not to mention that if Microsoft simply coughts up the fine indefinatley it will be raised to an amount they cannot ignore as easily
I don't think it's quite that simple. Under the law the Microsoft was prosecuted under, fines could be imposed for up to 10% of turnover or something like that.
That has (or is being) changed so it can be up to 30%
But I think to impose the higher fines will require another court case and I'm not sure they could be prosecuted for the same violations again (maybe if someone willfully disobeys a court order it's different)
(And it ought to be like this - imagine if the governments decided to multiple the fines for speeding by 10 and then reprosecute everyone previously found guilty just so they could collect more money. I would hope that the ECHR would have something to say about it)
Of course, the EU could create a new ability to fine companies 100%+ of turnover for ongoing willful disobedience of a court order and then fine based on the new law but M$ would be able to see that coming years in advance and obey just before it became law.
I suspect a lot of the difference is weight of the bike. I ride an unfaired windcheetah with rack and mudguards and a "racer" with rack and mudguards.
But I'm carrying something like 5-7kg more on the windcheetah. This is something approaching 10% more weight. And as soon as a hill gets steep enough than overcoming gravity becomes more significant than overcoming air drag that weight matters.
And you don't gain much by being fast on the descents. Assume a 70kg (rider+bike) that can sustain 350W on a 1 in 10 hill. They can vertically climb 0.5m/s so can do about 5m/s (10mph) up the hill. Make that 77kg and they can manage 4.5m/s up the hill. Now assume that the hill goes up for 10km and then down for 10km. It will take the 70kg example 2000s to ride up the hill and the 77kg example 2200s. The upright will be able to do something like 80km/h down the hill so another 450s. The recumbant rider will be able to manage something like 120km/h so 300s. So the DF is up by about 50s in about 40 minutes of riding. Put in some bends on the downhill so that terminal velocity is less of an issue and it's an even bigger advantage
I don't think it will ever be possible to make a recumbent as light as an upright. The geometry requires that the frame be stronger.
You can put more power in on a recumbent but that is rarely the limiting factor. On the windcheetah I can break the back wheel free when starting and can "spin" the back wheel if I hold the brakes on (it's not really spin, more like turn the pedals) even on the best of surfaces. On an upright you can put your full weight on the pedal without the rear wheel slipping unless the ground is slippery.
So how much of this tax will open source authors get?
After all, their work is copyright and some of us backup regularly. I probably have 20-30 copies of 5000+ copyright open source apps on my DVD backups. (I only do full backups once per month otherwise that 20-30 would be much higher)
And, to top it all off, 99%+ of all the calls that I've seen interfere with real life have been completely pointless. I've never heard someone say "OK I'll be at the firehouse in 20 mins" and rush off. Never "I'll be in surgery ASAP." It's always "I can't believe she said that, what a bitch!" or "No, you can't eat any ice cream. Put your sister on the phone." And every time the subject comes up, it's all about the poor doctors, firemen and crucial IT projects.
I have once. I'm not sure whether the police called the caretaker who interrupted the rehersal or whether he had left his phone with the caretaker. Either way, his phone didn't interrupt the rehersal, an emergency did.
So for 600nm (red) light, and a 6mm pupil with a viewing distance of 1m there is a theoretical resolving of dots separated by about 0.1mm.
In practice, the eye won't give this limit but I wouldn't be surprised if the human eye only misses this by a factor of about 2. (I would also expect that birds of prey probably come pretty close to the theoretical limit)
And if you'd read Knuth you would know that the FFT can be done entirely in integers. It's in the section "how fast can we multiply". IIRC the "all integer convolution algorithm" is set as one of the problems.
Knuth derives an upper bound on the required number of bits for each integer which (IMO) comes out surprisingly low.
I've got a sony ericsson with about 10million functions I don't want. My first call was made on 17th June 05 to "Bolt ons" - I was turning some automatic facility off. My first proper call was made on 8th October and I've made 7 "proper calls" in total. My last three calls were to "voicemail on", "voicemail off", "voicemail" when I accidentally called voicemail and then needed to turn it off again. (I generally don't even use the phone book, preferring to know the numbers I need to call)
I've had to charge up the phone once (other than immediately after I bought it) and that only because I accidentally left it turned on in my bag.
Very occasionally I've also turned it on because I'm expecting a call. But I find it embarrassing to have my phone go off and interrupt while I'm supposed to be with someone else or have it go off on a train and annoying when someone elses does. (ditto watches that beep every hour although that fad at least seems to have gone for the most part - don't think my watch even has an hourly chime although it can be set up to alarm if my pulse rate goes above or below a preset threshold and I'm wearing the chest strap)
You're walking down the highstreet on a Saturday morning and a shop you want to visit has a "closed" sign up. Do you A) try the door anyway on the assumption that the owner has forgotten to change the sign around or B) say "oh well, obviously closed"
And if you try the door and find that you can open it because the lock is faulty but the shop really is closed do you A) keep quiet about it or B) tell the shop owner that their door lock is faulty.
(and note also that it's very common for people to push, pull, push doors to shops when the door is stiffer than they expect and they can't work out which way it opens)
Something very similar to this happened to a friend of mine. He went out one lunchtime to buy some sandwiches and went into the bakery. There were several other people in the shop. After about 15 minutes of no service they began to wonder what was going on - only then someone noticed that the door was "locked" but the bolt wasn't engaged so rather than the lock preventing the door from being opened, it was preventing the door from fully closing.
(at which point the owner returned - having completely run out of change and had to make an emergency dash to the bank - so the question of whether to leave the money on the counter or not buy anything became moot)
Wrong. A faraday cage _has_ to be a completely closed structure. Even a tiny gap is enough for it to not totally exclude radiation.
Example: I've got a stainless steel fridge. Yet when I was worried about it's temperature, a battery powered "weather station" outdoors transmitter was perfectly sufficient to send a signal to the weather station at the other side of the house from inside the closed fridge.
But when thinking about then encoding on the disk it can make sense to consider it as pits and flats as there are certain clever features that are lost if you just think of it at the EFM level. (see for example http://www.laesieworks.com/digicom/Storage_CD_8to1 4.html)
It gets more complicated because the signal is (approximately) DC free - there are three merge bits between every 14bit code word that can be chosen at random (provided the other requirements of the encoding are met[1]) and _should_ (not always are) be chosen so that the DC content of the signal is kept as close to zero as possible. This doesn't make sense when thinking about transitions as being a 1 and non transitions being a 0 because because of [1] there must be at least 2x as many non transitions as transitions
[1] A pit (or flat) must be at least 3 bits long and no more than (I think) 14 bits long. (this means the data can be self clocking)
The encoding on the disk involves converting 192 bits of data to 588 bits of pit/flat. Because there are always at least 3 bits (pit/flat) the same together, the final bandwidth of the signal recorded on the disk is only 2% higher than the bandwidth required to transmit the original data despite the fact that there is masses of error correction on the disk. (This is a rather beautiful application of a theorem of Shannon that states that you can add as much error correction as you like to a signal with an arbitrarily small increase in bandwidth required to transmit it - [for various limitations like infinitely long data stream etc which a CD only approximates])
October 25 2004 - The TUC is continuing its campaign for three new bank holidays to bring British workers' public holiday entitlement up to the European average of 11 days.
Does the Government have any plans to ensure that employers do not include bank holidays as part of the 20 days statutory annual leave entitlement?
The Government proposed in its 2005 election manifesto that during its third term in office it would extend the entitlement to 4 weeks annual leave making it additional to time equivalent to bank holidays. As with the existing entitlement this would be on a pro-rata basis for those working part time. As a first step, the Government has taken an enabling power in the Work and Families Bill 2005. A full and extensive consultation with stakeholders, in line with better regulation principles, will be undertaken before any detailed changes are proposed in order to ensure proposals take full account of all the issues involved including the wide variety of flexible and non-standard working patterns that exist.
Unfortunately, this is wrong. In the UK Statutory minimum leave is 20 days including bank holidays. (I'm in the UK and I get 15 days leave plus 8 days bank holidays.)
I believe that the rest of the EU gets 20days + bank holidays and IIRC this Government promised that if they won the last election they would increase the UK holidays to the same but it hasn't happened yet.
I'd agree with you.. except I'm trying not to injure my knee again. I can manage running and using a stationary bike if I'm careful, but I don't know how well I'd do at real-world biking at this point.
Keep in a low gear and make sure your saddle is high enough. Most people seem to ride in too low a gear (you need a cadence of at least 80) with a too low saddle (good approximation is that you should be able to put your heel on the pedal with your leg extended). Saddle too low and cadence too low are both bad for the knees. (Saddle too high can be bad for the hips but very few people ride with a saddle too high)
Cycling is a very low impact exercise and ought to be better for your joints than running.
Nope. In order to generate X-rays you need to accelerate the electrons to >30kev before they hit the target. This requires a vacuum between the cathode and the anode target.
In a gas the electrons will never reach more than a few tens ev. As they accelerate they strike another atom and their energy goes in ionizing the gas.
Your calculations are wrong. (using your figures) Transmission efficiency * transformer efficiency * charging efficiency * storage to motor efficiency * drivetrain efficiency =.7*.95*.8*.85*.95 =.43 (57% loss)
This is better than pump to wheel for an IC engine powered car.
I don't have, and can't find, the figures for refining crude but I've seen claims that the cost of refining a barrel of oil in 2004 was $10 so I'll assume 25% loss.
Gas fired electricity plants say 50% efficient. (probably can do better).43*.5 = 22% efficiency for an electric car powered by gas fired powerstation..3*.75 = 23% efficiency for a gasoline powered car. (Not sure what you meant when you said "Right there is enough, to make them equal" with regards to the 25-30% losses in transmission - this is losses in transmission, but efficiency for a car - read about the air otto cycle in any undergraduate thermodynamics textbook if you really think cars are getting 70-75% thermal efficiency)
The best you are ever going to get from an IC engine is about 50% efficiency - the biggest marine diesels can just exceed 50% thermal efficiency when run in their most efficient configuration.
Push that powerstation efficiency up to 60% and you are going to struggle to build an IC engined car that doesn't have more losses in the car than the entire energy chain has for the electric car.
2) Why? There are plenty of good roads. The surface quality of British roads is deteriorating (and due to our below freezing nights and above freezing days in winter they have always suffered a lot from frost damage in winter anyway) but, on the whole, so long as you stay more than about 75cm from the curb or edge of the road where there is no pavement (sidewalk) the surface is usually perfectly servicable. (I cycle almost everywhere and so long as you keep of the cycle routes and cycle lanes and on the road proper - cycle routes are usually gravel tracks and cycle lanes are usually the 1m of surface right at the edge of the road where potholes breed - you can easily and comfortably cycle at 30km/h (20mph) on 22mm tyres at 120psi - hills permitting:-) )[1]
For all intents and purposes, you can get from anywhere to anywhere in England on metalled roads. (I'd guess that's true for the whole of the UK but I don't really know Scotland outside of the major cities.
And while the famous Washington is up in the North East on the Tyne and Wear, there's also one down near the south coast. Neither of these are particularly close (for English towns) to Boston etc.
Slashdot Mirror
not to mention that if Microsoft simply coughts up the fine indefinatley it will be raised to an amount they cannot ignore as easily
I don't think it's quite that simple. Under the law the Microsoft was prosecuted under, fines could be imposed for up to 10% of turnover or something like that.
That has (or is being) changed so it can be up to 30%
But I think to impose the higher fines will require another court case and I'm not sure they could be prosecuted for the same violations again (maybe if someone willfully disobeys a court order it's different)
(And it ought to be like this - imagine if the governments decided to multiple the fines for speeding by 10 and then reprosecute everyone previously found guilty just so they could collect more money. I would hope that the ECHR would have something to say about it)
Of course, the EU could create a new ability to fine companies 100%+ of turnover for ongoing willful disobedience of a court order and then fine based on the new law but M$ would be able to see that coming years in advance and obey just before it became law.
Tim.
Dunno what UK you've been to, but in my UK we do things the US way. 1,000,000,000 is almost always a billion.
And even when it wasn't (1970's and before?) 1,000,000,000 was a thousand million.
I've never heard milliard used in the UK.
Tim.
I suspect a lot of the difference is weight of the bike. I ride an unfaired windcheetah with rack and mudguards and a "racer" with rack and mudguards.
But I'm carrying something like 5-7kg more on the windcheetah. This is something approaching 10% more weight. And as soon as a hill gets steep enough than overcoming gravity becomes more significant than overcoming air drag that weight matters.
And you don't gain much by being fast on the descents.
Assume a 70kg (rider+bike) that can sustain 350W on a 1 in 10 hill.
They can vertically climb 0.5m/s so can do about 5m/s (10mph) up the hill.
Make that 77kg and they can manage 4.5m/s up the hill.
Now assume that the hill goes up for 10km and then down for 10km. It will take the 70kg example 2000s to ride up the hill and the 77kg example 2200s.
The upright will be able to do something like 80km/h down the hill so another 450s. The recumbant rider will be able to manage something like 120km/h so 300s.
So the DF is up by about 50s in about 40 minutes of riding. Put in some bends on the downhill so that terminal velocity is less of an issue and it's an even bigger advantage
I don't think it will ever be possible to make a recumbent as light as an upright. The geometry requires that the frame be stronger.
You can put more power in on a recumbent but that is rarely the limiting factor. On the windcheetah I can break the back wheel free when starting and can "spin" the back wheel if I hold the brakes on (it's not really spin, more like turn the pedals) even on the best of surfaces. On an upright you can put your full weight on the pedal without the rear wheel slipping unless the ground is slippery.
Tim.
So how much of this tax will open source authors get?
After all, their work is copyright and some of us backup regularly. I probably have 20-30 copies of 5000+ copyright open source apps on my DVD backups. (I only do full backups once per month otherwise that 20-30 would be much higher)
Tim.
And, to top it all off, 99%+ of all the calls that I've seen interfere with real life have been completely pointless. I've never heard someone say "OK I'll be at the firehouse in 20 mins" and rush off. Never "I'll be in surgery ASAP." It's always "I can't believe she said that, what a bitch!" or "No, you can't eat any ice cream. Put your sister on the phone." And every time the subject comes up, it's all about the poor doctors, firemen and crucial IT projects.
I have once. I'm not sure whether the police called the caretaker who interrupted the rehersal or whether he had left his phone with the caretaker. Either way, his phone didn't interrupt the rehersal, an emergency did.
Tim.
For small angles:
theta = lambda/D
where D is the aperture size.
So for 600nm (red) light, and a 6mm pupil with a viewing distance of 1m there is a theoretical resolving of dots separated by about 0.1mm.
In practice, the eye won't give this limit but I wouldn't be surprised if the human eye only misses this by a factor of about 2. (I would also expect that birds of prey probably come pretty close to the theoretical limit)
Tim.
You aren't reading it properly.
For example. (and this is why they don't supply the figures)
last year Windows had 15 minutes of uptime, 365 days of downtime. Linux had 365 days of uptime and no downtime.
This year Windows had 18 minutes of uptime, 365 days of downtime, Linux had 365 days of uptime and no downtime.
Windows has 20% MORE uptime this year.
Tim.
I wrote it a long time ago and haven't looked at it since but have a look at
http://www.locofungus.btinternet.co.uk/calc/
Javascript based calculator that will convert from ATM bandwidth to Application bandwidth for a PPPoATM connection.
Has the constants predefined.
Allows you to decrease the MTU and see the benefit
Tim.
And if you'd read Knuth you would know that the FFT can be done entirely in integers. It's in the section "how fast can we multiply". IIRC the "all integer convolution algorithm" is set as one of the problems.
Knuth derives an upper bound on the required number of bits for each integer which (IMO) comes out surprisingly low.
I've got a sony ericsson with about 10million functions I don't want.
My first call was made on 17th June 05 to "Bolt ons" - I was turning some automatic facility off. My first proper call was made on 8th October and I've made 7 "proper calls" in total. My last three calls were to "voicemail on", "voicemail off", "voicemail" when I accidentally called voicemail and then needed to turn it off again. (I generally don't even use the phone book, preferring to know the numbers I need to call)
I've had to charge up the phone once (other than immediately after I bought it) and that only because I accidentally left it turned on in my bag.
Very occasionally I've also turned it on because I'm expecting a call. But I find it embarrassing to have my phone go off and interrupt while I'm supposed to be with someone else or have it go off on a train and annoying when someone elses does. (ditto watches that beep every hour although that fad at least seems to have gone for the most part - don't think my watch even has an hourly chime although it can be set up to alarm if my pulse rate goes above or below a preset threshold and I'm wearing the chest strap)
Tim.
You're walking down the highstreet on a Saturday morning and a shop you want to visit has a "closed" sign up. Do you A) try the door anyway on the assumption that the owner has forgotten to change the sign around or B) say "oh well, obviously closed"
And if you try the door and find that you can open it because the lock is faulty but the shop really is closed do you A) keep quiet about it or B) tell the shop owner that their door lock is faulty.
(and note also that it's very common for people to push, pull, push doors to shops when the door is stiffer than they expect and they can't work out which way it opens)
Something very similar to this happened to a friend of mine. He went out one lunchtime to buy some sandwiches and went into the bakery. There were several other people in the shop. After about 15 minutes of no service they began to wonder what was going on - only then someone noticed that the door was "locked" but the bolt wasn't engaged so rather than the lock preventing the door from being opened, it was preventing the door from fully closing.
(at which point the owner returned - having completely run out of change and had to make an emergency dash to the bank - so the question of whether to leave the money on the counter or not buy anything became moot)
Tim.
Wrong. A faraday cage _has_ to be a completely closed structure. Even a tiny gap is enough for it to not totally exclude radiation.
Example: I've got a stainless steel fridge. Yet when I was worried about it's temperature, a battery powered "weather station" outdoors transmitter was perfectly sufficient to send a signal to the weather station at the other side of the house from inside the closed fridge.
Tim.
True
1 4.html)
It's the transitions that are detected.
But when thinking about then encoding on the disk it can make sense to consider it as pits and flats as there are certain clever features that are lost if you just think of it at the EFM level. (see for example http://www.laesieworks.com/digicom/Storage_CD_8to
It gets more complicated because the signal is (approximately) DC free - there are three merge bits between every 14bit code word that can be chosen at random (provided the other requirements of the encoding are met[1]) and _should_ (not always are) be chosen so that the DC content of the signal is kept as close to zero as possible. This doesn't make sense when thinking about transitions as being a 1 and non transitions being a 0 because because of [1] there must be at least 2x as many non transitions as transitions
[1] A pit (or flat) must be at least 3 bits long and no more than (I think) 14 bits long. (this means the data can be self clocking)
The encoding on the disk involves converting 192 bits of data to 588 bits of pit/flat. Because there are always at least 3 bits (pit/flat) the same together, the final bandwidth of the signal recorded on the disk is only 2% higher than the bandwidth required to transmit the original data despite the fact that there is masses of error correction on the disk. (This is a rather beautiful application of a theorem of Shannon that states that you can add as much error correction as you like to a signal with an arbitrarily small increase in bandwidth required to transmit it - [for various limitations like infinitely long data stream etc which a CD only approximates])
Tim.
and http://www.hrmguide.co.uk/rewards/public_holidays. htm:
October 25 2004 - The TUC is continuing its campaign for three new bank holidays to bring British workers' public holiday entitlement up to the European average of 11 days.
Tim.
PUBLIC HOLIDAYS IN EU MEMBER STATES 2005
http://www.ibeurope.com/Factfile/44hols.htm
This includes Saturdays but not Sundays. No UK bank holiday ever falls on a Saturday or Sunday.
Tim.
The DTI disagrees with you:
http://www.dti.gov.uk/er/bankfaq.htm
Does the Government have any plans to ensure that employers do not include bank holidays as part of the 20 days statutory annual leave entitlement?
The Government proposed in its 2005 election manifesto that during its third term in office it would extend the entitlement to 4 weeks annual leave making it additional to time equivalent to bank holidays. As with the existing entitlement this would be on a pro-rata basis for those working part time. As a first step, the Government has taken an enabling power in the Work and Families Bill 2005. A full and extensive consultation with stakeholders, in line with better regulation principles, will be undertaken before any detailed changes are proposed in order to ensure proposals take full account of all the issues involved including the wide variety of flexible and non-standard working patterns that exist.
Tim.
You should also remember that the per head costs of the health service in the UK is about half the per head costs of medical care in the US.
It would be interesting to know how rich you actually have to be before the US system looks like a better deal.
Tim.
Unfortunately, this is wrong. In the UK Statutory minimum leave is 20 days including bank holidays. (I'm in the UK and I get 15 days leave plus 8 days bank holidays.)
I believe that the rest of the EU gets 20days + bank holidays and IIRC this Government promised that if they won the last election they would increase the UK holidays to the same but it hasn't happened yet.
Tim.
I'd agree with you.. except I'm trying not to injure my knee again. I can manage running and using a stationary bike if I'm careful, but I don't know how well I'd do at real-world biking at this point.
Keep in a low gear and make sure your saddle is high enough. Most people seem to ride in too low a gear (you need a cadence of at least 80) with a too low saddle (good approximation is that you should be able to put your heel on the pedal with your leg extended). Saddle too low and cadence too low are both bad for the knees. (Saddle too high can be bad for the hips but very few people ride with a saddle too high)
Cycling is a very low impact exercise and ought to be better for your joints than running.
Tim.
Nope. In order to generate X-rays you need to accelerate the electrons to >30kev before they hit the target. This requires a vacuum between the cathode and the anode target.
In a gas the electrons will never reach more than a few tens ev. As they accelerate they strike another atom and their energy goes in ionizing the gas.
Tim.
Your calculations are wrong. (using your figures) .7*.95*.8*.85*.95 = .43 (57% loss)
.43*.5 = 22% efficiency for an electric car powered by gas fired powerstation. .3*.75 = 23% efficiency for a gasoline powered car. (Not sure what you meant when you said "Right there is enough, to make them equal" with regards to the 25-30% losses in transmission - this is losses in transmission, but efficiency for a car - read about the air otto cycle in any undergraduate thermodynamics textbook if you really think cars are getting 70-75% thermal efficiency)
Transmission efficiency * transformer efficiency * charging efficiency * storage to motor efficiency * drivetrain efficiency =
This is better than pump to wheel for an IC engine powered car.
I don't have, and can't find, the figures for refining crude but I've seen claims that the cost of refining a barrel of oil in 2004 was $10 so I'll assume 25% loss.
Gas fired electricity plants say 50% efficient. (probably can do better)
The best you are ever going to get from an IC engine is about 50% efficiency - the biggest marine diesels can just exceed 50% thermal efficiency when run in their most efficient configuration.
Push that powerstation efficiency up to 60% and you are going to struggle to build an IC engined car that doesn't have more losses in the car than the entire energy chain has for the electric car.
Tim.
1) Doesn't work:. stm
:-) )[1]
0 318&Y=182951&A=Y&Z=1
http://news.bbc.co.uk/1/hi/england/london/4867880
(signs telling people not to park where it floods - people still don't move their cars even when the locals tell them it will flood)
2) Why? There are plenty of good roads. The surface quality of British roads is deteriorating (and due to our below freezing nights and above freezing days in winter they have always suffered a lot from frost damage in winter anyway) but, on the whole, so long as you stay more than about 75cm from the curb or edge of the road where there is no pavement (sidewalk) the surface is usually perfectly servicable. (I cycle almost everywhere and so long as you keep of the cycle routes and cycle lanes and on the road proper - cycle routes are usually gravel tracks and cycle lanes are usually the 1m of surface right at the edge of the road where potholes breed - you can easily and comfortably cycle at 30km/h (20mph) on 22mm tyres at 120psi - hills permitting
For all intents and purposes, you can get from anywhere to anywhere in England on metalled roads. (I'd guess that's true for the whole of the UK but I don't really know Scotland outside of the major cities.
[1] The westbound carriageway of the Euston Road outside Kings Cross is the exception that proves this rule
http://www.streetmap.co.uk/streetmap.dll?G2M?X=53
Tim.
Incidently, one of the many New Yorks is only about 15km (10 miles) away:4 500&Y=355500&A=Y&Z=5
http://www.streetmap.co.uk/streetmap.dll?G2M?X=52
(Because of the stupid way they create the arrows there's no way to get it to point at the village instead of being on top of it)
And while the famous Washington is up in the North East on the Tyne and Wear, there's also one down near the south coast. Neither of these are particularly close (for English towns) to Boston etc.
Boston's not all that far from Cambridge (pretty much due north)
4 660&Y=344265&A=Y&Z=5
5 000&Y=295000&A=Y&Z=9
http://www.streetmap.co.uk/streetmap.dll?G2M?X=53
http://www.streetmap.co.uk/streetmap.dll?G2M?X=54
Tim.
1.
I can compress anything you give me by a factor of at least 1 (inclusive of my own output).
"-1 pedantic", I know.
It would be more pedantic if it were accurate...
Actually it could be accurate.
However, if true, the following statement is also true:
I [can] compress anything [you give me] by a factor of no more than 1 (inclusive of my own output).
The proof is left as an exercise for the reader.
At which point the algorithm becomes trivial.