Paris-Brest-Paris 2023

August 20, 2023

It’s 8:45 pm on a balmy Sunday evening, and I’m ready to head out on a cycle. No ordinary spin mind, it's the 2023 edition of Paris-Brest-Paris, the oldest continuously running cycling event, a 1200 km cycle from the edge of Paris, to Brest, and back again. Non-stop. Inside 90 hours. It’s a tall ask, and I’m genuinely nervous, but pretty excited too. I’ve spent a long time getting to this point - but I’ll write about that separately.

Start Line

At this point of the evening, most of the 7000 odd participants have rolled out in groups of 250, starting at 4pm. Myself and Deck McGrath are here with a bunch of 150 or so and slowly making our way through the bike-check that happens at the start, as well as getting our first stamp on our brevet card. The crowds watching have thinned out by now, but there’s still a few to see us off. The hooter goes, and we’re underway.

The adrenalin is off-the-scale at this stage. The reality is that neither myself nor Deck have much experience with cycling in large groups, but we know enough that we need to stay out of trouble. At the same time, sticking with a bunch will keep our average speeds up. We settle for concentrating on avoiding crowds for the first 30 minutes or so until the crowd has thinned out, before trying to sit on the back of stable and steady-looking groups.

The event starts in a suburb of Paris called Rambouillet, and aside from some cobbles on the exit from the park, the road surfaces are incredibly good. We’d been told that surfaces would be good, but this had to be felt to be believed. The intense heat earlier in the day has eased off, and there’s a little bit of daylight left for the first 50 km or so, so truth be told, this might be the easiest cycling I’ve ever managed. We’re sitting in groups, taking turns to break the wind. The initial nervousness and tension has eased off, and I get chatting to a Scot living in Singapore and an Englishman living in France - indeed within a few km of the route.

Our average speed is closer to 25 kmph, way faster than planned, but it hardly feels like we’re expending any effort. The first stop is a roadside pop-up stall when we get some water and take a nature break. This does have the effect of breaking up the group we had been sitting with, but it turns out that forming new groups is pretty easy and we make steady progress until the first services stop in Mortagne-au-Perche at about 120 km. After all the horror stories about overwhelmed services and controls, we were pleasantly surprised with how well this was run. Plenty of room, no queues for coffee, water or toilets. We didn’t faff around much here - drank our coffee, ate some snacks and hit the road again. We did say a quick hello to Caroline from Audax Ireland who had already made up the 15 minute gap on us, having started in the last group.

Back out on the road, and we’re really flying now. We’re sitting in groups, but not pushing too hard. We spent a good while behind two very-steady Brazilian riders, chatted to some Americans briefly and swapped positions on the road with Caroline as the cornfields passed by. Truly, the route felt more downhill than flat and we’re less than 20km from the first control and things were looking great.

Deck calls that he has a puncture, so we pull in to the side to give ourselves some space to get it sorted. It isn’t quite daylight yet, so head-torches are on and we set to work. The Gatorskins are hard to work with, but eventually the tube is back in and I start pumping. Something isn’t right - the tube isn’t inflating despite repeated efforts to make sure the valve is connected to the pump properly. Out comes the tube again for a closer inspection, and it appears that somehow I’ve managed to give it a pinch-flat while putting it back into the wheel. So onto tube number two, being as careful as possible, but it appears I repeat the trick. We’re two tubes down now, and time is ticking on, and we’re over 30 mins on the side of the road. The groups of cyclists passing have significantly reduced, but we’re looking for a plan B. I start calling out for a spare tyre, more in hope than expectation, as it's about the only thing I can think of that we could try next. As if by miracle, within maybe 10 mins of calling to groups, a Japanese cyclist based in Germany stops and hands us a fresh new tyre. I get to work, and get the new tyre on, with a fresh tube. But unbelievably, the same thing happens. We’re over an hour on the side of the road now, there aren’t many cyclists passing at all now.

It’s daylight, and we considered calling into a nearby house to see if they could give Deck a lift to the control, but it’s barely 6am, so that was ruled out. In the end, Deck starts off walking the bike to the control. I pack up the tools and tubes and start on my way. But just before I get on the bike, I spot a van and flag it down. “Vous parlez Anglais?” - “Non!” I use my very best Junior Cert French in an attempt to explain the situation and ask him to stop Deck up the road and give him a lift to the control. I even wrote down a note for Deck to explain the story. The driver heads on and I start cycling, but I spot Deck just up the road. “Did the van driver not stop for you?” “What van driver?” It would appear the van driver thought I was mentally unhinged, or just didn’t understand me. Either way, he wasn’t going to stop and pick up a random cyclist. So the next plan - we’re onto D or E at this stage - is for me to take Deck’s rear wheel to the control, get it fixed, and somehow get it back to him. I cycled about 15km with a wheel in my hand, and made it to the control at Villianes-la-Juhel. I explain the situation to the mechanic on duty, and he sets to work. I try to find some officials to see if they can help. And because we’re very much at the back of the pack, and there are fewer people around, they’re happy to help. In between my broken French and their broken English, one man agrees to drive the wheel back to Deck. We rendezvous at the mechanic’s stall and I give Deck a call to see where he is. As luck would have it, a bar owner in the village of St-Paul-La-Gaultier took pity on Deck as he was passing and insisted he stop to rest and have a coffee. So we know exactly where he is, and the wheel is on the way back to him.

I wasn’t too sure what I should do at that point, but I knew I would have plenty of time to kill. I put on my flip-flops and got out of my cycling shoes. I’ve had bad problems with sore toes on the longer audaxes, so this was my attempt to keep my feet cooler and freer while stopped at a control. It worked. No feet problems over the entire trip.

I ate some food at the canteen, filled my bottles, got the all-important card stamped, and then I waited. It felt like an eternity. All the time we had built-up over the first 200 km was now gone, and we were falling behind schedule. Still though, if the man in the van could find Deck, and he got back on track, we’d still be in the game.

And so it proved to be. Deck arrived in, and I helped him get some quick food, filled the bottles, stamped the card and headed out back on the road. We bumped into a few of the Irish crew in the restaurant here, but I can’t remember the names. The difference was that they had stopped for a few hours of sleep and were playing a different game to us, schedule-wise!

I honestly wasn’t too sure how to feel at this stage. We’d lost about 3 hours in total, but we were only maybe 1 hour down on our plan. The main thing was that we were still in the game, and still moving. Having lost so much time, there weren’t nearly as many cyclists on the road. We made the best of this, and used them as targets to catch and would then sit behind them for a little while, occasionally working as small groups. The sun was well up by now, and it was starting to get warm. The high-vis gilet was discarded and sun-cream applied at the pop-up stalls in Le Ribay, with a mental note added to make this a longer stop in 2027!


We made good time to Fougeres, and up the hill to the control. Again, being back-markers, we weren’t encountering queues so we fed and watered ourselves quickly and got back on the road. Even in the best of circumstances, we couldn’t afford to waste time at the controls, but we were now up against it to make the control closing times all the way to Brest. It was hot leaving Fougeres, but we kept going well, and still reeled in other cyclists all the way to Tinténiac. It was here we encountered something new - crowds. Not enough to slow us down, but rather enough to cheer us up and prove that we were making good progress. Working through the hottest part of the day had taken its toll somewhat, and coupled with the fact it was now Monday afternoon, almost 30 hours since we woke up, and with 300 km in our legs, a break was called for. We found some space in a quiet hallway, and lied down on the floor. I set an alarm for 30 mins, but didn’t really think I’d manage any sleep. As suddenly as I lied down, I was jolted awake by the alarm. Turns out that I was indeed tired. But the ‘microsleep’ worked wonders, and we were two well refreshed cyclists as we rolled out of the control. The weather had cooled a little, and we hit for Loudeac.

Along The way

We skipped the services at Tinteniac, and hit Loudeac at around 11pm, and by now, back on schedule. Loudeac was busy - proper busy - as many people target it for a longer stop, and drop-bag services. Again, the sight of a busy control rejuvenated us somewhat. We had some food, and got back on the road. The road was busier now. We had company pretty much all the time as far as the secret control in Canihuel just after 2 am, and we pushed onto our 1st planned sleep stop at the services in St Nicholas. I was a bit disappointed with the food options, but in hindsight, expecting a hot meal at 4am was a bit presumptuous. I had yet another baguette before looking for the dorms. Luckily there was still some space, and we asked to be woken in 2 hours. It could well have been a bed of nails, but it felt like the most comfortable sleep I had ever had. Again, it felt like I was woken instantly by the volunteer, and it took me a little while and a coffee to feel somewhat normal. Even on schedule, we were going to be tight to make the cut-off for the next control at Carhaix. I got up to speed a little quicker than Deck, and pushed onto Carhaix. The sun had risen now and I was feeling great. I got into Carhaix before Deck. Not far enough to get food for us both, but enough to find the actual control for stamping the cards. Carhaix felt a bit disjointed as a control, with food, stamping and water taps all spread out, or so it seemed at 7am with about 3 hours sleep over 2 nights. Deck rolled in and I made an executive decision to send him straight back out on the road once his card was stamped. We didn’t have time to spare, and needed to be in Brest by 1pm. He rolled out, and I decided it was time to get my gears looked at. They hadn’t been quite right for some time so I was sticking to the little ring up front. The rear derailleur wasn’t much better and changing up a gear required two shifts up and one back to get it running. Highly annoying, but not a ride-stopper. While the mechanic worked his magic, I secured some portable breakfast to carry up the roads like the decent domestique that I am, and then picked up the bike from the mechanic. Initially it appeared he had worked some magic, but a few km out the road, the old misfiring gears reared their head again. As long as it didn’t get any worse, I could live with it, but it was a problem I could have lived without.

Deck had obviously found a second wind and it took maybe 2 hours to reel him in, having given him maybe a 20 minute head start. It was odd cycling on my own, but I fell in with a Polish rider and we worked well on the now increasingly hilly terrain till I finally caught Deck on the longest climb of the cycle, maybe 50km outside Brest. We settled on getting somewhere near the top of the hill before we’d stop to eat the breakfast, and lash on the sunscreen. A couple of campervans were parked in on a lay-by and that looked like a good enough spot to stop. And what a decision that was. Up to now, we’d missed most of the roadside tables setup by families as we really didn’t have the time to stop. This set of three campervans were working together to feed and water any cyclists that passed. Nothing was too big of a deal - coffee, cake, sunscreen - they even let us use their toilet. I’d read and heard plenty about this roadside hospitality and the fact that it was what made PBP the unique event that it is. We had been so focussed on making the controls that even a 10 minute stop felt like a luxury we couldn’t afford. This was a real shame, and I decided there and then that if I do come back to PBP, I’ll be a faster cyclist that can afford to make these unplanned stops without worrying about breaking the ‘time’ bank.

We spent a good bit of time at this stop, but none of it was wasted. Sunscreen applied and pretty much constant eating to make sure we were set for the push to Brest. What felt like the longest downhill I’ve ever cycled was next on the agenda - maybe 15 km downhill, and soon we were on the outskirts of Brest, easily the worst section of the route. In between Rambouillet and Brest, for the most part, we were kings and queens of the quiet country roads, the main act in a celebration of cycling. However, for maybe the last 5 or 10km into the Brest control, we were very much a secondary act to life in a busy town. Traffic, traffic lights, tram tracks and complicated junctions were all to be negotiated before we finally pulled into the control at around 12:30 - 30 mins ahead of schedule and crucially, 30 mins before the control close time.

We were elated. Making Brest in 40 hours had been suggested as good advice long before the ACP made it mandatory as per the control close times. Our mechanical troubles of the previous morning seemed very distant. Congratulatory texts were sent and received. I had opted to stay off Whatsapp for the duration of the trip so communication to the outside world was limited to texts to Deirdre. As if she didn’t have enough to do, she kept friends and family updated on my progress too. We really did feel like we were back on track. Brest was a very busy control and we bumped into Trevor from Mayo, Martin the Irishman from Audax Bristol, as well as Caroline again. We negotiated the most complex food ordering system I’ve ever encountered at the cafeteria to get some decent food in the end. On paper, we weren't meant to spend much time here, but it was the hottest part of the day and we needed rest anyway, so we figured a small nap was in order. I slept for maybe 30 mins in the shade outside while Deck opted for a couch inside on the advice of Andrew who was worried he might have to pull out. We were back on the road by 3pm, but it was still very hot. We got through the still very urban edge of Brest before the obligatory photo on the bridge leaving town. I spent the last 2 years reading various blogs and seeing other people’s photos from this bridge, so I was delighted to have my very own.

Brest Bridge

You can read all the route profiles you like, and while I did know that the section from Brest back to Carhaix was going to be the toughest of the entire trip, the heat, the lack of sleep and the 600km in the legs meant that this section took an awful lot out of us. On paper, none of the climbs look too bad, but they just kept on coming. And because they didn’t last too long, you never really got a good momentum going. No two were ever quite the same.

It was about this time that I started putting together my wishlist for a new bike and improved gear. It’s not that I have a bad bike really, but as Deck gleefully pointed out, it was probably the worst bike at PBP. His own was in the running for second worst perhaps!. Mine was bought secondhand in 2014 with the assistance of Barry Phelan, but I don’t think he expected it to last as long as it has. The truth is I’ve been spoiled by having one of the best bike mechanics in the county keep it as well maintained as any machine at PBP. Thanks Joe Kelly!

We made it to the secret control in Playben, but again, couldn’t linger as we were tight for time to make the cut-off at Carhaix. It was evening now, and it had cooled somewhat but we never got much speed up on the tough section into Carhaix and arrived 10 mins behind the official control close time. We’d be warned often enough just to try and get the card stamped and keep moving - being behind at 1 or 2 controls was generally overlooked if we did finish on time overall. Dining options were limited somewhat at Carhaix, but we got some food into us and had a table-based micronap to try and get going into the night. Our plan called for continuing through the night before getting some sleep at Loudeac. Deck was adjusting his bags so I headed off out the road to use the facilities, as it were. Business done, I was standing waiting for Deck at the side of the road, when the phone rang. It was Deck, and he was in trouble. His gear cable had snapped, just as he was leaving the control. I told him to go find the mechanic at the control and I’d meet him there. In the end, we arrived at the mechanic’s stall at the same time, but he was all packed up as the control was closed by now. We pleaded our case, and against the advice of his partner, he agreed to meet us at his bike shop where he would attempt a repair. Luckily it was only 5 mins away, and we made our way there. One gear would have to suffice Deck in the meantime. As we waited inside the bike shop, 2 more cyclists arrived. It turned out that one of them had been told to abandon the cycle on medical advice, and his friend stayed with him. Their needs were slightly different in that they needed somewhere to store their velomobiles until they were able to arrange transport. The noises from the workshop improved and our mechanic hero returned with the bike ready to roll again. Much like our earlier puncture woes, this cost us time, perhaps an hour, but like a punch-drunk fighter, we were still standing, or still pedalling forward at least.

It was around 11pm now, but being PBP there were plenty of cyclists still around, and we formed little groups as we pushed onto the services at Gouarec. Navigation up to now had been trivial. Plenty of arrows to follow in the unlikely event that there weren’t a bunch of cyclists ahead of us on the road. So it came as a bit of a shock when after a slow climb up a hill, we encountered a road-block. For better or worse, we seemed to have a confused bunch of about 10 more cyclists with us. For the first time in the trip, the smart-phone was deployed and maps consulted. We had indeed missed a turning at the bottom on the climb. There was no option but to descend and get back on the route. At this point, a proper GPS bike computer was added to my mental shopping list, alongside double-wrapped bar tape and a decent saddle. Morale was low now. We knew we were well behind schedule and making the control close time at Loudeac wasn’t going to be likely. On reaching Gouraec, the tiredness really kicked in and I couldn’t go on. A 15 min nap wasn’t going to be enough and I let Deck know he could plough on if he wanted. Turns out he wasn’t much better and we decided to try and get a few hours sleep there. The dorms were full so I made do with some space under a table. I only felt a little self-conscious inflating my sleep mat, but I’d carried it all this way and was determined to use it. I think I managed an hour and a half or so, and when I woke to use the toilets, I could see Deck was awake at a table too. We figured we were as well off being back on the bikes, so that’s just what we did.

We were into the unknown by now. Unsure if controls would be open, whether there would be many cyclists on the road or whether they would just pack and get the train. We arrived into Loudeac with plenty of cyclists around, so we weren’t on our own at least. By now, we were with the full-value 84 hr cyclists who had started on Monday morning and were themselves on the verge of running out of time. We still managed to get our cards stamped without issue, and got something approaching breakfast in the cafe. I’d been looking forward to having a shower for a long time by now, and almost cried with relief that they were still open. Better than that, the water was still hot and there were no queues to contend with. While I knew we were well behind schedule, all I could think was that I needed some sleep. There was a concerning interaction with the man in charge of the dorms. I thought he said they were closed, but in the end we understood that they were still open for now, but the volunteers to wake us up were gone home. We settled down for a few hours of sleep, in the hope that it would deliver some clearer thinking when we awoke.

Beds in Loudeac

Three blissful hours of sleep later, we awoke to an almost deserted control, which was rapidly being dismantled. Luckily our bikes were still there and while we slept a new gear cable was installed in mine which meant I had fully functioning gears for the first time in maybe 500km. We set out on the road, not entirely sure what our plans were, other than just following the route. Uncertain if controls would be open, I called my wife to see if she could find a hotel for us somewhere en-route, in the eventuality that the controls were closed. She looked for train options too, should the legs run out. My emotions got the better of me on this call, and I had a little cry. I hadn’t realised quite how sore I was, nor how tired I was and the sight of the dismantled control had hit me hard. We weren’t going to make it back inside the time limit. Whatever chance we had, was gone. It was a bitter pill to swallow, and while I really didn’t want to quit, I knew that we had to make it back to Rambouillet somehow. And it didn’t seem like we had the legs nor the time to do that.

The one thing that was still present, however, were cyclists. We might have been ‘out of time’, but we weren’t alone. Many of the 84hr cyclists were still there, and curiously to me, still confident of making their Thursday evening cut-off time. We cycled on. If these lads could make Thursday at 6pm, maybe we would be able to make it back too. If not on time, we’d still complete the route. The legs were fine even if my bottom wasn’t. The hardest of the hills were now behind us and we kept a steady pace that Wednesday morning and afternoon through to Tinténiac. Another snooze there kept us ticking along, and the control was still open at Fougères at 10pm when we arrived. Our plan now was to sleep a few hours at this control before setting out into the night for the last 300km home. Sadly, this control was closing, and even the option of sleeping on the floor was denied to us. Brevet card stamped, we had to make a call as to what to do. It seems others in our predicament had decided on getting a hotel room and setting out the next morning. Two quick phone-calls later, and we were booked into a hotel on the edge of town. The food at the restaurant was excellent, and we carb-loaded before setting off to find our lodgings.

I wasn’t thrilled at the idea of sleeping at a hotel, but neither pressing on, nor sleeping on a grass verge at night seemed like better options. The hotel was basic, but clean as a whistle and they let us put the bikes in a meeting room for safe-keeping. Breakfast for 5am was booked and we got a decent night's sleep before setting out into the dawn. We passed our first cyclist as we headed up the hill out of town, as we wondered what the day might bring. The temptation to quit wasn’t strong, which was useful when we passed the village of Ambriere. Aside from an excellent Boulangerie, they had helpfully added handmade signs to the nearest train station for anyone looking for an easier route back to Paris!

Bail Out

The next control at Villianes was 60 km further down the road and we reached there at noon. Sadly, the timing company was in the process of removing their equipment now, and the control for stamping was long closed. I wasn’t to be deterred so I set about finding anyone who could stamp my Brevet card as proof-of-passage. In the end, the staff at the town hall did the necessary and the last few volunteers at the control found some coffee and sandwiches for us too. Two French riders joined us at the table and I found myself defending the ACP and the 90 hour limit, whereas they felt it was too harsh and more time should be allowed. I didn’t really feel expending energy on the debate and was more concerned whether I had 200km more in my legs.

In other circumstances, we would have taken some shelter from the afternoon heat, but we needed to keep pressing on. The closest thing to shelter was eating indoors at Alencon that afternoon. I’d been dreaming of a burger with chips for a while now, and the one served up gave me nearly enough calories for the last 150 km run home! Alencon was also the last realistic option to bail out and take the train. We passed, and pushed on for Mortagne. It was about now that the directional arrows that had faithfully pointed us home - apart from that one miscue earlier - began to become less prominent. Even though every rider had been given a souvenir arrow in their welcome-pack, by now perhaps the locals figured it was safe to take an arrow or two for their own personal collection. Turn-by-turn directions from Komoot in my headphones was enough to keep me on the straight and narrow, and up the hill into Mortagne-au-Perche. If the lack of signs was one indication that the event was over, then the fully-closed control was another. No timing mats, no stamps, no food even. I wasn’t going to pass through without some proof of passage though, and we hit for the main square. The young man working in the tabac was only delighted to use his Anglais, and even better, had no problem stamping and signing our cards. Only 120 km to go now and we rolled out in good spirits fuelled by Coca-Cola and got as far as Senoches at around 9pm. Alarmingly, this felt like a ghost-town with no sign of life at all. Some young kids pointed us to a mini-supermarket and I struggled to decide what food I could eat now, and what else to buy for the last 80km home. I just didn’t know what else would be open from here on in, so I bought random biscuits, some dried fruit and God knows what else. Bananas were unsurprisingly sold out. Some of this was scoffed down outside, while the local drunk tried to engage me in conversation. I was very tired, very cranky and just trying to eat some food. Still though, he kept talking, and tried to convince me that PBP was all over.

It wasn’t for me, and indeed for a few cyclists still on the road. At a crossroads maybe 20 km up the road there was a mini-convention to agree on what the correct direction was, road-signs now absent and GPS devices not all quite agreeing with each other. The next 20 km into Dreux was along some of the flattest and fastest roads I’ve ever ridden, and we got to the outskirts of Dreux in good spirits. Somehow I managed to lose Deck on the road, and I pulled in to the side to wait. And wait I did, before getting a phone-call from a slightly alarmed Deck who had lost me, navigation on his device, and more crucially, phone-signal for a while. I went back up the road, found him, and made sure he kept my wheel into the control.

Or rather, to somewhere near where the control should have been. The control was long gone, and the school which was a hive of activity over the previous 72 hours was now just a school again. While this wasn’t entirely unsurprising, it was a little discomfiting. The Subway sandwich bar next door was closed too, but the father of one of the employees struck up conversation with us and Bob, a veteran American rider who we had exchanged places on the road a little over the previous 30 km. Our predicament explained, he went to the Subway and demanded that his son pause his cleanup duties and find the stamp for our Brevet cards! Just one more before we had the set complete. Bob was in a little trouble and seemed to be bonking a bit. I threw him a pack of biscuits and almost immediately he seemed to perk up. We agreed to ride together to the finish as it was almost midnight now and any little extra company seemed like a good idea.

Over the next 30 km Bob regaled us with tales of his previous 4 PBPs, the first way back in the 80’s, and the chat shortened the route. But about 10km outside Rambouillet, things got a bit weird. It was at this time that I expected a rush of adrenalin as the finish line approached. The opposite happened - the dawning realisation that we were actually going to complete this thing actually caused both body and spirit to relax and it turns out that I had been high on adrenalin for most of the last few hours, pushing to the finish. The last 10km was a struggle. Every ache and pain that had been hiding bubbled up the surface. We slowed right down, and barely kept moving. We eventually found the park, and rolled down to the finish line. 100 hours after we had started. Tired, sore, but not broken. We’d made it. Almost 2 years of preparation for this moment, and honestly, it was more relief than anything else as the first emotion. There was one more job to do. It turned out we were too late to get stamped and receive our finishers' medals - but only by about an hour, so there was still a stamp to be procured. Bob had wisely chosen to stay at the Mercure close to the finish line, so we trundled along with him and the night porter eventually found the stamp which marked our ride as complete.

Brevet Complete

Two happy cyclists walked up the main street and made short work of the last 2 km to our hotel. Job done. We’d made it - and we were going to do it all again in 4 years time.

There's a lot of people to thank for getting me this far. Barry Phelan talked me into cycling long distances. Joe Kelly keeps the worst bike at PBP on the road. Enda Dooley was the first person to mentioned Audax to me. All of Audax Ireland have helped along the way, but a special word to Seamus O'Dowd whose calm reassurance meant I didn't give up too easily. Deck McGrath was the only one mad enough to take on the challenge with me when I put out a call for volunteers almost 2 years ago. Mike Browne and Adrian Ryan patiently listen to me talk shite about cycling.

My parents keep half an eye on me still, and there's great reassurance that my Dad would come collect me anytime, anywhere if needed. My 2 kids have been a great source of encouragement and training partners on the school runs. But above all else, I owe a great debt of thanks to Deirdre, my wife. Equal parts encouragement and cajoling with no small amount of logistical help, and picking up the pieces when I was away. Thanks!

Done and Dusted Line

© Alan Burke 2023, Built with Gatsby