/4,50/15,50/10,50/8,50/3,50/2,50/20,50/25,50/10,50/8,50/50,50/5,50/5,50/50,50/10,50/10,50/10,50/5,50/5,50/4,50/10,50/50,50/5,50/50,50/8,50/8,50/50,50/50,50/10,50/12,50/2,50/5,55/10,55/10,55/5,55/5,60/3,60/25,60/4,60/60,60/30,60/25,60/6,60/6,60/10,60/5,60/5,60/3,60/10,60/5,60/5,60/10,60/30,60/6,60/5,60/10,60/60,70/10,70/10,75/15,75/3,75/4,75/10,75/20,75/5,75/6,75/8,75/6,75/7,75/75,75/7,75/15,75/25,75/15,75/7,75/3,75/15,75/8,75/30,75/75,75/8,75/8,75/5,75/20,75/75,75/6,75/30,75/15,75/75,75/8,75/25,75/15,75/7,75/75,75/10,75/4,80/5,80/5,90/50,90/50,100/7,100/10,100/10,100/10,100/10,100/10,100/8,100/20,100/10,100/20,100/20,100/5,100/25,100/8,100/5,100/100,100/8,100/20,100/8,100/10,100/20,100/7,100/6,100/50,100/15,100/10,100/2,100/35,100/10,100/10,100/35,100/30,100/100,100/5,100/40,100/35,100/100,100/50,100/35,100/30,100/7,100/10,100/10,100/7,100/25,100/100,100/40,100/5,100/15,100/6,100/7,100/20,100/10,100/2,100/20,105/10,105/20,105/10,105/20,120/15,120/10,120/15,120/15,150/150,150/150,150/75,150/20,150/20,150/20,150/30,150/75,150/25,150/15,150/25,150/150,150/15,150/6,150/6,150/30,150/20,200/15,200/15,200/20,200/10,200/40,200/15,200/40,200/50,200/7,200/20,200/15,200/25,200/20,200/7,200/15,200/7,200/15,200/20,200/20,200/200,200/15,200/50,200/10,200/20,200/20,200/20,200/200,200/20,200/25,200/7,240/15,240/15,250/20,250/50,250/20,250/10,250/10,250/25,250/250,250/250,250/25,250/50,250/25,300/20,300/20,300/30,300/7,300/20,300/300,300/300,300/20,300/30,300/20,300/7,300/10,300/20,300/20,300/30,300/20,300/7,300/7,300/20,300/30,300/30,300/300,300/50,300/300,300/30,300/10,300/300,300/300,300/50,300/300,400/20,400/20,400/25,400/25,450/50,450/50,500/500,500/50,500/50,500/50,500/50,500/500,500/500,500/500,500/35,500/25,500/35,500/25,500/500,600/40,600/40,1000/20,1000/40,1000/20,1000/1000,1000/20,1000/35,1000/1000,1000/20,1000/50,1000/500,1000/50,1000/50,1000/1000,1000/500,1000/1000,1000/35,1000/40', ',' ) ) as value
) as sub
) sub_outer
group by value
order by min_row_num
) sub_outermost;
/* return value
1/1,2/1,2/2,3/1,3/2,3/3,4/1,5/2,5/5,5/1,6/1,6/3,6/6,7/1,7/3,7/5,8/1,8/2,8/6,9/2,9/1,10/4,10/2,10/1,10/10,10/8,10/3,10/5,12/5,12/3,12/1,12/2,12/0.768,14/3,15/1,15/10,15/2,15/3,15/15,15/4,15/5,16/3,18/4,18/3,18/1,18/2,20/20,20/5,20/0.896,20/1,20/2,20/3,20/4,20/10,24/3,24/4,24/2,25/3,25/4,25/10,25/25,25/6,25/1,25/7,25/2,25/5,25/14,30/2,30/7,30/3,30/8,30/15,30/1,30/4,30/5,30/30,30/10,35/5,35/12,35/10,35/3,35/4,40/15,40/4,40/40,40/2,40/10,40/5,40/3,45/6,50/8,50/4,50/50,50/15,50/7,50/3,50/20,50/25,50/5,50/12,50/10,50/2,55/10,55/5,60/3,60/25,60/4,60/60,60/30,60/6,60/10,60/5,70/10,75/15,75/3,75/4,75/10,75/20,75/5,75/6,75/8,75/7,75/75,75/25,75/30,80/5,90/50,100/7,100/10,100/8,100/20,100/5,100/25,100/100,100/6,100/50,100/15,100/2,100/35,100/30,100/40,105/10,105/20,120/15,120/10,150/150,150/75,150/20,150/30,150/25,150/15,150/6,200/15,200/20,200/10,200/40,200/50,200/7,200/25,200/200,240/15,250/20,250/50,250/10,250/25,250/250,300/20,300/30,300/7,300/300,300/10,300/50,400/20,400/25,450/50,500/500,500/50,500/35,500/25,600/40,1000/20,1000/40,1000/1000,1000/35,1000/50,1000/500
*/
If you don't need the order maintained, it becomes a much simpler problem and you can strip off some of this complexity.
"Markhof, Ingolf" <ingolf.markhof@de.verizon.com> writes:
> BRIEF:
> regexp_replace(source,pattern,replacement,flags) needs very (!) long to
> complete or does not complete at all (?!) for big input strings (a few k
> characters). (Oracle SQL completes the same in a few ms)
Regexps containing backrefs are inherently hard --- every engine has
strengths and weaknesses. I doubt it'd be hard to find cases where
our engine is orders of magnitude faster than Oracle's; but you've
hit on a case where the opposite is true.
The core of the problem is that it's hard to tell how much of the
string could be matched by the (,\1)* subpattern. In principle, *all*
of the remaining string could be, if it were N repetitions of the
initial word. Or it could be N-1 repetitions followed by one other
word, and so on. The difficulty is that since our engine guarantees
to find the longest feasible match, it tries these options from
longest to shortest. Usually the actual match (if any) will be pretty
short, so that you have O(N) wasted work per word, making the runtime
at least O(N^2).
I think your best bet is to not try to eliminate multiple duplicates
at a time. Get rid of one dup at a time, say by
str := regexp_replace(str, '([^,]+)(,\1)?($|,)', '\1\3', 'g');
and repeat till the string doesn't get any shorter.
I did come across a performance bug [1] while poking at this, but
alas fixing it doesn't move the needle very much for this example.
regards, tom lane
[1] https://www.postgresql.org/message-id/1808998.1629412269%40sss.pgh.pa.us
"Markhof, Ingolf" <ingolf.markhof@de.verizon.com> writes:
> BRIEF:
> regexp_replace(source,pattern,replacement,flags) needs very (!) long to
> complete or does not complete at all (?!) for big input strings (a few k
> characters). (Oracle SQL completes the same in a few ms)
Regexps containing backrefs are inherently hard --- every engine has
strengths and weaknesses. I doubt it'd be hard to find cases where
our engine is orders of magnitude faster than Oracle's; but you've
hit on a case where the opposite is true.
The core of the problem is that it's hard to tell how much of the
string could be matched by the (,\1)* subpattern. In principle, *all*
of the remaining string could be, if it were N repetitions of the
initial word. Or it could be N-1 repetitions followed by one other
word, and so on. The difficulty is that since our engine guarantees
to find the longest feasible match, it tries these options from
longest to shortest. Usually the actual match (if any) will be pretty
short, so that you have O(N) wasted work per word, making the runtime
at least O(N^2).
I think your best bet is to not try to eliminate multiple duplicates
at a time. Get rid of one dup at a time, say by
str := regexp_replace(str, '([^,]+)(,\1)?($|,)', '\1\3', 'g');
and repeat till the string doesn't get any shorter.
I did come across a performance bug [1] while poking at this, but
alas fixing it doesn't move the needle very much for this example.
regards, tom lane
[1] https://urldefense.proofpoint.com/v2/url?u=https-3A__www.postgresql.org_message-2Did_1808998.1629412269-2540sss.pgh.pa.us&d=DwIBAg&c=udBTRvFvXC5Dhqg7UHpJlPps3mZ3LRxpb6__0PomBTQ&r=ivZWA-ECVj3XrXBe0obDwKY7Ui7K5Nj9oD2KKWLm0Bw&m=q11bVTHCxVx8BQu2pjn6-3nOY8aN8hORXofVK38HqF8&s=hJxrzmTT6G7AUomoeFgh0IGDO3NcUP4gB9kvYHnt3m0&e=
Verizon Deutschland GmbH - Sebrathweg 20, 44149 Dortmund, Germany - Amtsgericht Dortmund, HRB 14952 - Geschäftsführer: Detlef Eppig - Vorsitzender des Aufsichtsrats: Francesco de Maio
Verizon Deutschland GmbH - Sebrathweg 20, 44149 Dortmund, Germany - Amtsgericht Dortmund, HRB 14952 - Geschäftsführer: Detlef Eppig - Vorsitzender des Aufsichtsrats: Francesco de Maio
"Markhof, Ingolf" <ingolf.markhof@de.verizon.com> writes: > thank you very much for your reply. Actually, I was assuming all these > regular expressions are based on the same core implementation. They are not. There are at least three fundamentally different implementation technologies (DFA, NFA, hybrid). Friedl's "Mastering Regular Expressions" cites multiple different programs using each of those, every one of which behaves a bit differently when you start poking at corner cases. And that's just in the open-source world; I don't know what Oracle is using, but I bet it ain't open source. > I am also surprised that you say the (\1)+ subpattern is computationally > expensive. Regular expressions are greedy by default. I.e. in case of a* > matching against a string of 1000 a's, the system will not try a, aa, aaa, > ... and so on, right? Instead, it will consume all the a's in one go. "a*" is easy. "(a*)\1" is less easy --- if you let the a* consume the whole string, you will not get a match, even though one is possible. In general, backrefs create a mess in what would otherwise be a pretty straightforward concept :-(. regards, tom lane
> On Aug 20, 2021, at 9:52 AM, Tom Lane <tgl@sss.pgh.pa.us> wrote: > > "a*" is easy. "(a*)\1" is less easy --- if you let the a* consume the > whole string, you will not get a match, even though one is possible. > In general, backrefs create a mess in what would otherwise be a pretty > straightforward concept :-(. The following queries take radically different time to run: \timing select regexp_replace( repeat('someone,one,one,one,one,one,one,', 60), '(?<=^|,)([^,]+)(?:,\1)+(?=$|,)', '\1', -- replacement 'g' -- apply globally (all matches) ); Time: 16476.529 ms (00:16.477) select regexp_replace( repeat('someone,one,one,one,one,one,one,', 60), '(?<=^|,)([^,]+)(?:,\1){5}(?=$|,)', '\1', -- replacement 'g' -- apply globally (all matches) ); Time: 1.452 ms The only difference in the patterns is the + vs. the {5}. It looks to me like the first pattern should greedily match five",one" matches and be forced to stop since ",someone" doesn't match, and the second pattern should grab the five ",one"matches it was told to grab and not try to grab the ",someone", but other than that, they should be performing thesame work. I don't see why the performance should be so different. — Mark Dilger EnterpriseDB: http://www.enterprisedb.com The Enterprise PostgreSQL Company
The following queries take radically different time to run:
repeat('someone,one,one,one,one,one,one,', 60),
'(?<=^|,)([^,]+)(?:,\1){1,20}(?=$|,)',
'\1', -- replacement
'g' -- apply globally (all matches)
);
> On Aug 20, 2021, at 12:51 PM, Miles Elam <miles.elam@productops.com> wrote: > > Unbounded ranges seem like a problem. Seems so. The problem appears to be in regcomp.c's repeat() function which handles {1,SOME} differently than {1,INF} > Seems worth trying a range from 1 to N where you play around with N to find your optimum performance/functionality tradeoff.{1,20} is like '+' but clamps at 20. For any such value (5, 20, whatever) there can always be a string with more repeated words than the number you've chosen,and the call to regexp_replace won't do what you want. There is also an upper bound at work, because values above255 will draw a regex compilation error. So it seems worth a bit of work to determine why the regex engine has badperformance in these cases. It sounds like the OP will be working around this problem by refactoring to call regexp_replace multiple times until allrepeats are eradicated, but I don't think such workarounds should be necessary. — Mark Dilger EnterpriseDB: http://www.enterprisedb.com The Enterprise PostgreSQL Company
"Markhof, Ingolf" <ingolf.markhof@de.verizon.com> writes:
> thank you very much for your reply. Actually, I was assuming all these
> regular expressions are based on the same core implementation.
They are not. There are at least three fundamentally different
implementation technologies (DFA, NFA, hybrid). Friedl's "Mastering
Regular Expressions" cites multiple different programs using each
of those, every one of which behaves a bit differently when you start
poking at corner cases. And that's just in the open-source world;
I don't know what Oracle is using, but I bet it ain't open source.
> I am also surprised that you say the (\1)+ subpattern is computationally
> expensive. Regular expressions are greedy by default. I.e. in case of a*
> matching against a string of 1000 a's, the system will not try a, aa, aaa,
> ... and so on, right? Instead, it will consume all the a's in one go.
"a*" is easy. "(a*)\1" is less easy --- if you let the a* consume the
whole string, you will not get a match, even though one is possible.
In general, backrefs create a mess in what would otherwise be a pretty
straightforward concept :-(.
regards, tom lane
Verizon Deutschland GmbH - Sebrathweg 20, 44149 Dortmund, Germany - Amtsgericht Dortmund, HRB 14952 - Geschäftsführer: Detlef Eppig - Vorsitzender des Aufsichtsrats: Francesco de Maio
'one,one,one,two,two,three,three',
'([^,]+)(,\1)?($|,)',
'\1\3',
'g'
) as res;
Ingolf Markhof <ingolf.markhof@de.verizon.com>
International Network Product - International Access <INP-IntlAccess@verizon.com>
Sebrathweg 20, 44149 Dortmund, GermanyOffice: +49 231 972 1475 | Vnet: 317-1475
Hi Tom,thank you very much for your reply. Actually, I was assuming all these regular expressions are based on the same core implementation. Interestingly, this doesn't seem to be true...I am also surprised that you say the (\1)+ subpattern is computationally expensive. Regular expressions are greedy by default. I.e. in case of a* matching against a string of 1000 a's, the system will not try a, aa, aaa, ... and so on, right? Instead, it will consume all the a's in one go. Likewise, I was expecting that the system would eat all the repetitions of a word in one go. Your proposal to use (\1)? instead at the first glance seems to require more effort, because the same word and it's matching successor will need to be matched again and again and again. Roughly, 2N matches are to be done instead of just N.However, you are perfectly right: When I use (\1)? instead of (\1)+, the expression is evaluates quickly!Thank you very much for looking into this and for proposing the alternative approach which is working fine.RegardsIngolfOn Fri, Aug 20, 2021 at 12:42 AM Tom Lane <tgl@sss.pgh.pa.us> wrote:"Markhof, Ingolf" <ingolf.markhof@de.verizon.com> writes:
> BRIEF:
> regexp_replace(source,pattern,replacement,flags) needs very (!) long to
> complete or does not complete at all (?!) for big input strings (a few k
> characters). (Oracle SQL completes the same in a few ms)
Regexps containing backrefs are inherently hard --- every engine has
strengths and weaknesses. I doubt it'd be hard to find cases where
our engine is orders of magnitude faster than Oracle's; but you've
hit on a case where the opposite is true.
The core of the problem is that it's hard to tell how much of the
string could be matched by the (,\1)* subpattern. In principle, *all*
of the remaining string could be, if it were N repetitions of the
initial word. Or it could be N-1 repetitions followed by one other
word, and so on. The difficulty is that since our engine guarantees
to find the longest feasible match, it tries these options from
longest to shortest. Usually the actual match (if any) will be pretty
short, so that you have O(N) wasted work per word, making the runtime
at least O(N^2).
I think your best bet is to not try to eliminate multiple duplicates
at a time. Get rid of one dup at a time, say by
str := regexp_replace(str, '([^,]+)(,\1)?($|,)', '\1\3', 'g');
and repeat till the string doesn't get any shorter.
I did come across a performance bug [1] while poking at this, but
alas fixing it doesn't move the needle very much for this example.
regards, tom lane
[1] https://urldefense.proofpoint.com/v2/url?u=https-3A__www.postgresql.org_message-2Did_1808998.1629412269-2540sss.pgh.pa.us&d=DwIBAg&c=udBTRvFvXC5Dhqg7UHpJlPps3mZ3LRxpb6__0PomBTQ&r=ivZWA-ECVj3XrXBe0obDwKY7Ui7K5Nj9oD2KKWLm0Bw&m=q11bVTHCxVx8BQu2pjn6-3nOY8aN8hORXofVK38HqF8&s=hJxrzmTT6G7AUomoeFgh0IGDO3NcUP4gB9kvYHnt3m0&e=
Ingolf: On Mon, Aug 23, 2021 at 2:39 PM Markhof, Ingolf <ingolf.markhof@de.verizon.com> wrote: > Yes, When I use (\1)? instead of (\1)+, the expression is evaluated quickly, but it doesn't return what I want. Once aword is written, it is not subject to matching again. i.e. > select regexp_replace( --> remove double entries > 'one,one,one,two,two,three,three', > '([^,]+)(,\1)?($|,)', > '\1\3', > 'g' > ) as res; > ... > Honestly, this behaviour seems to be incorrect for me. Once the system replaces the first two 'one,one,' by a single 'one,',I'd expect to match this replaced one 'one,' with the next 'one,' following, replacing these two by another, single'one,', again... I think your expectation is misguided. All the regexp engines I've used do it this way, when asked to match "g"lobally they do non-overlapping matches, they do not substitute and recurse with the modified string. Also, your way opens the door to run-away or infinite loops ( rr('a','a','aa','g') or rr('a','a','a','g'), not to speak of r('x','','','g') ). Even a misguided r(str, '_+','_','g'), used sometimes to normalize space runs and similar things, can go into a loop. Francisco Olarte.
Ingolf:
On Mon, Aug 23, 2021 at 2:39 PM Markhof, Ingolf
<ingolf.markhof@de.verizon.com> wrote:
> Yes, When I use (\1)? instead of (\1)+, the expression is evaluated quickly, but it doesn't return what I want. Once a word is written, it is not subject to matching again. i.e.
> select regexp_replace( --> remove double entries
> 'one,one,one,two,two,three,three',
> '([^,]+)(,\1)?($|,)',
> '\1\3',
> 'g'
> ) as res;
>
...
> Honestly, this behaviour seems to be incorrect for me. Once the system replaces the first two 'one,one,' by a single 'one,', I'd expect to match this replaced one 'one,' with the next 'one,' following, replacing these two by another, single 'one,', again...
I think your expectation is misguided. All the regexp engines I've
used do it this way, when asked to match "g"lobally they do
non-overlapping matches, they do not substitute and recurse with the
modified string.
Also, your way opens the door to run-away or infinite loops (
rr('a','a','aa','g') or rr('a','a','a','g'), not to speak of
r('x','','','g') ). Even a misguided r(str, '_+','_','g'), used
sometimes to normalize space runs and similar things, can go into a
loop.
Francisco Olarte.
Verizon Deutschland GmbH - Sebrathweg 20, 44149 Dortmund, Germany - Amtsgericht Dortmund, HRB 14952 - Geschäftsführer: Detlef Eppig - Vorsitzender des Aufsichtsrats: Francesco de Maio