關於 the way you make me fee ，我們在網路上蒐集到這些相關的討論、資訊與評價

10/10 - Free islandwide delivery @wearetwiceyoung on 10/10!
Celebrating a smol milestone of 1000 pints and 2000 cookies 🥳

It’s been 9 months since the inception of Twice Young and it certainly hasn’t been an easy journey. There were lots to figure out along the way, and I’m still learning and improving. But I’m beyond grateful for the immense support that Twice Young has received - all the positive reviews and feedback that were sent our way, local businesses who have worked with us, loyal customers etc. And I’m extremely thankful for friends and family who have been spreading the word and sharing about my smol biz.

It really isn’t easy working out of my small apartment, and I really struggle with the space constraints(not being able to buy ingredients/goods in bulk, not enough space in my freezer etc) and there were times when I got really frustrated with the lack of space to even bake. I probably take 3-4 times the amount of time that others would take to churn out the same products. Eg : it took me 11 hours to bake and pack 330 cookies.

You probably hear this a lot - running a biz is like a rollercoaster ride and it’s not easy. Well, it’s true, but I wouldn’t have it any other way.

So to say thank you for keeping me going, on 10/10, Twice Young will be offering free islandwide delivery on all orders above $35

Place an order on www.wearetwiceyoung.com, key in 10/10 in “delivery date” box and transfer the stated amount without the shipping fee! Or simply place an order via DM. Orders have to be placed by 6th October 2359 (because I need to make the ice cream and cookie dough!!)

Drop me a DM if you have any questions okay! 🥳 Thank you for being part of my journey ❤️

📷 : Miss Tam Chiak

📜 [專欄新文章] Uniswap v3 Features Explained in Depth

✍️ 田少谷 Shao

📥 歡迎投稿： https://medium.com/taipei-ethereum-meetup #徵技術分享文 #使用心得 #教學文 #medium

Once again the game-changing DEX 🦄 👑

Image source: https://uniswap.org/blog/uniswap-v3/

Outline

0. Intro1. Uniswap & AMM recap2. Ticks 3. Concentrated liquidity4. Range orders: reversible limit orders5. Impacts of v36. Conclusion

0. Intro

The announcement of Uniswap v3 is no doubt one of the most exciting news in the DeFi place recently 🔥🔥🔥

While most have talked about the impact v3 can potentially bring on the market, seldom explain the delicate implementation techniques to realize all those amazing features, such as concentrated liquidity, limit-order-like range orders, etc.

Since I’ve covered Uniswap v1 & v2 (if you happen to know Mandarin, here are v1 & v2), there’s no reason for me to not cover v3 as well ✅

Thus, this article aims to guide readers through Uniswap v3, based on their official whitepaper and examples made on the announcement page. However, one needs not to be an engineer, as not many codes are involved, nor a math major, as the math involved is definitely taught in your high school, to fully understand the following content 😊😊😊

If you really make it through but still don’t get shxt, feedbacks are welcomed! 🙏

There should be another article focusing on the codebase, so stay tuned and let’s get started with some background noise!

1. Uniswap & AMM recap

Before diving in, we have to first recap the uniqueness of Uniswap and compare it to traditional order book exchanges.

Uniswap v1 & v2 are a kind of AMMs (automated market marker) that follow the constant product equation x * y = k, with x & y stand for the amount of two tokens X and Y in a pool and k as a constant.

Comparing to order book exchanges, AMMs, such as the previous versions of Uniswap, offer quite a distinct user experience:

AMMs have pricing functions that offer the price for the two tokens, which make their users always price takers, while users of order book exchanges can be both makers or takers.

Uniswap as well as most AMMs have infinite liquidity¹, while order book exchanges don’t. The liquidity of Uniswap v1 & v2 is provided throughout the price range [0,∞]².

Uniswap as well as most AMMs have price slippage³ and it’s due to the pricing function, while there isn’t always price slippage on order book exchanges as long as an order is fulfilled within one tick.

In an order book, each price (whether in green or red) is a tick. Image source: https://ftx.com/trade/BTC-PERP

¹ though the price gets worse over time; AMM of constant sum such as mStable does not have infinite liquidity

² the range is in fact [-∞,∞], while a price in most cases won’t be negative

³ AMM of constant sum does not have price slippage

2. Tick

The whole innovation of Uniswap v3 starts from ticks.

For those unfamiliar with what is a tick:

Source: https://www.investopedia.com/terms/t/tick.asp

By slicing the price range [0,∞] into numerous granular ticks, trading on v3 is highly similar to trading on order book exchanges, with only three differences:

The price range of each tick is predefined by the system instead of being proposed by users.

Trades that happen within a tick still follows the pricing function of the AMM, while the equation has to be updated once the price crosses the tick.

Orders can be executed with any price within the price range, instead of being fulfilled at the same one price on order book exchanges.

With the tick design, Uniswap v3 possesses most of the merits of both AMM and an order book exchange! 💯💯💯

So, how is the price range of a tick decided?

This question is actually somewhat related to the tick explanation above: the minimum tick size for stocks trading above 1$ is one cent.

The underlying meaning of a tick size traditionally being one cent is that one cent (1% of 1$) is the basis point of price changes between ticks, ex: 1.02 — 1.01 = 0.1.

Uniswap v3 employs a similar idea: compared to the previous/next price, the price change should always be 0.01% = 1 basis point.

However, notice the difference is that in the traditional basis point, the price change is defined with subtraction, while here in Uniswap it’s division.

This is how price ranges of ticks are decided⁴:

Image source: https://uniswap.org/whitepaper-v3.pdf

With the above equation, the tick/price range can be recorded in the index form [i, i+1], instead of some crazy numbers such as 1.0001¹⁰⁰ = 1.0100496621.

As each price is the multiplication of 1.0001 of the previous price, the price change is always 1.0001 — 1 = 0.0001 = 0.01%.

For example, when i=1, p(1) = 1.0001; when i=2, p(2) = 1.00020001.

p(2) / p(1) = 1.00020001 / 1.0001 = 1.0001

See the connection between the traditional basis point 1 cent (=1% of 1$) and Uniswap v3’s basis point 0.01%?

Image source: https://tenor.com/view/coin-master-cool-gif-19748052

But sir, are prices really granular enough? There are many shitcoins with prices less than 0.000001$. Will such prices be covered as well?

Price range: max & min

To know if an extremely small price is covered or not, we have to figure out the max & min price range of v3 by looking into the spec: there is a int24 tick state variable in UniswapV3Pool.sol.

Image source: https://uniswap.org/whitepaper-v3.pdf

The reason for a signed integer int instead of an uint is that negative power represents prices less than 1 but greater than 0.

24 bits can cover the range between 1.0001 ^ (2²³ — 1) and 1.0001 ^ -(2)²³. Even Google cannot calculate such numbers, so allow me to offer smaller values to have a rough idea of the whole price range:

1.0001 ^ (2¹⁸) = 242,214,459,604.341

1.0001 ^ -(2¹⁷) = 0.000002031888943

I think it’s safe to say that with a int24 the range can cover > 99.99% of the prices of all assets in the universe 👌

⁴ For implementation concern, however, a square root is added to both sides of the equation.

How about finding out which tick does a price belong to?

Tick index from price

The answer to this question is rather easy, as we know that p(i) = 1.0001^i, simply takes a log with base 1.0001 on both sides of the equation⁴:

Image source: https://www.codecogs.com/latex/eqneditor.php

Let’s try this out, say we wanna find out the tick index of 1000000.

Image source: https://ncalculators.com/number-conversion/log-logarithm-calculator.htm

Now, 1.0001¹³⁸¹⁶² = 999,998.678087146. Voila!

⁵ This formula is also slightly modified to fit the real implementation usage.

3. Concentrated liquidity

Now that we know how ticks and price ranges are decided, let’s talk about how orders are executed in a tick, what is concentrated liquidity and how it enables v3 to compete with stablecoin-specialized DEXs (decentralized exchange), such as Curve, by improving the capital efficiency.

Concentrated liquidity means LPs (liquidity providers) can provide liquidity to any price range/tick at their wish, which causes the liquidity to be imbalanced in ticks.

As each tick has a different liquidity depth, the corresponding pricing function x * y = k also won’t be the same!

Each tick has its own liquidity depth. Image source: https://uniswap.org/blog/uniswap-v3/

Mmm… examples are always helpful for abstract descriptions 😂

Say the original pricing function is 100(x) * 1000(y) = 100000(k), with the price of X token 1000 / 100 = 10 and we’re now in the price range [9.08, 11.08].

If the liquidity of the price range [11.08, 13.08] is the same as [9.08, 11.08], we don’t have to modify the pricing function if the price goes from 10 to 11.08, which is the boundary between two ticks.

The price of X is 1052.63 / 95 = 11.08 when the equation is 1052.63 * 95 = 100000.

However, if the liquidity of the price range [11.08, 13.08] is two times that of the current range [9.08, 11.08], balances of x and y should be doubled, which makes the equation become 2105.26 * 220 = 400000, which is (1052.63 * 2) * (110 * 2) = (100000 * 2 * 2).

We can observe the following two points from the above example:

Trades always follow the pricing function x * y = k, while once the price crosses the current price range/tick, the liquidity/equation has to be updated.

√(x * y) = √k = L is how we represent the liquidity, as I say the liquidity of x * y = 400000 is two times the liquidity of x * y = 100000, as √(400000 / 100000) = 2.

What’s more, compared to liquidity on v1 & v2 is always spread across [0,∞], liquidity on v3 can be concentrated within certain price ranges and thus results in higher capital efficiency from traders’ swapping fees!

Let’s say if I provide liquidity in the range [1200, 2800], the capital efficiency will then be 4.24x higher than v2 with the range [0,∞] 😮😮😮 There’s a capital efficiency comparison calculator, make sure to try it out!

Image source: https://uniswap.org/blog/uniswap-v3/

It’s worth noticing that the concept of concentrated liquidity was proposed and already implemented by Kyper, prior to Uniswap, which is called Automated Price Reserve in their case.⁵

⁶ Thanks to Yenwen Feng for the information.

4. Range orders: reversible limit orders

As explained in the above section, LPs of v3 can provide liquidity to any price range/tick at their wish. Depending on the current price and the targeted price range, there are three scenarios:

current price < the targeted price range

current price > the targeted price range

current price belongs to the targeted price range

The first two scenarios are called range orders. They have unique characteristics and are essentially fee-earning reversible limit orders, which will be explained later.

The last case is the exact same liquidity providing mechanism as the previous versions: LPs provide liquidity in both tokens of the same value (= amount * price).

There’s also an identical product to the case: grid trading, a very powerful investment tool for a time of consolidation. Dunno what’s grid trading? Check out Binance’s explanation on this, as this topic won’t be covered!

In fact, LPs of Uniswap v1 & v2 are grid trading with a range of [0,∞] and the entry price as the baseline.

Range orders

To understand range orders, we’d have to first revisit how price is discovered on Uniswap with the equation x * y = k, for x & y stand for the amount of two tokens X and Y and k as a constant.

The price of X compared to Y is y / x, which means how many Y one can get for 1 unit of X, and vice versa the price of Y compared to X is x / y.

For the price of X to go up, y has to increase and x decrease.

With this pricing mechanism in mind, it’s example time!

Say an LP plans to place liquidity in the price range [15.625, 17.313], higher than the current price of X 10, when 100(x) * 1000(y) = 100000(k).

The price of X is 1250 / 80 = 15.625 when the equation is 80 * 1250 = 100000.

The price of X is 1315.789 / 76 = 17.313 when the equation is 76 * 1315.789 = 100000.

If now the price of X reaches 15.625, the only way for the price of X to go even higher is to further increase y and decrease x, which means exchanging a certain amount of X for Y.

Thus, to provide liquidity in the range [15.625, 17.313], an LP needs only to prepare 80 — 76 = 4 of X. If the price exceeds 17.313, all 4 X of the LP is swapped into 1315.789 — 1250 = 65.798 Y, and then the LP has nothing more to do with the pool, as his/her liquidity is drained.

What if the price stays in the range? It’s exactly what LPs would love to see, as they can earn swapping fees for all transactions in the range! Also, the balance of X will swing between [76, 80] and the balance of Y between [1250, 1315.789].

This might not be obvious, but the example above shows an interesting insight: if the liquidity of one token is provided, only when the token becomes more valuable will it be exchanged for the less valuable one.

…wut? 🤔

Remember that if 4 X is provided within [15.625, 17.313], only when the price of X goes up from 15.625 to 17.313 is 4 X gradually swapped into Y, the less valuable one!

What if the price of X drops back immediately after reaching 17.313? As X becomes less valuable, others are going to exchange Y for X.

The below image illustrates the scenario of DAI/USDC pair with a price range of [1.001, 1.002] well: the pool is always composed entirely of one token on both sides of the tick, while in the middle 1.001499⁶ is of both tokens.

Image source: https://uniswap.org/blog/uniswap-v3/

Similarly, to provide liquidity in a price range < current price, an LP has to prepare a certain amount of Y for others to exchange Y for X within the range.

To wrap up such an interesting feature, we know that:

Only one token is required for range orders.

Only when the current price is within the range of the range order can LP earn trading fees. This is the main reason why most people believe LPs of v3 have to monitor the price more actively to maximize their income, which also means that LPs of v3 have become arbitrageurs 🤯

I will be discussing more the impacts of v3 in 5. Impacts of v3.

⁷ 1.001499988 = √(1.0001 * 1.0002) is the geometric mean of 1.0001 and 1.0002. The implication is that the geometric mean of two prices is the average execution price within the range of the two prices.

Reversible limit orders

As the example in the last section demonstrates, if there is 4 X in range [15.625, 17.313], the 4 X will be completely converted into 65.798 Y when the price goes over 17.313.

We all know that a price can stay in a wide range such as [10, 11] for quite some time, while it’s unlikely so in a narrow range such as [15.625, 15.626].

Thus, if an LP provides liquidity in [15.625, 15.626], we can expect that once the price of X goes over 15.625 and immediately also 15.626, and does not drop back, all X are then forever converted into Y.

The concept of having a targeted price and the order will be executed after the price is crossed is exactly the concept of limit orders! The only difference is that if the range of a range order is not narrow enough, it’s highly possible that the conversion of tokens will be reverted once the price falls back to the range.

As price ranges follow the equation p(i) = 1.0001 ^ i, the range can be quite narrow and a range order can thus effectively serve as a limit order:

When i = 27490, 1.0001²⁷⁴⁹⁰ = 15.6248.⁸

When i = 27491, 1.0001²⁷⁴⁹¹ = 15.6264.⁸

A range of 0.0016 is not THAT narrow but can certainly satisfy most limit order use cases!

⁸ As mentioned previously in note #4, there is a square root in the equation of the price and index, thus the numbers here are for explantion only.

5. Impacts of v3

Higher capital efficiency, LPs become arbitrageurs… as v3 has made tons of radical changes, I’d like to summarize my personal takes of the impacts of v3:

Higher capital efficiency makes one of the most frequently considered indices in DeFi: TVL, total value locked, becomes less meaningful, as 1$ on Uniswap v3 might have the same effect as 100$ or even 2000$ on v2.

The ease of spot exchanging between spot exchanges used to be a huge advantage of spot markets over derivative markets. As LPs will take up the role of arbitrageurs and arbitraging is more likely to happen on v3 itself other than between DEXs, this gap is narrowed … to what extent? No idea though.

LP strategies and the aggregation of NFT of Uniswap v3 liquidity token are becoming the blue ocean for new DeFi startups: see Visor and Lixir. In fact, this might be the turning point for both DeFi and NFT: the two main reasons of blockchain going mainstream now come to the alignment of interest: solving the $$ problem 😏😏😏

In the right venue, which means a place where transaction fees are low enough, such as Optimism, we might see Algo trading firms coming in to share the market of designing LP strategies on Uniswap v3, as I believe Algo trading is way stronger than on-chain strategies or DAO voting to add liquidity that sort of thing.

After reading this article by Parsec.finance: The Dex to Rule Them All, I cannot help but wonder: maybe there is going to be centralized crypto exchanges adopting v3’s approach. The reason is that since orders of LPs in the same tick are executed pro-rata, the endless front-running speeding-competition issue in the Algo trading world, to some degree, is… solved? 🤔

Anyway, personal opinions can be biased and seriously wrong 🙈 I’m merely throwing out a sprat to catch a whale. Having a different voice? Leave your comment down below!

6. Conclusion

That was kinda tough, isn’t it? Glad you make it through here 🥂🥂🥂

There are actually many more details and also a huge section of Oracle yet to be covered. However, since this article is more about features and targeting normal DeFi users, I’ll leave those to the next one; hope there is one 😅

If you have any doubt or find any mistake, please feel free to reach out to me and I’d try to reply AFAP!

Stay tuned and in the meantime let’s wait and see how Uniswap v3 is again pioneering the innovation of DeFi 🌟

Uniswap v3 Features Explained in Depth was originally published in Taipei Ethereum Meetup on Medium, where people are continuing the conversation by highlighting and responding to this story.

👏 歡迎轉載分享鼓掌

=================================
「グッとこらえる」は英語で？
=================================
　
辛い状況下でも耐え忍び頑張ることや、じっと苦痛をこらえることを「歯を食いしばる」と言いますが、英語でどのように表現するのが自然でしょうか？
　
　　
--------------------------------------------------
Bite the bullet
→ 「歯を食いしばって耐える」
--------------------------------------------------　
　
の表現は、困難な状況にも歯を食いしばって耐えることや、辛い仕事を我慢してやることなどの意味としてよく使われる日常表現です。直訳は「弾丸を噛む」となり、戦争で負傷した兵士が麻酔をせずに手術を受けた際に、弾丸を噛ませて痛みを我慢させていたことから由来した表現です。どんなに嫌なことがあってもグッとこらえてやるニュアンスがあります。
　
✔「Put up with（我慢する・辛抱する）」も同様の意味です。詳しい解説は、関連記事「我慢」を意味する自然な英語（https://hapaeikaiwa.com/?p=10355）をご覧ください。
　
＜例文＞
　　
You just have to bite the bullet and do it.
（歯を食いしばって頑張るしかないよ。）
　
We are just going to have to bite the bullet and make the best of it.
（辛いかもしれませんが、我慢して最善を尽くすしかありません。）
　
I had to bite the bullet and shell out thousands of dollars.
（嫌でしたが数千ドルの大金を払いました。）
　
Put up with it for one more day.
（もう1日の辛抱だよ。）
　
〜会話例１〜

A: The early termination fee is way too high.
（その早期解約金は高すぎます。）

B: We have to bite the bullet and pay it. We have to cut our losses.
（我慢して支払うしかありません。これ以上、損失を出さないうちに手を引かないと。）
　
〜会話例２〜

A: The fire alarm has been going off for almost an hour now.
（あの火災報知器が鳴りだしてからもう1時間くらい経ってんで。）

B: I can't put up with it anymore. It's driving me crazy.
（もう我慢できへんわ。めっちゃイラつく。）
　
　
　
　
　
～～～～～～～～～～～～～～～～～～～
　
無料メルマガ『1日1フレーズ！生英語』配信中！
　
通勤・通学などのちょとした合間を利用して英語が学べるメルマガ『1日1フレーズ！生英語』を平日の毎朝6時に配信中！ただ単にフレーズを紹介しているだけではなく、音声を使った学習プロセスが組み込まれているので、メルマガを読むこと自体が学習方法！
　
https://hapaeikaiwa.com/mailmagazine/
　
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♥My COOKBOOK available WORLDWIDE レシピ本もよろしくね♥
https://www.amazon.com/dp/4046014822/
http://www.amazon.co.jp/gp/product/4046014822/ref=as_li_ss_tl?ie=UTF8&camp=247&creative=7399&creativeASIN=4046014822&linkCode=as2&tag=shopping072-22

Amazon Japan may be Cheaper ($10 plus shipping fee).
How to Order My Cookbook from Amazon Japan:
https://www.youtube.com/watch?v=mWsrMmA7AnI

Okara (soy pulp) is perfect diet to LOSE WEIGHT ;)

You can make very moist and tasty chocolate cupcake by only mixing and microwaving =D Must try recipe!!!

I recommend you keeping them in the fridge. Taste even delicious when chilled :3

Note: Okara (soy pulp or tofu dregs) remains after making soy milk / tofu. Rich in fiber and minerals.

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Okara (Soy Pulp) Chocolate Cupcakes

Difficulty: Super Easy
Time: 15min
Number of servings: 12 microwavable Bento cups

Ingredients:
150g (5.3oz.) Okara (soy pulp)
2 eggs
80ml soy milk
3 tbsp. granulated sugar
4 tbsp. cocoa powder
1 tsp. baking powder

Directions:
1. Put all ingredients in a bowl and mix well.
2. Put the mixture into microwavable bento cups.
3. Place them on a microwavable dish, cover, then microwave at 600W for 5 minutes. Garnish with nuts and/or powdered sugar if you like.

レシピ（日本語）
http://cooklabo.blogspot.jp/2017/02/blog-post.html
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Music by
YouTube Audio Library
Payday

♥Most Popular Videos 人気の動画♥
https://www.youtube.com/watch?v=dVvPOE-C7AE
https://www.youtube.com/watch?v=OqlllgigAbw
https://www.youtube.com/watch?v=S9TQzPOGwmM

♥Utensils I use in my videos♥
http://astore.amazon.co.jp/shopping072-22

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♥Original T-SHIRTS♥
http://www.youtube.com/watch?v=FFsQE0qd_4w

♥Visit my Blog to know more about ME♥
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http://cookpad.com/ami
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♥My COOKBOOK available WORLDWIDE レシピ本もよろしくね♥
https://www.amazon.com/dp/4046014822/
http://www.amazon.co.jp/gp/product/4046014822/ref=as_li_ss_tl?ie=UTF8&camp=247&creative=7399&creativeASIN=4046014822&linkCode=as2&tag=shopping072-22

Amazon Japan may be Cheaper ($10 plus shipping fee).
How to Order My Cookbook from Amazon Japan:
https://www.youtube.com/watch?v=mWsrMmA7AnI

Revised the old version since it has a copyright issue.
過去にアップしたものは著作権の都合上編集し直しました。
https://www.youtube.com/watch?v=GTkyOjRUy6c

Katsu Sando is Cutlet Sandwich. It is perfect for Bento (lunchbox item) and potluck parties, too!

Instead of using boneless pork chops, I used thinly sliced pork! In this way, you don't have to pound the meat to tenderize ;D

Deep Frying Oil I used:
http://www.nisshin-oillio.com/goods/vegeoil/product/index.shtml

Very popular Tonkatsu Sauce I recommend:
http://astore.amazon.co.jp/shopping072-22/detail/B00Z9P6Q4A
http://astore.amazon.co.jp/shopping072-22/detail/B00Z63F0BU

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Katsu Sando

Difficulty: Easy
Time: 25min
Number of servings: 2

Ingredients:
((Tonkatsu))
8 thinly sliced pork
salt and ground black pepper
* flour
* beaten egg
* Panko (bread crumbs)
vegetable oil for deep frying
((Katsu Sando))
2 Tonkatsu
4 slices of bread
butter
whole-grain mustard
shredded cabbage
Tonkatsu sauce

Directions:
((Tonkatsu))
1. Layer 4 slices of pork to make 1 Tonkatsu and season both sides with salt and pepper.
2. Flour the pork lightly, dip in beaten egg, then coat with Panko. Use one hand for coating flour and Panko, and use the other to dip in egg to keep one of your hands dry.
3. Deep fry them in oil at 170C (340F) until thoroughly cooked golden brown. (Turn the pork over to cook evenly.) Remove the Tonkatsu from the oil and drain.
((Katsu Sando))
1. Brush one side of 4 slices of bread with butter. Brush one side of 2 slices of bread with whole-grain mustard. (You can toast the bread if you like.)
2. Sandwich the Tonkatsu with shredded cabbage and tonkatsu sauce.
3. Cut into 2-3 pieces. You can cut off the crusts if you prefer. Mostly the crusts are off when sold at stores in Japan.

↓レシピ（日本語）
http://cooklabo.blogspot.com/2011/08/blog-post_17.html
---------------------------------

Music by
YouTube Audio Library
Summer Smile

♥Utensils I use in my videos♥
http://astore.amazon.co.jp/shopping072-22

♥FOLLOW ME HERE♥
https://www.facebook.com/ochikeron
https://plus.google.com/+ochikeron
http://twitter.com/ochikeron
http://instagram.com/ochikeron/

♥Original T-SHIRTS♥
http://www.youtube.com/watch?v=FFsQE0qd_4w

♥Visit my Blog to know more about ME♥
http://createeathappy.blogspot.com/

♥My Recipe Posts in Japanese♥
http://cooklabo.blogspot.jp/
http://cookpad.com/ami
http://twitter.com/alohaforever

♥and of course PLEASE SUBSCRIBE♥
http://www.youtube.com/user/ochikeron?sub_confirmation=1