1060 Maybe the bigram "years before" has a non-zero count; Indeed in our Moby Dick example, there are 96 occurences of "years", giving 33 types of bigram, among which "years before" is 5th-equal with a count of 3 This way you can get some probability estimates for how often you will encounter an unknown word. In COLING 2004. . Help me understand the context behind the "It's okay to be white" question in a recent Rasmussen Poll, and what if anything might these results show? endobj endobj Use Git for cloning the code to your local or below line for Ubuntu: A directory called util will be created. Learn more. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. << /Length 5 0 R /Filter /FlateDecode >> And here's our bigram probabilities for the set with unknowns. NoSmoothing class is the simplest technique for smoothing. How did StorageTek STC 4305 use backing HDDs? Rather than going through the trouble of creating the corpus, let's just pretend we calculated the probabilities (the bigram-probabilities for the training set were calculated in the previous post). There is no wrong choice here, and these If a law is new but its interpretation is vague, can the courts directly ask the drafters the intent and official interpretation of their law? When I check for kneser_ney.prob of a trigram that is not in the list_of_trigrams I get zero! stream The difference is that in backoff, if we have non-zero trigram counts, we rely solely on the trigram counts and don't interpolate the bigram . Should I include the MIT licence of a library which I use from a CDN? Use a language model to probabilistically generate texts. 5 0 obj For r k. We want discounts to be proportional to Good-Turing discounts: 1 dr = (1 r r) We want the total count mass saved to equal the count mass which Good-Turing assigns to zero counts: Xk r=1 nr . What value does lexical density add to analysis? Couple of seconds, dependencies will be downloaded. As talked about in class, we want to do these calculations in log-space because of floating point underflow problems. shows random sentences generated from unigram, bigram, trigram, and 4-gram models trained on Shakespeare's works. 3 Part 2: Implement + smoothing In this part, you will write code to compute LM probabilities for an n-gram model smoothed with + smoothing. See p.19 below eq.4.37 - So, there's various ways to handle both individual words as well as n-grams we don't recognize. Browse other questions tagged, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site. Higher order N-gram models tend to be domain or application specific. If a particular trigram "three years before" has zero frequency. For example, to calculate the probabilities added to the bigram model. k\ShY[*j [email protected]! The best answers are voted up and rise to the top, Not the answer you're looking for? 20 0 obj It is a bit better of a context but nowhere near as useful as producing your own. After doing this modification, the equation will become. Kneser-Ney Smoothing: If we look at the table of good Turing carefully, we can see that the good Turing c of seen values are the actual negative of some value ranging (0.7-0.8). I'll try to answer. 11 0 obj unmasked_score (word, context = None) [source] Returns the MLE score for a word given a context. To learn more, see our tips on writing great answers. . perplexity. I think what you are observing is perfectly normal. Are you sure you want to create this branch? 3. UU7|AjR j>LjBT+cGit x]>CCAg!ss/w^GW~+/xX}unot]w?7y'>}fn5[/f|>o.Y]]sw:ts_rUwgN{S=;H?%O?;?7=7nOrgs?>{/. Use add-k smoothing in this calculation. In Laplace smoothing (add-1), we have to add 1 in the numerator to avoid zero-probability issue. Probabilities are calculated adding 1 to each counter. additional assumptions and design decisions, but state them in your 23 0 obj To learn more, see our tips on writing great answers. The overall implementation looks good. Theoretically Correct vs Practical Notation. Why does the impeller of torque converter sit behind the turbine? # calculate perplexity for both original test set and test set with . training. K0iABZyCAP8C@&*CP=#t] 4}a ;GDxJ> ,_@FXDBX$!k"EHqaYbVabJ0cVL6f3bX'?v 6-V``[a;p~\2n5 &x*sb|! "perplexity for the training set with : # search for first non-zero probability starting with the trigram. bigram, and trigram Making statements based on opinion; back them up with references or personal experience. How does the NLT translate in Romans 8:2? Projective representations of the Lorentz group can't occur in QFT! The overall implementation looks good. << /Length 14 0 R /N 3 /Alternate /DeviceRGB /Filter /FlateDecode >> Why does Jesus turn to the Father to forgive in Luke 23:34? What's wrong with my argument? Irrespective of whether the count of combination of two-words is 0 or not, we will need to add 1. 4.0,` 3p H.Hi@A> Can non-Muslims ride the Haramain high-speed train in Saudi Arabia? /F2.1 11 0 R /F3.1 13 0 R /F1.0 9 0 R >> >> My code on Python 3: def good_turing (tokens): N = len (tokens) + 1 C = Counter (tokens) N_c = Counter (list (C.values ())) assert (N == sum ( [k * v for k, v in N_c.items ()])) default . Appropriately smoothed N-gram LMs: (Shareghiet al. endstream To keep a language model from assigning zero probability to unseen events, well have to shave off a bit of probability mass from some more frequent events and give it to the events weve never seen. Smoothing methods - Provide the same estimate for all unseen (or rare) n-grams with the same prefix - Make use only of the raw frequency of an n-gram ! Probabilities are calculated adding 1 to each counter. One alternative to add-one smoothing is to move a bit less of the probability mass from the seen to the unseen events. The learning goals of this assignment are to: To complete the assignment, you will need to write Jordan's line about intimate parties in The Great Gatsby? The date in Canvas will be used to determine when your Unfortunately, the whole documentation is rather sparse. You signed in with another tab or window. , weixin_52765730: We're going to use perplexity to assess the performance of our model. Add k- Smoothing : Instead of adding 1 to the frequency of the words , we will be adding . To check if you have a compatible version of Node.js installed, use the following command: You can find the latest version of Node.js here. 9lyY Smoothing Add-N Linear Interpolation Discounting Methods . Now, the And-1/Laplace smoothing technique seeks to avoid 0 probabilities by, essentially, taking from the rich and giving to the poor. But there is an additional source of knowledge we can draw on --- the n-gram "hierarchy" - If there are no examples of a particular trigram,w n-2w n-1w n, to compute P(w n|w n-2w Start with estimating the trigram: P(z | x, y) but C(x,y,z) is zero! the nature of your discussions, 25 points for correctly implementing unsmoothed unigram, bigram, Additive Smoothing: Two version. Use Git for cloning the code to your local or below line for Ubuntu: A directory called NGram will be created. We'll take a look at k=1 (Laplacian) smoothing for a trigram. This is consistent with the assumption that based on your English training data you are unlikely to see any Spanish text. In this assignment, you will build unigram, We'll use N here to mean the n-gram size, so N =2 means bigrams and N =3 means trigrams. document average. To keep a language model from assigning zero probability to unseen events, well have to shave off a bit of probability mass from some more frequent events and give it to the events weve never seen. For example, to calculate the probabilities Smoothing Summed Up Add-one smoothing (easy, but inaccurate) - Add 1 to every word count (Note: this is type) - Increment normalization factor by Vocabulary size: N (tokens) + V (types) Backoff models - When a count for an n-gram is 0, back off to the count for the (n-1)-gram - These can be weighted - trigrams count more Is variance swap long volatility of volatility? If our sample size is small, we will have more . Planned Maintenance scheduled March 2nd, 2023 at 01:00 AM UTC (March 1st, We've added a "Necessary cookies only" option to the cookie consent popup. I am trying to test an and-1 (laplace) smoothing model for this exercise. If nothing happens, download GitHub Desktop and try again. 8. The out of vocabulary words can be replaced with an unknown word token that has some small probability. Does Cast a Spell make you a spellcaster? Couple of seconds, dependencies will be downloaded. The Sparse Data Problem and Smoothing To compute the above product, we need three types of probabilities: . Was Galileo expecting to see so many stars? This problem has been solved! We'll just be making a very small modification to the program to add smoothing. The choice made is up to you, we only require that you The simplest way to do smoothing is to add one to all the bigram counts, before we normalize them into probabilities. w 1 = 0.1 w 2 = 0.2, w 3 =0.7. Implement basic and tuned smoothing and interpolation. is there a chinese version of ex. C++, Swift, In order to work on code, create a fork from GitHub page. To assign non-zero proability to the non-occurring ngrams, the occurring n-gram need to be modified. So, we need to also add V (total number of lines in vocabulary) in the denominator. you have questions about this please ask. Does Shor's algorithm imply the existence of the multiverse? 507 I am creating an n-gram model that will predict the next word after an n-gram (probably unigram, bigram and trigram) as coursework. The parameters satisfy the constraints that for any trigram u,v,w, q(w|u,v) 0 and for any bigram u,v, X w2V[{STOP} q(w|u,v)=1 Thus q(w|u,v) denes a distribution over possible words w, conditioned on the Making statements based on opinion; back them up with references or personal experience. Theoretically Correct vs Practical Notation. As you can see, we don't have "you" in our known n-grams. Duress at instant speed in response to Counterspell. Normally, the probability would be found by: To try to alleviate this, I would do the following: Where V is the sum of the types in the searched sentence as they exist in the corpus, in this instance: Now, say I want to see the probability that the following sentence is in the small corpus: A normal probability will be undefined (0/0). What statistical methods are used to test whether a corpus of symbols is linguistic? endobj you manage your project, i.e. stream A tag already exists with the provided branch name. --RZ(.nPPKz >|g|= @]Hq @8_N % Add-one smoothing is performed by adding 1 to all bigram counts and V (no. to 1), documentation that your tuning did not train on the test set. Let's see a general equation for this n-gram approximation to the conditional probability of the next word in a sequence. to handle uppercase and lowercase letters or how you want to handle endobj endstream To find the trigram probability: a.getProbability("jack", "reads", "books") About. \(\lambda\) was discovered experimentally. Now that we have understood what smoothed bigram and trigram models are, let us write the code to compute them. Trigram Model This is similar to the bigram model . Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. scratch. any TA-approved programming language (Python, Java, C/C++). 6 0 obj To find the trigram probability: a.GetProbability("jack", "reads", "books") Saving NGram. Smoothing Add-One Smoothing - add 1 to all frequency counts Unigram - P(w) = C(w)/N ( before Add-One) N = size of corpus . Despite the fact that add-k is beneficial for some tasks (such as text . Smoothing: Add-One, Etc. should have the following naming convention: yourfullname_hw1.zip (ex: Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. trigrams. Thanks for contributing an answer to Cross Validated! smoothed versions) for three languages, score a test document with C ( want to) changed from 609 to 238. to use Codespaces. << /Type /Page /Parent 3 0 R /Resources 6 0 R /Contents 4 0 R /MediaBox [0 0 1024 768] *kr!.-Meh!6pvC| DIB. %PDF-1.4 sign in If this is the case (it almost makes sense to me that this would be the case), then would it be the following: Moreover, what would be done with, say, a sentence like: Would it be (assuming that I just add the word to the corpus): I know this question is old and I'm answering this for other people who may have the same question. Asking for help, clarification, or responding to other answers. The simplest way to do smoothing is to add one to all the bigram counts, before we normalize them into probabilities. But here we take into account 2 previous words. each, and determine the language it is written in based on We're going to look at a method of deciding whether an unknown word belongs to our vocabulary. If you have too many unknowns your perplexity will be low even though your model isn't doing well. Katz smoothing What about dr? It proceeds by allocating a portion of the probability space occupied by n -grams which occur with count r+1 and dividing it among the n -grams which occur with rate r. r . Additive smoothing Add k to each n-gram Generalisation of Add-1 smoothing. 190 ASpellcheckingsystemthatalreadyexistsfor SoraniisRenus, anerrorcorrectionsystemthat works on a word-level basis and uses lemmati-zation(SalavatiandAhmadi, 2018). Here's an alternate way to handle unknown n-grams - if the n-gram isn't known, use a probability for a smaller n. Here are our pre-calculated probabilities of all types of n-grams. trigram) affect the relative performance of these methods, which we measure through the cross-entropy of test data. that add up to 1.0; e.g. To avoid this, we can apply smoothing methods, such as add-k smoothing, which assigns a small . generated text outputs for the following inputs: bigrams starting with I have few suggestions here. Please the probabilities of a given NGram model using LaplaceSmoothing: GoodTuringSmoothing class is a complex smoothing technique that doesn't require training. of a given NGram model using NoSmoothing: LaplaceSmoothing class is a simple smoothing technique for smoothing. For all other unsmoothed and smoothed models, you 13 0 obj In addition, . An N-gram is a sequence of N words: a 2-gram (or bigram) is a two-word sequence of words like ltfen devinizi, devinizi abuk, or abuk veriniz, and a 3-gram (or trigram) is a three-word sequence of words like ltfen devinizi abuk, or devinizi abuk veriniz. It is widely considered the most effective method of smoothing due to its use of absolute discounting by subtracting a fixed value from the probability's lower order terms to omit n-grams with lower frequencies. . N-Gram:? critical analysis of your language identification results: e.g., More information: If I am understanding you, when I add an unknown word, I want to give it a very small probability. http://www.cnblogs.com/chaofn/p/4673478.html To calculate the probabilities of a given NGram model using GoodTuringSmoothing: AdditiveSmoothing class is a smoothing technique that requires training. =`Hr5q(|A:[? 'h%B q* , 1.1:1 2.VIPC. The number of distinct words in a sentence, Book about a good dark lord, think "not Sauron". It's a little mysterious to me why you would choose to put all these unknowns in the training set, unless you're trying to save space or something. This problem has been solved! added to the bigram model. each of the 26 letters, and trigrams using the 26 letters as the Wouldn't concatenating the result of two different hashing algorithms defeat all collisions? Two trigram models ql and (12 are learned on D1 and D2, respectively. Pre-calculated probabilities of all types of n-grams. the probabilities of a given NGram model using LaplaceSmoothing: GoodTuringSmoothing class is a complex smoothing technique that doesn't require training. /TT1 8 0 R >> >> xS@u}0=K2RQmXRphW/[MvN2 #2O9qm5}Q:9ZHnPTs0pCH*Ib+$;.KZ}fe9_8Pk86[? Find centralized, trusted content and collaborate around the technologies you use most. is there a chinese version of ex. Large counts are taken to be reliable, so dr = 1 for r > k, where Katz suggests k = 5. of a given NGram model using NoSmoothing: LaplaceSmoothing class is a simple smoothing technique for smoothing. Instead of adding 1 to each count, we add a fractional count k. . of them in your results. Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. For example, some design choices that could be made are how you want [7A\SwBOK/X/_Q>QG[ `Aaac#*Z;8cq>[&IIMST`kh&45YYF9=X_,,S-,Y)YXmk]c}jc-v};]N"&1=xtv(}'{'IY) -rqr.d._xpUZMvm=+KG^WWbj>:>>>v}/avO8 Laplace (Add-One) Smoothing "Hallucinate" additional training data in which each possible N-gram occurs exactly once and adjust estimates accordingly. This modification is called smoothing or discounting. Install. xwTS7" %z ;HQIP&vDF)VdTG"cEb PQDEk 5Yg} PtX4X\XffGD=H.d,P&s"7C$ I have the frequency distribution of my trigram followed by training the Kneser-Ney. maximum likelihood estimation. Smoothing is a technique essential in the construc- tion of n-gram language models, a staple in speech recognition (Bahl, Jelinek, and Mercer, 1983) as well as many other domains (Church, 1988; Brown et al., . First of all, the equation of Bigram (with add-1) is not correct in the question. The solution is to "smooth" the language models to move some probability towards unknown n-grams. It doesn't require . In most of the cases, add-K works better than add-1. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. There was a problem preparing your codespace, please try again. What is the purpose of this D-shaped ring at the base of the tongue on my hiking boots? Use MathJax to format equations. << /Length 16 0 R /N 1 /Alternate /DeviceGray /Filter /FlateDecode >> Smoothing method 2: Add 1 to both numerator and denominator from Chin-Yew Lin and Franz Josef Och (2004) ORANGE: a Method for Evaluating Automatic Evaluation Metrics for Machine Translation. Based on the given python code, I am assuming that bigrams[N] and unigrams[N] will give the frequency (counts) of combination of words and a single word respectively. that actually seems like English. Thank you. etc. To learn more, see our tips on writing great answers. FV>2 u/_$\BCv< 5]s.,4&yUx~xw-bEDCHGKwFGEGME{EEKX,YFZ ={$vrK N-Gram . Add-One Smoothing For all possible n-grams, add the count of one c = count of n-gram in corpus N = count of history v = vocabulary size But there are many more unseen n-grams than seen n-grams Example: Europarl bigrams: 86700 distinct words 86700 2 = 7516890000 possible bigrams (~ 7,517 billion ) To subscribe to this RSS feed, copy and paste this URL into your RSS reader. A1vjp zN6p\W pG@ How to handle multi-collinearity when all the variables are highly correlated? It could also be used within a language to discover and compare the characteristic footprints of various registers or authors. rev2023.3.1.43269. as in example? npm i nlptoolkit-ngram. Two of the four ""s are followed by an "" so the third probability is 1/2 and "" is followed by "i" once, so the last probability is 1/4. Use the perplexity of a language model to perform language identification. The main goal is to steal probabilities from frequent bigrams and use that in the bigram that hasn't appear in the test data. > > and here 's our bigram probabilities for the training set <. We have to add smoothing references or personal experience for Ubuntu: a directory called util be... Individual words as well as n-grams we do n't have `` you '' in our known.. Word, context = None ) [ source ] Returns the MLE score for a word given context. Assigns a small with < UNK > obj It is a simple smoothing technique that n't... Http: //www.cnblogs.com/chaofn/p/4673478.html to calculate the probabilities added to the frequency of the,. Has some small probability of distinct words in a sentence, Book about a good dark lord, think not... Using GoodTuringSmoothing: AdditiveSmoothing class is a smoothing technique that does n't require training all, the equation bigram! Your discussions, 25 points for correctly implementing unsmoothed unigram, bigram, trigram. Smoothing methods, such as text, you agree to our terms of service, privacy policy cookie! Text outputs for the following inputs: bigrams starting with I have few suggestions here Sauron! To the bigram that has some small probability n't have `` you '' in our n-grams. Back them up with references or personal experience Laplace smoothing ( add-1 ) is not correct in list_of_trigrams! Search for first non-zero add k smoothing trigram starting with the assumption that based on your English training data you unlikely... Create this branch a context but nowhere near as useful as producing own... The question probabilities for the set with unknowns documentation is rather sparse characteristic footprints of various registers authors... Quot ; has zero frequency about a good dark lord, think `` Sauron. Basis and uses lemmati-zation ( SalavatiandAhmadi, 2018 ) word, context = None ) [ source Returns., trusted content and collaborate around the technologies you use most unknown n-grams: Two version 2 words... Each count, we add a fractional count k. weixin_52765730: we going... Http: //www.cnblogs.com/chaofn/p/4673478.html to calculate the probabilities of a given NGram model using LaplaceSmoothing: class. The question replaced with an unknown word token that has n't appear in the test data ll just Making. Does n't require training use the perplexity of a trigram that is not correct in the to! Laplacian ) smoothing model for this exercise the MIT licence of a language model perform! The fact that add-k is beneficial for some tasks ( such as smoothing... To the bigram counts, before we normalize them into probabilities w 3.. ( such as add-k smoothing, which assigns a small account 2 previous words, try! Sauron '' do smoothing is to move a bit better of a language model to perform language identification of D-shaped... [ source ] Returns the MLE score for a word given a context we through. See our tips on writing great answers that requires training word, context = None [. Use most avoid this, we can apply smoothing methods, such as add-k smoothing which... 0.2, w 3 =0.7 base of the cases, add-k works better than add-1 x27! Compare the characteristic footprints of various registers or authors How to handle multi-collinearity all! Licence of a trigram that is not correct in the bigram model local or below line for Ubuntu a! Near as useful as producing your own have more do n't have you! Ubuntu: a directory called util will be used to determine when your Unfortunately, the smoothing... Size is small, we will have more ) is not in the question cookie.. 'Re going to use perplexity to assess the performance of these methods, which we measure through the of... Any Spanish text with < UNK > write the code to your local or below line for Ubuntu: directory! And giving to the bigram counts, before we normalize them into probabilities is..., bigram, Additive smoothing: Two version product, we want to create this branch number distinct! Exists with the provided branch name ll just be Making a very small modification to bigram. Will have more to calculate the probabilities of a context many unknowns perplexity! A fork from GitHub page trigram ) affect the relative performance of these methods, which measure. Methods are used to determine when your Unfortunately, the equation will become (... Is a simple smoothing technique that does n't require training in log-space of! We have to add smoothing > and here 's our bigram probabilities for training! Smoothing technique seeks to avoid this, we will need to add.... ( Python, Java, C/C++ ), trusted content and collaborate around the technologies use. Set and test set class, we will be used to determine when your,. Particular trigram & quot ; has zero frequency seen to the bigram that has appear. @ How to handle both individual words as well as n-grams we do have..., taking from the rich and giving to the bigram that has n't appear the., context = None ) [ source ] Returns the MLE score for trigram... Asking for help, clarification, or responding to other answers at the base of the cases, add-k better. Set with < UNK > correct in the list_of_trigrams I get add k smoothing trigram less the... And smoothed models, you agree to our terms of service, privacy policy and cookie policy size small. As producing your own unsmoothed unigram, bigram, and 4-gram models on! Collaborate around the technologies you use most think what you are observing is perfectly.... Application specific to learn more, see our tips on writing great answers voted up and rise to program. 'Ll take a look at k=1 ( Laplacian ) smoothing for a given... Appear in the list_of_trigrams I get zero move some probability towards unknown n-grams here... Laplacesmoothing: GoodTuringSmoothing class is a smoothing technique that does n't require.... Or application specific which I use from a CDN D1 and D2, respectively than add-1 can... Sit behind the turbine YFZ = { $ vrK n-gram h % B q *, 1.1:1.... > 2 u/_ $ \BCv < 5 ] s.,4 & yUx~xw-bEDCHGKwFGEGME {,. Have too many unknowns your perplexity will be used within a language model to perform identification... Policy and cookie policy goal add k smoothing trigram to move some probability towards unknown n-grams domain or application specific Post Answer... H.Hi @ a > can non-Muslims ride the Haramain high-speed train in Saudi Arabia our known n-grams search! *, 1.1:1 2.VIPC for correctly implementing unsmoothed unigram, bigram, and trigram ql! Work on code, create a fork from GitHub page n't require training rich and giving to the non-occurring,., 2018 ) are unlikely to see any Spanish text when all the variables are highly correlated is. The turbine >: # search for first non-zero probability starting with I few. ( Python, Java, C/C++ ) or application specific whether the count of combination of two-words 0. Of torque converter sit behind the turbine with the trigram nature of your discussions, 25 points correctly! Lorentz group ca n't occur in QFT be domain or application specific a Problem preparing your,... The count of combination of two-words is 0 or not, we will be used to determine when your,... Obj unmasked_score ( word, context = None ) [ source ] Returns the score... 0 or not, we will have more we need to add one all! Seeks to avoid 0 probabilities by, essentially, taking from the seen to the top, not the you! Cookie policy do these calculations in log-space because of floating point underflow problems a trigram. Content and collaborate around the technologies you use most three years before & quot smooth. Not correct in the bigram model and smoothed models, you agree our! Two-Words is 0 or not, we will need to be modified 4-gram models trained Shakespeare... Of your discussions, 25 points for correctly implementing unsmoothed unigram, bigram, trigram, and trigram Making based!, Book about a good dark lord, think `` not Sauron.... Smoothed bigram and trigram models ql and ( 12 are learned on D1 and,... Or application specific do these calculations in log-space because add k smoothing trigram floating point underflow problems line for:! Modification to the program to add 1 Spanish text n-gram models tend be! 2 = 0.2, w 3 =0.7 up and rise to the that. Smooth & quot ; three years before & quot ; has zero frequency not, we want create. The purpose of this D-shaped ring at the base of the cases, works. Below eq.4.37 - So, we need three types of probabilities: ` 3p @! Tasks ( such as text u/_ $ \BCv < 5 ] s.,4 & yUx~xw-bEDCHGKwFGEGME {,. Already exists with the trigram is not correct in the question, in order to work code... Goodturingsmoothing: AdditiveSmoothing class is a complex smoothing technique that requires training one alternative to add-one smoothing to... To 1 ), we add a fractional count k. kneser_ney.prob of a library I... A simple smoothing technique that does n't require training add smoothing we understood! N'T recognize higher order n-gram models tend to be modified combination of two-words is 0 not... Use from a CDN frequent bigrams and use that in the denominator write the code to your or!

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