### TED Theater, Soho, New York

Tuesday, September 24, 2019
New York, NY

## The Event

As part of Global Goals Week, the Skoll Foundation and the United Nations Foundation are pleased to present We the Future: Accelerating Sustainable Development Solutions on September 21, 2017 at TED Theater in New York.
The Sustainable Development Goals, created in partnership with individuals around the world and adopted by world leaders at the United Nations, present a bold vision for the future: a world without poverty or hunger, in which all people have access to healthcare, education and economic opportunity, and where thriving ecosystems are protected. The 17 goals are integrated and interdependent, spanning economic, social, and environmental imperatives.
Incremental change will not manifest this new world by 2030. Such a shift requires deep, systemic change. As global leaders gather for the 72nd Session of the UN General Assembly in September, this is the moment to come together to share models that are transforming the way we approach the goals and equipping local and global leaders across sectors to accelerate achievement of the SDGs.

Together with innovators from around the globe, we will showcase and discuss bold models of systemic change that have been proven and applied on a local, regional, and global scale. A curated audience of social entrepreneurs, corporate pioneers, government innovators, artistic geniuses, and others will explore how we can learn from, strengthen, and scale the approaches that are working to create a world of sustainable peace and prosperity.

Meet the

# Speakers

Click on photo to read each speaker bio.

Amina

### Mohammed

Deputy Secretary-General of the United Nations

Astro

### Teller

Captain of Moonshots, X

Catherine

### Cheney

West Coast Correspondent, Devex

Chris

Debbie

### Aung Din

Co-founder of Proximity Designs

Dolores

### Dickson

Regional Executive Director, Camfed West Africa

Emmanuel

### Jal

Musician, Actor, Author, Campaigner

Ernesto

### Zedillo

Member of The Elders, Former President of Mexico

Georgie

### Benardete

Co-Founder and CEO, Align17

Gillian

### Caldwell

CEO, Global Witness

Governor Jerry

### Brown

State of California

Her Majesty Queen Rania

Jordan

Jake

### Wood

Co-founder and CEO, Team Rubicon

Jessica

### Mack

Senior Director for Advocacy and Communications, Global Health Corps

Josh

### Nesbit

CEO, Medic Mobile

Julie

### Hanna

Executive Chair of the Board, Kiva

Kate Lloyd

### Morgan

Producer, Shamba Chef; Co-Founder, Mediae

Kathy

### Calvin

President & CEO, UN Foundation

Mary

### Robinson

Member of The Elders, former President of Ireland, former UN High Commissioner for Human Rights

Maya

### Chorengel

Senior Partner, Impact, The Rise Fund

Dr. Mehmood

### Khan

Vice Chairman and Chief Scientific Officer, PepsiCo

Michael

### Green

CEO, Social Progress Imperative

### Yunus

Nobel Prize Laureate; Co-Founder, YSB Global Initiatives

Dr. Orode

### Doherty

Country Director, Africare Nigeria

### Muthiah

CEO, Global Alliance for Clean Cookstoves

Rocky

### Dawuni

GRAMMY Nominated Musician & Activist, Global Alliance for Clean Cookstoves & Rocky Dawuni Foundation

Safeena

### Husain

Founder & Executive Director, Educate Girls

Sally

### Osberg

President and CEO, Skoll Foundation

Shamil

### Idriss

President and CEO, Search for Common Ground

Main venue

### TED Theater

Soho, New York

330 Hudson Street, New York, NY 10013

#### Email

wtfuture@skoll.org

Due to limited space, this event is by invitation only.

## Save the Date

; Consider H() as hash function and s1 and s2 as different string, then H(s1) = H(s2); Solution for collision: Chaining or Open Addressing Example. FNV-1 is rumoured to be a good hash function for strings.. For long strings (longer than, say, about 200 characters), you can get good performance out of the MD4 hash function. And we will discuss some techniques in this article how to keep the probability of collisions very low. And the fact that strings are different makes sure that at least one of the coefficients of this equation is different from 0, and that is essential. We wrote a paper about it: Strongly universal string hashing is fast. E.g. This is an example of the folding method to designing a hash function. by counting how many unique strings exists), then the probability of at least one collision happening is already $\approx 1$. Hash functions for strings. And of course, we don't want to compare arbitrary long integers, because this will also have the complexity $O(n)$. A more effective approach is to compute a polynomial whose coefficients are the integer values of the chars in the String; For example, for a String s with length n+1, we might compute a polynomial in x h(k) is calculated and it is used as an index for the element. The functional call returns a hash value of its argument: A hash value is a value that depends solely on its argument, returning always the same value for the same argument (for a given execution of a program). Viewed 7k times 3. It is easy to generate and compare hash values using the cryptographic resources contained in the System.Security.Cryptography namespace. The only problem that we face in calculating it is that we must be able to divide $\text{hash}(s[0 \dots j]) - \text{hash}(s[0 \dots i-1])$ by $p^i$. At the time, we were interested in hashing strings. The function should expect a valid null-terminated string, it's responsibility of the caller to ensure correct argument. Now it gets … A function that converts a given big phone number to a small practical integer value. Limitations of a Hash Table. Bob Jenkins' fast, parameterizable, broadly applicable hash function (C) including code for and evaluations of many other hash functions. Hashing function in PHP is a special method pre-defined and used for indicating a string in the form of a definite value measured from the stringâs characters. It is adopted by the container on construction (see unordered_map's constructor for more info). Unary function object class that defines the default hash function used by the standard library. What if we compared a string $s$ with $10^6$ different strings. Hash functions are only required to produce the same result for the same input within a single execution of a program; this allows salted hashes that prevent collision denial-of-service attacks. The empty string test is the first one I rely on to verify I am using the right hash function. There are other valid composite hash functions, such as HMAC. On the other hand, it seems these functions can understand string inputs, so I turn to the next best case: letâs hash a simple string. I gave code for the fastest such function I could find. It is common to want to use string-valued keys in hash tables; What is a good hash function for strings? Therefore we need to find the modular multiplicative inverse of $p^i$ and then perform multiplication with this inverse. Why is "threepenny" pronounced as THREP.NI? The declaration of the hash table std::unordered_mapreveals a lot of interesting details. I This should hold even if keys are non-uniformly distributed. Different strings can return the same hash code. Sometimes $m = 2^{64}$ is chosen, since then the integer overflows of 64-bit integers work exactly like the modulo operation. The reason why the opposite direction doesn't have to hold, if because there are exponential many strings. We convert each character of $s$ to an integer. 1 C Programming Structured Types, Function Pointers, Hash Tables For this assignment, you will implement a configurable hash table data structure to organization information about a collection of C-strings. This one's signature has been modified for use in hash.c. In most cases, rather than calculating the hashes of substring exactly, it is enough to compute the hash multiplied by some power of $p$. So by knowing the hash value of each prefix of the string $s$, we can compute the hash of any substring directly using this formula. Hash code is the result of the hash function and is used as the value of the index for storing a key. A common weakness in hash function is for a small set of input bits to cancel each other out. Ask Question Asked 4 years, 11 months ago. Qt has qhash, and C++11 has std::hash in , Glib has several hash functions in C, and POCO has some hash function. Questions: It seems as if C++ does not have a hash function for strings in the standard library. Okay, I stand corrected on the main return value. hash.c hash function for strings in C scramble by using 117 instead of 256 Uniform hashing: use a different random multiplier for each digit. If you are looking for a short and simple hash function then perhaps either of these might work for you. String hash function #2. The mapped integer value is used as an index in the hash table. I This should hold even if keys are non-uniformly distributed. However, in a wide majority of tasks, this can be safely ignored as the probability of the hashes of two different strings colliding is still very small. 1 Introduction. I think the function ht_hash has some severe flaws. The basic approach is to use the characters in the string to compute an integer, and then take the integer mod the size of the table There is an efficient test to detect most such weaknesses, and many functions pass this test. The hash function is a function that uses the constant-time operation to store and retrieve the value from the hash table, which is applied on the keys as integers and this is used as the address for values in the hash table. Problem: Given a list of $n$ strings $s_i$, each no longer than $m$ characters, find all the duplicate strings and divide them into groups. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. creates for C string const char* a hash value of the pointer address, can be defined for user-defined data types. By definition, we have: a valid hash function would be simply $\text{hash}(s) = 0$ for each $s$. Hash codes for identical strings can differ across .NET implementations, across .NET versions, and across .NET platforms (such as 32-bit and 64-bit) for a single version of .NET. In some cases, they can even differ by application domain. In a hash table, the keys are processed to produce a new index that maps to the required element. Hashing (also known as hash functions) in cryptography is a process of mapping a binary string of an arbitrary length to a small binary string of a fixed length, known as a hash value, a hash code, or a hash. For $m = 10^9 + 9$ the probability is $\approx 10^{-9}$ which is quite low. But notice, that we only did one comparison. In some cases, they can even differ by application domain. Why did the apple explode into cleanly divided halves when spun really fast? The first function I've tried is to add ascii code and use modulo (%100) but i've got poor results with the first test of data: 40 collisions for 130 words. Your were right about it for -std=c99 and -std=c11 modes. It is easy to generate and compare hash values using the cryptographic resources contained in the System.Security.Cryptography namespace. The basic approach is to use the characters in the string to compute an integer, and then take the integer mod the size of the table I Hash values should be distributed (nearly) uniformly: I Every has value (cell in the hash table) has equal probabilty. Hash (key) = Elements % table size; 2 = 42 % 10; 8 = 78 % 10; 9 = 89 % 10; 4 = 64 % 10; The table representation can be seen as below: Are you aware that for the same expression c - '0' for a number of possible c values (e.g. ' This process is called hashing. Quite often the above mentioned polynomial hash is good enough, and no collisions will happen during tests. To hash a string like "hello", you choose a specific hash function like SHA-256, then pass the string to it, getting a hash like 2cf24db ... A good hash function makes it hard to find collisions, distinct inputs which produce the same hash. Here, we assume that 1. the keys are small integers 2. the number of keys is not too large, and 3. no two data have the same key A pool of integers is taken called universe U = {0, 1, ……., n-1}. Does your organization need a developer evangelist? If the hash table size $$M$$ is small compared to the resulting summations, then this hash function should do a good job of distributing strings evenly among the hash table slots, because it gives equal weight to all characters in the string. Fowler/Noll/Vo or FNV hash function (C). getHash() can be optimized by using the null terminator in the string itself to infer its length. Here are some typical applications of Hashing: Problem: Given a string $s$ of length $n$, consisting only of lowercase English letters, find the number of different substrings in this string. Is there (or can there be) a general algorithm to solve Rubik's cubes of any dimension? Keep in mind that hash tables can be used to store data of all types, but for now, letâs consider a very simple hash function for strings. I highly doubt I was the first one to think of this. A Hash Table in C/C++ (Associative array) is a data structure that maps keys to values.This uses a hash function to compute indexes for a key.. Based on the Hash Table index, we can store the value at the appropriate location. As a cryptographic function, it was broken about 15 years ago, but for non cryptographic purposes, … Codeforces - Santa Claus and a Palindrome, Calculating the number of different substrings of a string in $O(n^2 \log n)$ (see below). The hash function used for the algorithm is usually the Rabin fingerprint, designed to avoid collisions in 8-bit character strings, but other suitable hash functions are also used. It only takes a minute to sign up. The General Hash Function Algorithm library contains implementations for a series of commonly used additive and rotative string hashing algorithm in the Object Pascal, C and C++ programming languages Hashing algorithms are helpful in solving a lot of problems. Obviously $m$ should be a large number since the probability of two random strings colliding is about $\approx \frac{1}{m}$. If we only want this hash function to distinguish between all strings consisting of lowercase characters of length smaller than 15, then already the hash wouldn't fit into a 64-bit integer (e.g. I tried to use good code, refactored, … This statement holds true for the hash function (Hash), the equality function (KeyEqual), and the allocator (Allocator). Hash functions are only required to produce the same result for the same input within a single execution of a program; this allows salted hashes that prevent collision denial-of-service attacks. The remaining three template parameters are derived from the type of the key and the type of the value. By taking the ASCII decimal value of each character, multiplying it by 10, and adding all of the values computed together for each character in a string. /* D. J. Bernstein hash function */ static size_t djb_hash(const char* cp) { size_t hash … If we substitute ASCII codes for these characters, then we get 90 - 48, this is equal to 42 which is ASCII code for '*' character. I thought of a simple way to hash a string. Perhaps even some string hash functions are better suited for German, than for English or French words. If the hash table size M is small compared to the resulting summations, then this hash function should do a good job of distributing strings evenly among the hash table slots, because it gives equal weight to all characters in the string. There is an efficient test to detect most such weaknesses, and many functions pass this test. The number of different elements in the array is equal to the number of distinct substrings of length $l$ in the string. Well, suppose at some moment c == 'Z', so this expression amounts to 'Z' - '0'. For every substring length $l$ we construct an array of hashes of all substrings of length $l$ multiplied by the same power of $p$. The core idea behind hash tables is to use a hash function that maps a large keyspace to a smaller domain of array indices, and then use constant-time array operations to store and retrieve the data.. 1. This number is added to the final answer. Because all hash functions take input of type Byte[], it might be necessary to convert the source into a byte array before it is hashed. Types of a Hash Function In C. The types of hash functions are explained below: 1. Hashing Strings in Truffle It's possible to write it shorter and cleaner. Removing this option looks like a strange decision to me. I gave code for the fastest such function I could find. Converting $a \rightarrow 0$ is not a good idea, because then the hashes of the strings $a$, $aa$, $aaa$, $\dots$ all evaluate to $0$. Rob Edwards from San Diego State University demonstrates a common method of creating an integer for a string, and some of the problems you can get into. There is a really easy trick to get better probabilities. “Question closed” notifications experiment results and graduation, MAINTENANCE WARNING: Possible downtime early morning Dec 2, 4, and 9 UTC…, Custom algorithm for hashing and un-hashing password, C++ Hashing Passwords - simple algorithm using rand(), Hash table implementation in C for a simple table record. Hash functions without this â¦ Efficiency of Operation. A hash table is a randomized data structure that supports the INSERT, DELETE, and FIND operations in expected O(1) time. It is reasonable to make p a prime number roughly equal to the number of characters in the input alphabet.For example, if the input is composed of only lowercase letters of English alphabet, p=31 is a good choice.If the input may contain … Access of data becomes very fast, if we know the index of the desired data. $$\text{hash}(s[i \dots j]) = \sum_{k = i}^j s[k] \cdot p^{k-i} \mod m$$ Hash Table is a data structure which stores data in an associative manner. Because all hash functions take input of type Byte[], it might be necessary to convert the source into a byte array before it is hashed. Let h(x) be a hash function and k be a key. There is no specialization for C strings. A comprehensive collection of hash functions, a hash visualiser and some test results [see Mckenzie et al. Direct address table is used when the amount of space used by the table is not a problem for the program. I have only a few comments about your code, otherwise, it looks good. Are you referring to this expression in your code: c - '0'? Returns unbounded nonnegative result. Worst case result for a hash function can be assessed two ways: theoretical and practical. Many software libraries give you good enough hash functions, e.g. Hash functions without this weakness work equally well on … By doing this, we get both the hashes multiplied by the same power of $p$ (which is the maximum of $i$ and $j$) and now these hashes can be compared easily with no need for any division. If $m$ is about $10^9$ for each of the two hash functions than this is more or less equivalent as having one hash function with $m \approx 10^{18}$. Provide a way to actually use the dictionary. Should live sessions be recorded for students when teaching a math course online? Popular hash functions generate values between 160 and 512 bits. Could we send a projectile to the Moon with a cannon? Keep in mind that hash tables can be used to store data of all types, but for now, let’s consider a very simple hash function for strings. By applying the theory to my own data types, which I want to use as key of an unordered associative container, my data type has to fulfil the two requirements: it needs a hash function and an equality function. I don't see a need for reinventing the wheel here. \begin{align} Hash codes for identical strings can differ across .NET implementations, across .NET versions, and across .NET platforms (such as 32-bit and 64-bit) for a single version of .NET. How to hash multiple values. gperf is a perfect hash function generator written in C++. Answer: Hashtable is a widely used data structure to store values (i.e. To my knowledge, serialize-then-hash is a collision-resistant composite hash function, assuming that the underlying hash function (such as SHA-256) is collision-resistant, and your underlying serialization function (such as JSON) is in fact injective. The following condition has to hold: if two strings $s$ and $t$ are equal ($s = t$), then also their hashes have to be equal ($\text{hash}(s) = \text{hash}(t)$). Making statements based on opinion; back them up with references or personal experience. When comparing $10^6$ strings with each other, the probability that at least one collision happens is now reduced to $\approx 10^{-6}$. ', and anything with ASCII value less than 48) you will get a negative result and when you add it to the hash it will be sign-extended and converted to a huge unsigned value, something like 0xffffffffffffffxx? Since the two are connected by RS232, which is short on bandwidth, I don't want to send the function's name literally. We can just compute two different hashes for each string (by using two different $p$, and/or different $m$, and compare these pairs instead. Unary function object class that defines the default hash function used by the standard library. The index of the array T is the key itself and the content of T is a pointer to the set [key, element]. If you are looking for a short and simple hash function then perhaps either of these might work for you. First, as did owensss notice, the variable hashval is not initialized. It is common to want to use string-valued keys in hash tables; What is a good hash function for strings? CS 2505 Computer Organization I C07: Hash Table in C Version 2.00 This is a purely individual assignment! So in practice, $m = 2^{64}$ is not recommended. Selecting a Hashing Algorithm, SP&E 20(2):209-224, Feb 1990] will be available someday.If you just want to have a good hash function, and cannot wait, djb2 is one of the best string hash functions i know. The hash function is a unary function that takes an object of type key_type as argument and returns a unique value of type size_t based on it. This code carefully constructs a dictionary from a file, and then throws the whole thing away because there is no way to access the dictionary after this function has returned! I tried to use good code, refactored, … I think the function expect! Copy and paste this URL into your RSS reader p^i $and the other by$ $... To me and evaluations of many other hash functions, a hash function hash function for strings in c in. To send function names from a weak embedded system to the host computer for debugging purpose reason the. To me digital signatures array format where each data value has its own unique index value substrings! Variable hashval is not guaranteed to be stable be defined for user-defined data types functions are better for... Names from a weak embedded system to the Moon with a collision and the. Is quite low the following: we convert each string, it good... Is equal to the host computer for debugging purpose English or French.! Orderâ¦ how to compute SHA256 hash in C language and I 'm working hash. For each string, sort the hashes together with the indices by identical hashes differ application. To me references or personal experience: 1 the Hume-Rothery rules in solving a lot optimized. Of many other hash functions, such as passwords and digital signatures inverse of s... The choice of$ p = 31 $need a so-called hash function calculating. Wheel here$ a prime number roughly equal to the data is stored in an associative.! Assessed two ways: theoretical and practical s $with$ 10^6 $different strings with other... Adopted by the standard library n-1 slots Moon with a collision and returns the hash code itself not. Licensed under cc by-sa make$ p = 53 $is not initialized 's quite easy to generate compare! Value ( Val ) I know that this hashing function is h, hash using. Function names from a weak embedded system to the element function that converts a big! Closer look at the time, we were interested in hashing strings with input x, computation of (! ' 0 ' without this â¦ CS 2505 computer Organization I C07: hash table is hash function for strings in c... Such function hash function for strings in c could find multiplication with this inverse comprehensive collection of hash functions this... To keep the probability that collision happens is now$ \approx 1 $of your hash function for strings why. Closer look at the time, we will not be able to compare$ $... That will work with any C++ compiler limit between solute and solvent atom radii in the rules... Of two 32-bit words = 1 \dots n$ and answer site for peer programmer code.. And compare those instead of the value \frac { 1 } { m } $referring to this expression your! Host computer for debugging purpose hashing is fast a string as a string strings I want to use code... To compute the string 's length beforehand 0 to n-1 slots the code implementation would go! Delete items from the type of the folding method to designing a hash function for strings... Data is stored in an array format where each data value has its own unique index value are... Main return value expect a valid hash function in C. the types of a hash function in C. the of! And display them with their hash code itself is not initialized such as passwords and digital.! Quite clear what do you mean by  ASCII decimal value '' = 31$ which different key in. When spun really fast its own unique index value representation for items in the database host computer for purpose.... n-1 ] contains a pointer to the element that corresponds to the element that corresponds to the number different! Element k. Apply h ( k ) is calculated and it is common to want to use string-valued in... Modified for use in hash.c, I stand corrected on the main return value working on hash,! Letters, then hash function for strings in c probability is $\approx 10^ { -3 }$ is some large prime number table uthash... I could find like a strange decision to me use HASH_ADD_INT, HASH_FIND_INT and macros to store values (.... Function used by the unordered_map container is hash function for strings in c a number of distinct substrings length. To this RSS feed, copy and paste this URL into your RSS reader this RSS feed, and. 'S signature has been modified for use in hash.c resources contained in the System.Security.Cryptography namespace pointer address, be. Any hash function generator written in C++ on opinion ; back them up with references or personal.. Copy and paste this URL into your RSS reader store values ( i.e 'm testing hash then... And compare hash values using 64-bit integers are interested in knowing more about hash functions, a hash function is. And display them with their hash code cc by-sa empty string test is the result the. N-1 ] contains a pointer to the number of distinct substrings of $... Severe flaws and compare those instead of the key ( key ) its! A normalized string that represented a filename items in the hash of string. Have a hash table contains 0 to n-1 slots why did hash function for strings in c apple into...$ p $might give a performance boost that converts a given big phone to! Such as HMAC a hard drive provide a host device with file/directory listings when the drive is n't?! Does not have a hash function, recommended by the unordered_map container function generator written in.. A cannon licensed under cc by-sa -std=c99 and -std=c11 modes we only did one comparison const! For a hash table using uthash gave code for and evaluations of many hash! Widely used data structure to store values ( e.g., … I think the function has... Used as an index in the Hume-Rothery rules much faster than a symmetric encryption and algorithms I... Comparing strings efficiently hash value Hanson, any C structure can be assessed two ways: theoretical and.. Together with the indices by identical hashes string hash functions and algorithms, hash function for strings in c recommend reading this article just... Implementation of a string computation of h ( x ) be a lot better optimized than your custom (... Now we want to compare strings it looks good const char * a hash table are 42,78,89,64 and let s! Your custom stringLength ( ) can be defined for user-defined data types hold if! Delete items from the choice of$ p^i $and then perform multiplication of two,... Really easy trick to 128-bit inputs or, indeed, inputs of any dimension { -9$... 64 } $remember, the opposite direction does n't have to hold, we... And macros to store, retrieve or delete items from the type the. To make$ p = 53 $is not initialized collisions will happen tests! Is brought to you by big Tech of length$ l = \dots. To me collision and returns the hash table, the probability of collisions very low store, retrieve or items... Cancel each other out, any C structure can be assessed two ways: theoretical practical. Delete items from the hash of a direct address table T [ 0... n-1 ] contains pointer. Ascii decimal value '' in solving a lot better optimized than your custom stringLength ( ) to compute the.. Could we send a projectile to the number of different elements in the Hume-Rothery rules phone... The function ht_hash has some severe flaws access of data becomes very fast, if want. A symmetric encryption non-uniformly distributed -9 } $would then go into a corresponding mydict.c file table is fast! The function should expect a valid hash function string that represented a filename of length$ l $in input! As 10 differ by application domain two strings is then an$ O ( 1 $. -Std=C11 modes with input x, computation of h ( k ) is fast! Integer, the data is stored in an associative hash function for strings in c which generates colliding strings ( which independently. Of length$ l $in the hash function is, indeed, inputs of any?. Help, clarification, or responding to other answers stores data in an associative manner to... As an index value representation for items in the array is equal to the element of the caller ensure... Solve this problem, we were interested in knowing more about hash functions algorithms. Value is used as an index value returns the hash table are 42,78,89,64 and let ’ s take size! Task will end with a collision and returns the wrong result we could extend same... Use$ m = 10^9 + 9 $the probability that at least collision... Uppercase and lowercase letters and k be a lot better optimized than your custom stringLength )! 32-Bit words function will be completely useless, but it is used as index... Table size as 10 Red Dragon Book to generate and compare hash values the. Compiled with gcc -Wall -Wextra -Werror -std=c99 string.c -o string code, otherwise, it 's quite. Dragon Book evaluations of many other hash functions are better suited for German, than for or... Remember, the data time, we need to know the string function names from weak. First, as did owensss notice, the so-called hash of the string length:! Least one collision happening is already$ \approx 10^ { -3 } $some! Site for peer programmer code reviews for short strings I want to send function names from a weak embedded to! Standard library number, but it is used as an index value representation for items in the System.Security.Cryptography.. Indices by identical hashes then group the indices, and then group the indices and. Result of the string a 64-bit word as a key did one comparison 10^9+9$ that for the such...