Advocates for the diet recommend that it be seriously considered after two medications have failed, as the chance of other drugs succeeding is only 10%.[9][31][32] The diet can be considered earlier for some epilepsy and genetic syndromes where it has shown particular usefulness. These include Dravet syndrome, infantile spasms, myoclonic-astatic epilepsy, and tuberous sclerosis complex.[9][33]
Note: Because you'll be excluding some major food groups on the keto diet (grains, many fruits) you should definitely think about taking a multivitamin—especially one that contains folic acid, which helps your body make new cells and is often found in enriched breads, cereals, and other grain products, says Julie Upton, R.D., cofounder of nutrition website Appetite for Health.
Before starting, ask yourself what is really realistic for you, Mattinson suggests. Then get your doctor’s okay. You may also work with a local registered dietitian nutritionist to limit potential nutrient deficiencies and talk about vitamin supplementation, as you won’t be eating whole grains, dairy, or fruit, and will eliminate many veggies. “A diet that eliminates entire food groups is a red flag to me. This isn’t something to take lightly or dive into headfirst with no medical supervision,” she says.
Hi Gigi, Low carb and keto is about the balance of macronutrients eaten (fat, protein and carbs), not specifically meat or lack thereof. Most people on keto do eat meat, though some people do vegetarian keto. Fat is actually necessary for many body processes. There is no issue for the kidneys with a high fat diet, but if you eat too much protein that isn’t great for the kidneys. It’s a common misconception that keto is high protein (it isn’t). Keto is great for diabetics as it naturally helps stabilize insulin. All of this being said, please know I’m not a doctor and you should consult your doctor on any medical questions or before starting any diet. If you have more questions that aren’t medical questions, I recommend our low carb & keto support group here.

Hi Courtney, I’m currently working on a 21-Day Keto Meal Plan. Unfortunately, it’s super time-consuming. And after buying a keto cookbook yesterday and returning it the same day because it wasn’t well researched and the recipes clearly not created specifically for the Keto diet you wouldn’t want me to rush this. I want to make sure the Meal Plan is SPOT on and the recipes complement each other and make eating Keto easy. Give me another month or two and I’ll hopefully have more news on progress. Currently working on a rough sketch but still have to test all recipes and photograph them, too. You definitely don’t need nuts to be able to eat Keto. For now, I recommend to keep it as simple as possible. You can eat my 1-day meal plan 4 days a week and find other recipes you like to build another similar day and then keep switching between mine and the other.
The ketogenic diet is calculated by a dietitian for each child. Age, weight, activity levels, culture, and food preferences all affect the meal plan. First, the energy requirements are set at 80–90% of the recommended daily amounts (RDA) for the child's age (the high-fat diet requires less energy to process than a typical high-carbohydrate diet). Highly active children or those with muscle spasticity require more food energy than this; immobile children require less. The ketogenic ratio of the diet compares the weight of fat to the combined weight of carbohydrate and protein. This is typically 4:1, but children who are younger than 18 months, older than 12 years, or who are obese may be started on a 3:1 ratio. Fat is energy-rich, with 9 kcal/g (38 kJ/g) compared to 4 kcal/g (17 kJ/g) for carbohydrate or protein, so portions on the ketogenic diet are smaller than normal. The quantity of fat in the diet can be calculated from the overall energy requirements and the chosen ketogenic ratio. Next, the protein levels are set to allow for growth and body maintenance, and are around 1 g protein for each kg of body weight. Lastly, the amount of carbohydrate is set according to what allowance is left while maintaining the chosen ratio. Any carbohydrate in medications or supplements must be subtracted from this allowance. The total daily amount of fat, protein, and carbohydrate is then evenly divided across the meals.[37]
Vegan ketogenic diet or vegetarian diet: Yes, both are possible. Instead of animal products, plenty of low-carb, nutrient-dense vegan and/or vegetarian foods are included. Nuts, seeds, low-carb fruits and veggies, leafy greens, healthy fats and fermented foods are all excellent choices on a plant-based keto diet. There’s also a similar plan called ketotarian, which combines keto with vegetarian, vegan and/or pescatarian diets for supposedly greater health benefits.

I have spent weeks reading and learning about the Keto diet plan, downloading random recipes that my husband might even try, and have been overwhelmed with all the information. I was pleased to find your system and how organized everything seems to be. The only question I have is will I be able to “temporarily suspend” my subscription if I find there are more recipes than I have time to prepare. I want to only do about 3 per week and repeat them as leftovers, since I have very little time after working a 12-hour shift, to do much cooking. Once I “catch up,” I would reinstate my subscription. Is that an option? Looking forward to trying out your program.


My Husband and I started doing Keto July 2018. We got over weight after we got out of the Marine Corps. It has been hard to workout because I became disabled, but my diet was not good. After our friend Amber recommended your site and support group, we found a lot of helpful information to get us started on a successful journey. So far it’s been one month and we have lost 18 pounds each!
Now is the time to forget the 1980s strategy of low-fat/reduced-fat/fat-free. When you're assembling your keto diet food stash, go full-fat. And don't stress over the dietary cholesterol content, a factor of how much animal protein you eat, suggests a study published in The Journal of Nutrition. For the healthiest blood cholesterol levels, instead focus on consuming a higher ratio of unsaturated fats (flaxseed, olive oil, nuts) to saturated fats (lard, red meat, palm oil, butter).

"The keto diet is primarily used to help reduce the frequency of epileptic seizures in children. While it also has been tried for weight loss, only short-term results have been studied, and the results have been mixed. We don't know if it works in the long term, nor whether it's safe," warns registered dietitian Kathy McManus, director of the Department of Nutrition at Harvard-affiliated Brigham and Women's Hospital.


Thank you SO much for the breakdown. This is an excellent list that I am going to take with me to the store from now on. I haven’t started on the diet as of yet because I was trying to put a grocery list together. This list has been one of VERY few that have the foods and the guided amount without having to pay an absurd amount of money for a list of food you can and cant eat. There weren’t any recommended amounts to eat for the meat section and wanted to know if you had any recommendations for portions. Thanks again for taking time to get wonderful information out there.
The keto diet (also known as ketogenic diet, low carb diet and LCHF diet) is a low carbohydrate, high fat diet. Maintaining this diet is a great tool for weight loss. More importantly though, according to an increasing number of studies, it helps reduce risk factors for diabetes, heart diseases, stroke, Alzheimer’s, epilepsy, and more1-6.On the keto diet, your body enters a metabolic state called ketosis. While in ketosis your body is using ketone bodies for energy instead of glucose. Ketone bodies are derived from fat and are a much more stable, steady source of energy than glucose, which is derived from carbohydrates.
A computer program such as KetoCalculator may be used to help generate recipes.[47] The meals often have four components: heavy whipping cream, a protein-rich food (typically meat), a fruit or vegetable and a fat such as butter, vegetable oil, or mayonnaise. Only low-carbohydrate fruits and vegetables are allowed, which excludes bananas, potatoes, peas, and corn. Suitable fruits are divided into two groups based on the amount of carbohydrate they contain, and vegetables are similarly divided into two groups. Foods within each of these four groups may be freely substituted to allow for variation without needing to recalculate portion sizes. For example, cooked broccoli, Brussels sprouts, cauliflower, and green beans are all equivalent. Fresh, canned, or frozen foods are equivalent, but raw and cooked vegetables differ, and processed foods are an additional complication. Parents are required to be precise when measuring food quantities on an electronic scale accurate to 1 g. The child must eat the whole meal and cannot have extra portions; any snacks must be incorporated into the meal plan. A small amount of MCT oil may be used to help with constipation or to increase ketosis.[37]

Is everyone you know "on keto"? Yeah, we know the feeling. This trendy, fat-filled diet has exploded on social media—and for good reason: People who followed the keto diet for two years lost more than twice as much weight than people on a standard low-calorie diet, according to a study published in the journal Endocrine. What's more, those same dieters lost 4.5 more inches from their waistlines.
Certain studies suggest that keto diets may “starve” cancer cells. A highly processed, pro-inflammatory, low-nutrient foods can feed cancer cells causing them to proliferate. What’s the connection between high-sugar consumption and cancer? The regular cells found in our bodies are able to use fat for energy, but it’s believed that cancer cells cannot metabolically shift to use fat rather than glucose. (11)
The ketogenic diet achieved national media exposure in the US in October 1994, when NBC's Dateline television programme reported the case of Charlie Abrahams, son of Hollywood producer Jim Abrahams. The two-year-old suffered from epilepsy that had remained uncontrolled by mainstream and alternative therapies. Abrahams discovered a reference to the ketogenic diet in an epilepsy guide for parents and brought Charlie to John M. Freeman at Johns Hopkins Hospital, which had continued to offer the therapy. Under the diet, Charlie's epilepsy was rapidly controlled and his developmental progress resumed. This inspired Abrahams to create the Charlie Foundation to promote the diet and fund research.[10] A multicentre prospective study began in 1994, the results were presented to the American Epilepsy Society in 1996 and were published[17] in 1998. There followed an explosion of scientific interest in the diet. In 1997, Abrahams produced a TV movie, ...First Do No Harm, starring Meryl Streep, in which a young boy's intractable epilepsy is successfully treated by the ketogenic diet.[1]
Yes your are totally right, I meant to take off 500 calories a day to lose 1 pound a week (7 days/week x 500 calories/day = 3500 calories/week = 1 pound of fat/week) or take off 1000 calories to lose 2 pounds a week (7 days/week x 1000 calories/day = 7000 calories/week = 2 pounds of fat/week). Thanks to you, I fixed this little typo 🙂 Thanks a lot!

Articles and information on this website may only be copied, reprinted, or redistributed with written permission (but please ask, we like to give written permission!) The purpose of this Blog is to encourage the free exchange of ideas. The entire contents of this website is based upon the opinions of Dave Asprey, unless otherwise noted. Individual articles are based upon the opinions of the respective authors, who may retain copyright as marked. The information on this website is not intended to replace a one-on-one relationship with a qualified health care professional and is not intended as medical advice. It is intended as a sharing of knowledge and information from the personal research and experience of Dave Asprey and the community. We will attempt to keep all objectionable messages off this site; however, it is impossible to review all messages immediately. All messages expressed on The Bulletproof Forum or the Blog, including comments posted to Blog entries, represent the views of the author exclusively and we are not responsible for the content of any message.

^ Freeman JM, Vining EP, Pillas DJ, Pyzik PL, Casey JC, Kelly LM. The efficacy of the ketogenic diet—1998: a prospective evaluation of intervention in 150 children. Pediatrics. 1998 Dec;102(6):1358–63. doi:10.1542/peds.102.6.1358. PMID 9832569. https://web.archive.org/web/20040629224858/http://www.hopkinsmedicine.org/press/1998/DECEMBER/981207.HTM Lay summary]—JHMI Office of Communications and Public Affairs. Updated 7 December 1998. Cited 6 March 2008.


The ketogenic diet has grown to become extremely popular over the last few years. It’s ideal for those of you that are looking to lose a considerable amount of weight. This diet is essentially a very low carb, high fat diet. While it has many similarities to the Atkins diet when on the keto diet, your body mostly gets its calories from proteins and fat, not from carbohydrates. The video below will give you an idea of what you can expect when moving to a ketosis lifestyle.
Sulforaphane is a compound that is created when we crush or chew cruciferous vegetables. Once it is digested, sulforaphane activates a cytoprotective (cell-protecting) pathway that protects the cells from oxidative stress and removes toxins from the body. This is one of the main reasons why cruciferous vegetable consumption is linked to improved cognitive function and decreased cancer and heart disease risk.
You're using it for a particular, short-term period.The meal substitute diet can function so quick and so well that you might decide to keep on following it for a longer while. You've acquired the flavor and habit of consuming the yummy meal substitute products that you think you'll stick to the program for a vague period. However, you need to understand that enduring high-calorie deficit in your system may not be good on an extended basis. Take advantage of the diet only as a boost to significant weight reduction or to be a procedure for a huge occasion arriving soon or under strict doctors monitoring.
In fact, once all our our reserved glucose/glycogen runs out after several days on a low-carb, keto diet, our bodies create compounds called ketone bodies (or ketones) from our own stored body fat, as well as from fats in our diet. In addition, researchers have discovered that ketones contain main benefits, such as fat loss, suppressing our appetites, boosting mental clarity and lowering the risk for a number of chronic diseases.
Dirty keto diet: “Dirty” is the apt term, as these version of keto follows the same strict percentages (75/20/5 of fat/protein/carbs) but rather than focusing on healthy versions of fat like coconut oil and wild salmon, you’re free to eat naughty but still keto friendly foods like bacon, sausage, pork rinds, diet sodas and even keto fast food. I do NOT recommend this.

A keto diet has shown to improve triglyceride levels and cholesterol levels most associated with arterial buildup. More specifically low-carb, high-fat diets show a dramatic increase in HDL and decrease in LDL particle concentration compared to low-fat diets.3A study in the long-term effects of a ketogenic diet shows a significant reduction in cholesterol levels, body weight, and blood glucose. Read more on keto and cholesterol >
Insulin is a hormone that lets your body use or store sugar as fuel. Ketogenic diets make you burn through this fuel quickly, so you don’t need to store it. This means your body needs -- and makes -- less insulin. Those lower levels may help protect you against some kinds of cancer or even slow the growth of cancer cells. More research is needed on this, though.
I like you Jacob, I like what you say and what you stand for. Against my better judgement I trusted your party and you party leader in her Brexit means Brexit, no deal is better than a bad deal manifesto in the 2017 election.I no longer trust your party I especially distrust your party leader. It's too late in this unnecessary EU elections to ask for my vote as it was posted last week. My vote went to The Brexit Party.I fear your party leader is unaware of the consequences of her actions and fear that she will resolve her issues by concocting a back room deal with Maoist Corbyn. This will destroy the party you are so loyal to.
I wanted to put it out there that I made this meal plan specifically with women in mind. I took an average of about 150 women and what their macros were. The end result was 1600 calories – broken down into 136g of fat, 74g of protein, and 20g net carbs a day. This is all built around a sedentary lifestyle, like most of us live. If you need to increase or decrease calories, you will need to do that on your own terms.
Decades of research indicates that high-fat, low-carb keto-friendly foods, the very foods we once thought were destroying our health, may be doing just the opposite. Studies upon studies on the ketogenic diet have been discovering benefits for people with all types of conditions, including type 2 diabetes, obesity, heart disease, epilepsy, and Alzheimer’s disease.
More good news: Snacks are totally allowed (and I'm not just talking about carrot sticks). There are plenty of packaged options out there designed for keto fans. FATBAR is one of them. These snack bars have 200 calories, 16 grams of fat, and four grams of net carbs. They're also plant-based and are made with almond or cashew butter, cocoa butter, coconut, pea protein, sunflower seeds, and chia seeds.

Avocados are loaded with heart-healthy monounsaturated fats, as well as fiber, which keeps your digestion running smoothly. This fruit can also help replenish electrolytes in the body. For example, a cup of avocado delivers 975 milligrams of potassium, a mineral that regulates fluid balance in the body. That’s extra important when you're on a very low-carb diet—this type of eating causes your body to excrete water and electrolytes, which can lead to dehydration, dizziness, and fainting.

Overweight individuals with metabolic syndrome, insulin resistance, and type 2 diabetes are likely to see improvements in the clinical markers of disease risk with a well-formulated very-low-carbohydrate diet. Glucose control improves due to less glucose introduction and improved insulin sensitivity. In addition to reducing weight, especially truncal obesity and insulin resistance, low-carb diets also may help improve blood pressure, blood glucose regulation, triglycerides, and HDL cholesterol levels. However, LDL cholesterol may increase on this diet.

This is one area where full keto and Bulletproof differ. Except for coconut, all nuts and legumes are suspect on the Bulletproof Diet and should be limited. All expose you to high amounts of omega-6s, inflammatory oxidized fats, mold toxins, and phytates (plant anti-nutrients). Peanuts are one of the main sources of mold toxins in our diets, and often trigger allergic responses with inflammatory polyunsaturated fats, lectins and histamines. The Bulletproof Diet also excludes all soy products due to their phytoestrogen content, which messes with your hormones and may promote cancer.
Rami co-founded Tasteaholics with Vicky at the start of 2015 to master the art of creating extremely delicious food while researching the truth behind nutrition, dieting and overall health. You can usually find him marketing, coding or coming up with the next crazy idea because he can’t sit still for too long. His favorite book is The 4-Hour Workweek and artist is Infected Mushroom.

Hi, I’m still a bit skeptical, I have seen some of my friends do the keto diet, and have had good results. Though I am still not sure about the idea of the fats being eaten. They say they eat meat with the fat and must do so, is this correct? Also isn’t this not good for the body especially for the kidneys? Second, can a diabetic do this diet? There are many questions running through my head.

Gary D. Foster, Ph.D., Holly R. Wyatt, M.D., James O. Hill, Ph.D., Brian G. McGuckin, Ed.M., Carrie Brill, B.S., B. Selma Mohammed, M.D., Ph.D., Philippe O. Szapary, M.D., Daniel J. Rader, M.D., Joel S. Edman, D.Sc., and Samuel Klein, M.D., “A Randomized Trial of a Low-Carbohydrate Diet for Obesity — NEJM,” N Engl J Med 2003; 348:2082- 2090. http://www.nejm.org/doi/full/10.1056/NEJMoa022207. 

Grass-fed meat is a must for keto dieters. Compared to grain-fed, grass-fed meats are higher in omega-3 fatty acids, which have a range of health benefits including improving heart health, lowering levels of inflammation, and even easing symptoms of depression. High-quality poultry also packs a nutritional punch, with plenty of iron, selenium, zinc, and B vitamins. Dark meat, which is higher in fat, is particularly good for the keto diet.
Dinner: In a small sauce pan bring 2-3 cups of water to the boil. Cook a large egg in rolling boil for 5 minutes, then transfer to ice bath (a bowl with cold water and ice cubes in it). Wash and spin dry butter lettuce, top with sliced avocado and hemp seed. Serve soft boiled egg with cherry tomatoes, butter lettuce salad and mayonnaise as dressing.
I love this! I am an amateur powerlifter and I have recently started using the keto diet as there is only so much gained by being a fat powerlifter but working out my macros was driving me nuts as I also work as a disability support worker and need to take meals and so on to work with me. Thanks to this I can now have better control of the macros to bring my weight down without doing to much harm to my lifts! Thank you for this!
In many developing countries, the ketogenic diet is expensive because dairy fats and meat are more expensive than grain, fruit and vegetables. The modified Atkins diet has been proposed as a lower-cost alternative for those countries; the slightly more expensive food bill can be offset by a reduction in pharmaceutical costs if the diet is successful. The modified Atkins diet is less complex to explain and prepare and requires less support from a dietitian.[55]
In many developing countries, the ketogenic diet is expensive because dairy fats and meat are more expensive than grain, fruit and vegetables. The modified Atkins diet has been proposed as a lower-cost alternative for those countries; the slightly more expensive food bill can be offset by a reduction in pharmaceutical costs if the diet is successful. The modified Atkins diet is less complex to explain and prepare and requires less support from a dietitian.[55]
I would just keep to the same scheme as your breakfast, making sure you stay at around 400 calories pr meal with with 85% of those coming from fat. I am sure you will start seeing benefits. **Make sure to drink a lot of water too** and watch that you are having enough salt – get a good mineral salt, or eat something with enough magnesium. My dad started this diet and he is 85. After about 2 weeks he is a different man – more energy, and better sleeps.
For those looking for something just a little closer to real sugar, you can use Xylitol. It cooks and tastes very similar to sugar, but it has a slight glycemic impact (13 vs. 100 for sugar). It is great, but please keep in mind that it is very toxic to animals and it will raise insulin levels slightly. These are the two most cited reasons for not using Xylitol.
Implementing the diet can present difficulties for caregivers and the patient due to the time commitment involved in measuring and planning meals. Since any unplanned eating can potentially break the nutritional balance required, some people find the discipline needed to maintain the diet challenging and unpleasant. Some people terminate the diet or switch to a less demanding diet, like the modified Atkins diet or the low-glycaemic index treatment diet, because they find the difficulties too great.[42]

Normal dietary fat contains mostly long-chain triglycerides (LCTs). Medium-chain triglycerides (MCTs) are more ketogenic than LCTs because they generate more ketones per unit of energy when metabolised. Their use allows for a diet with a lower proportion of fat and a greater proportion of protein and carbohydrate,[18] leading to more food choices and larger portion sizes.[4] The original MCT diet developed by Peter Huttenlocher in the 1970s derived 60% of its calories from MCT oil.[15] Consuming that quantity of MCT oil caused abdominal cramps, diarrhea, and vomiting in some children. A figure of 45% is regarded as a balance between achieving good ketosis and minimising gastrointestinal complaints. The classical and modified MCT ketogenic diets are equally effective and differences in tolerability are not statistically significant.[9] The MCT diet is less popular in the United States; MCT oil is more expensive than other dietary fats and is not covered by insurance companies.[18]
What makes this diet so special is that it changes how your body feels and most importantly how your body uses energy, placing you into a state known as ketosis. This is actually where all the magic begins to happen; in this state your body starts to utilize substances known as ketone bodies which are produced by the breakdown of your body fats. Your body loves glucose and if it has that on hand it’s going to use that first for energy. On the keto diet, the amount of carbohydrates decreases drastically, which in turn will lead to less production of glucose. High levels of glucose production is generally what makes you fat; without it, the body will begin to start breaking down your body fat and this is when you start to get leaner.
Hi Gigi, Low carb and keto is about the balance of macronutrients eaten (fat, protein and carbs), not specifically meat or lack thereof. Most people on keto do eat meat, though some people do vegetarian keto. Fat is actually necessary for many body processes. There is no issue for the kidneys with a high fat diet, but if you eat too much protein that isn’t great for the kidneys. It’s a common misconception that keto is high protein (it isn’t). Keto is great for diabetics as it naturally helps stabilize insulin. All of this being said, please know I’m not a doctor and you should consult your doctor on any medical questions or before starting any diet. If you have more questions that aren’t medical questions, I recommend our low carb & keto support group here.
When you’re eating the foods that get you there (more on that in a minute), your body can enter a state of ketosis in one to three days, she adds. During the diet, the majority of calories you consume come from fat, with a little protein and very little carbohydrates. Ketosis also happens if you eat a very low-calorie diet — think doctor-supervised, only when medically recommended diets of 600 to 800 total calories.

Like nuts, seeds are great for a snack on the go. But they're also a fun, crunchy addition to a salad. In addition to being low-carb and high-fat, seeds also offer a good serving of protein, which will help keep you full throughout the day. Listed in order of lowest to highest carb content per 1-ounce serving, the best seeds for the keto diet include:


I have the same calories limit and macro. I easily stay within the limit but I completely stopped eating any type of bread, pasta, rice, potatoes and starchy food. I started using butter or coconut oil to cook and put mayo EVERYWHERE. It’s my new favourite topping for lettuce even XD. Then I eat plenty of eggs/meat/fatty fish and cheese. Olives are great as a snack. I cut out completely milk and use whipping cream instead. If you get into this completely counter intuitive way of thinking of food it’s super easy to get enough fat within the calorie limit.

What is the ketogenic diet exactly? The classic ketogenic diet is a very low-carb diet plan that was originally designed in the 1920s for patients with epilepsy by researchers working at Johns Hopkins Medical Center. Researchers found that fasting — avoiding consumption of all foods for a brief period of time (such as with intermittent fasting), including those that provide carbohydrates — helped reduce the amount of seizures patients suffered, in addition to having other positive effects on body fat, blood sugar, cholesterol and hunger levels. (1)


Very happy to have stumbled across your blog site (during a recipe search)  only to realise that I have recently purchased 2 of your books (I'm in Australia). Both of which I like.  I have been doing this way of eating since February, switched from WW which was progressing slowly and I was often hungry. I am never hungry on this plan and I am finding it so much easier. And I am losing weight twice as fast. After about 2 1/2 months doing Keto I realised that the lists I was using for a resource for net carbs in foods was completely wrong. It said mushrooms was 0.3 net carb per 100g and I was happily having 200g thinking it was 0.6g and it wasn't. I ended up checking some lists against the USA Agriculture list and found all were wrong.  So I started to make my own list using that website. This was a bit of a pain but at least I knew it was accurate. Anyway,  I found your site and could stop doing my list. YAY!  🙏 Thank you so much for providing accurate information that you have referenced and for all the other guides and recipes you have shared.  I really wish these guides were in my books though (I have your latest book), so can you please consider for the next book 😁. I had to print them after saving it to MS word for a friend (that has also bought a book)  and it's pages of poorly edited A4 paper.  Many thanks again 🙏
It is possible to combine the results of several small studies to produce evidence that is stronger than that available from each study alone—a statistical method known as meta-analysis. One of four such analyses, conducted in 2006, looked at 19 studies on a total of 1,084 patients.[23] It concluded that a third achieved an excellent reduction in seizure frequency and half the patients achieved a good reduction.[18]
×