adjacency list representation of graph

Thanks for contributing an answer to Stack Overflow! What is the highest level 1 persuasion bonus you can have? There can be more than one path between two nodes. The complexity of Adjacency List representation This representation takes O (V+2E) for undirected graph, and O (V+E) for directed graph. This is similar to DFS traversal inbinary tree. Each Node in this Linked list represents the reference to the other vertices which share an edge with the current vertex. We can easily check if there is an edge between node u and v and we can also get the weight of the edge. //Add edges including adding nodes, Time O(1) Space O(1), #Add edges including adding nodes, Time O(1) Space O(1), //Find the edge between two nodes, Time O(n) Space O(1), n is number of neighbors, //Remove direct connection between a and b, Time O(n) Space O(1), //Remove a node including all its edges, Time O(V) Space O(1), V is number of vertics in graph, //Time O(V) Space O(1), V is number of vertics in graph, #Find the edge between two nodes, Time O(n) Space O(1), n is number of neighbors, #Remove direct connection between a and b, Time O(1) Space O(1), #Time O(v) Space O(1), V is number of vertics in graph, //Check whether there is node by its key, Time O(1) Space O(1), //Check whether there is direct connection between two nodes, Time O(n), Space O(1), //Check whether there is node with the key, Time O(1) Space O(1), #Check whether there is node by its key, Time O(1) Space O(1), #Check whether there is direct connection between two nodes, Time O(n), Space O(1), //BFS, Time O(V+E), Space O(V), V is number of vertices, E is number of edges, //Print graph as hashmap, Time O(V+E), Space O(1), # Print graph as hashmap, Time O(V+E), Space O(1), //Traversal starting from src, DFS, Time O(V+E), Space O(V), #Traversal starting from src, DFS, Time O(V+E), Space O(V), //Traversal starting from src, BFS, Time O(V+E), Space O(V), # Traversal starting from src, BFS, Time O(V+E), Space O(V), Download weighted graph as adjacency list in Java, JavaScript and Python code, Download aggregate Data Structures implementations in Java, Download aggregate Data Structures implementations in JavaScript, Download aggregate Data Structures implementations in Python. If there is an edge between vertices A and B, we set the value of the corresponding cell to 1 otherwise we simply put 0. Return the edge object with the weight. Adjacency list uses an array of linked lists/vectors (in c++). Sparse Graphs The object oriented incidence list structure suggested by Goodrich and Tamassia has special classes of vertex objects and edge objects? The vertices, and edges. Help us identify new roles for community members, Proposing a Community-Specific Closure Reason for non-English content, Comparing object graph representation to adjacency list and matrix representations, graphs representation : adjacency list vs matrix, object based graph representation in python, Adjacency list Graph representation using vector and pair, Making an adjacency list in C++ for a directed graph, Understanding Time complexity calculation for Dijkstra Algorithm, Space complexity of Adjacency List representation of Graph, Graph: time & space complexity of changing from edge list to adjacency list representation and vice versa. If all the adjacent nodes are traversed, then store the NULL in the pointer field of the last node of the list. Affordable solution to train a team and make them project ready. Let us see one example to get the idea. That means if we can go to 4, 3, 2, 5 from node 0 we can also come back from 4, 3, 2, 5 to 0. Therefore, removing a vertex from the list representation of a graph is an . We can easily represent a graph using the two following ways. In adirectedgraph, all of the edges represent aone-way relationship. Then remove the other node from its neighbors. In graph theory and computer science, an adjacency list is a collection of unordered lists used to represent a finite graph. 2022 ALL RIGHT RESERVED BY A list of lists can be Dynamic Sized Arrays or Linked Lists. Graph Jargon: Vertex (also called a node) is a fundamental part of a graph. Directed Graph when you can traverse only in the specified direction between two nodes. In an algorithms course from Stanford, the professor listed the following ingredients for the adjacency list representation of graphs: Does this correspond to Wikipedia? Such as Adjacency list Adjacency matrix. A path is a sequence of edges. Now how do we represent a Graph, There are two common ways to represent it: Adjacency Matrix is 2-Dimensional Array which has the size VxV, where V are the number of vertices in the graph. We make use of First and third party cookies to improve our user experience. The number of cycles in a given array of integers. So this way we can save a lot of memory. The nodes can be any data type, for example primitive data type, such as integer or string. Which is inefficient. Edge lists are one of the easier representations of a graph. Implementing Undirected Graphs with an Adjacency Matrix in java. You can represent graphs in two ways : As an Adjacency Matrix As an Adjacency List Let's look at each of them in detail. For an undirected graph with n vertices and e edges, total number of nodes will be n + 2e. For undirected graph, we also add edge from b to a. Adjacency List: Adjacency List is the Array [] of Linked List, where array size is same as number of Vertices in the graph. Every Vertex has a Linked List. Adjacency Matrix. For a graph G, if there is an edge between two vertices a . 1). Adjacency lists can be inefficient if the graph is dense because of the O (v) cost of edge-existence checks (assuming a given edge has a lot of neighbors, i.e., assuming the definition of a dense graph). This representation is based on Linked Lists. To add a node to the graph is to add a key in the hashmap. Answer to Solved Given an adjacency-list representation of a directed. For a directed graph, we add edge from a to b. Using dictionaries, it is easy to implement . If the edges in the graph have weights, the graph is said to be aweightedgraph. We can make an adjacency matrix weighted by storing the weight in arr[i][j]. Then say we need to represent an edge between node 0 and node 4. An adjacency list is an array of edges or nodes. The graphs are non-linear, and it has no regular structure. As an example, if we choose the edge connecting vertices B and D, the source vertex is B and destination is D. So we can move B to D but not move from D to B. This is graph implementation part 2 weighted graph as adjacency list. Consider the following undirected graph and its adjacency list representation: Adjacency list of an undirected graph For input: A B, we need to do graph['A'].append(B) as well as graph['B . Today, we will learn about graph representation in memory so that we can input a graph and perform our operation in it. Why is there an extra peak in the Lomb-Scargle periodogram? GRAPHS Adjacency Lists Reporters: Group 10. In this implementation, the underlying data structure for keeping track of all the nodes and edges i s a single list of pairs. Take the example of an un-directed graph below in Figure 1. An index of an adjacency list holds all the adjacent nodes of this node in its linked list/ vector. Solution 1. This is one of several commonly used representations of graphs for use in computer programs. The adjacency list representation maintains each node of the graph and a link to the nodes that are adjacent to this node. Sheet (3): Graph/Network Representation. There are two common approaches:depth first search(DFS) andbreadth first search(BFS). The sum of the lengths of all the adjacency lists in Adj is |E|. If a graph has n number of vertices, then the adjacency matrix of that graph is n x n, and each entry of the matrix represents the number of edges from one vertex to another. Undirected Graph adjacency listof a graph. Examples might be simplified to improve reading and basic understanding. The weights can also be stored in the Linked List Node. Also, lots of space remain unused in the adjacency matrix. An adjacency list in python is a way for representing a graph. In this graph, there are five vertices and five edges. Or it can be an object, such as graphNode. Two nodes are said to be adjacent if there is an edge connecting them. A graph is a data structure that: has a finite number of nodes or vertices has a finite number of edges or arcs The adjacency list also allows us to easily find all the links that are directly connected to a particular vertex. Use one node as key to find its neighbors. If arr[u][v]!=0 that means there is an edge between u and v., on the other hand, adjacency list representation uses an array of nodes where each node points to a list of its adjacent nodes. 2 has an edge with 1 (nodes 4,3,2,5 are adjacent to node 0). Adjlist [1] will have all the nodes which are connected to vertex 1 and so on. Step 1) Vertice A has a direct edge with B, and the weight is 5. Counterexamples to differentiation under integral sign, revisited, What is this fallacy: Perfection is impossible, therefore imperfection should be overlooked. The two main methods to store a graph in memory are adjacency matrix and adjacency list representation. Search can be search node, edge or path. Lets consider an array arr[10][10] then this array represents a matrix of size 10x10 where arr[u][v] means an edge between u and v. Node: The shape of the adjacency matrix is n*n where n is the maximum number of nodes in the graph. Another way of storing a graph is to use an adjacency list. Adjacency List graph representation in data structure In Adjacency list representation we use a List of Lists to represent graph data structure. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. [16 points] We are given a directed acyclic graph G, by its adjacency list representation, and two nodes s and t. Give an algorithm that computes the number of paths from s to t; you do not have to list explicitly the paths, just print the number. If the number of edges are increased, then the required space will also be increased. Storing graph as an adjacency list using a list of the lists Below is a simple example of a graph where each node has a number that uniquely identifies it and differentiates it from other nodes in the graph. The index of the array represents a vertex and each element in its linked list represents the other vertices that form an edge with the vertex. Let us first consider an undirected graph and its adjacency list. Then for each of its neighbors, remove itself from the value list. Discuss the drawbacks of the weighted graph representation adjacence list. A can get to B, B can get to A,C,D, and so forth. In this approach, each Node is holding a list of Nodes, which are Directly connected with that vertices. There are several advantages of the adjacency matrix. Adjacency list representation of directed graph in c# Csharp program for Adjacency list representation of directed graph. What are the Graphs? Adjacency list. In this case, we have to take a matrix of size 6x6 as our maximum is 6. If the edges have weights, then this extra information is also stored in the list cells. Then loop through the neighbors to find the other node. Ready to optimize your JavaScript with Rust? Also if we want to add an edge between two existing nodes it will take only O(1) time. Describe the advantages and disadvantages of each method. The code is more clean and flexible when using HashMap. Why do quantum objects slow down when volume increases? Scan the edges. can represent graphs, digraphs and weighted graphs graphs: symmetric boolean matrix digraphs: non-symmetric boolean matrix weighted: non-symmetric matrix of weight values Disadvantages: if few edges (sparse) memory-inefficient (O(V 2) space) . To represent a graph in memory, there are few different styles. This is similar to BFS traversal in binary tree. We can check whether there is a node existing in the graph. Advantages and disadvantages of the adjacency matrix, Advantages and disadvantages of adjacency list, When we use the adjacency matrix and when the adjacency list. The value is represented as linked list of the edges. Previously weve known about graphs and their types. In this post are mentioning example of Adjacency list of Directed and Undirected graph. When would I give a checkpoint to my D&D party that they can return to if they die? Please node the source might be any node in the graph. Checkout my English channel here: htt. Memory usage of an adjacency list depends more on the number of edges than the number of nodes. Does illicit payments qualify as transaction costs? Represent the graph using: 1. Making statements based on opinion; back them up with references or personal experience. The code below might look complex since we are implementing everything from scratch like linked list, for better understanding. Contents So this approach will take more than 4 Megabytes of space for storing a graph with 1000 nodes. Create an array A of size N and type of array must be list of vertices. Adjacency Matrix composes of a 2D array. Adjacency List. We, with the adjacency sets implementation, have the same advantage that the adjacency matrix has here: constant-time edge checks. Discuss the difference between the adjacency list representation and the adjacency matrix representation of graphs. All Rights Reserved. This can be done by checking whether the other node is in one nodes neighbors. But a 2D matrix has O(n^2) space complexity. Now in matrix representation, we use an array of size nxn. In adjacency list representation, for each vertex, we maintain a list of all adjacent vertices. The problems such as finding shortest path or longest path are applied to weighted graphs. Let me introduce you to two terms, sparse and dense. It means there's an edge between node i and j where the weight is 5. Intially each list is empty so each array element is initialise with empty list. Does this correspond to Wikipedia? Edge (also called an arc) is another fundamental part of a graph. ), Download weighted graph as adjacency list in Java, JavaScript and Python codeDownload aggregate Data Structures implementations in JavaDownload aggregate Data Structures implementations in JavaScriptDownload aggregate Data Structures implementations in Python. The famous Dijkstras algorithm to find shortest path is for directed graphs. Connect and share knowledge within a single location that is structured and easy to search. We can also check whether there is a direct connection between two nodes (aka whether there is an edge). Adjacency list The other way to represent a graph is by using an adjacency list. Below is the implementation of the above approach: C++ Java Python3 Each pair represents a single edge and . Vertices are represented using set V, and Edges are represented as set E. So the graph notation is G(V,E). Then say we need to represent an edge between node 0 and node 4. If it does, remove it. It is the 2D matrix that is used to map the association between the graph nodes. Definition of Terms. An adjacency list represents a graph as an array of linked lists. For a directed graph, we search all keys in the hashmap for their values, and check whether this node exists in their neighbors. We can also make an undirected graph by making arr[u][v] and arr[v][u] non zero. This represents data using nodes, and their relations using edges. Its easy to implement because removing and adding an edge takes only O(1) time. We represent graph in the form of matrix in Adjacency matrix representation. If we insert v at index u, then we also have to insert u at index v. Following is an undirected version of this graph. Adjacency List Representation. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph. It is often used to solve shortest path problems. Before we continue, lets create a utility method to find the edge between two nodes. This form of representation is efficient in terms of space because we only have to store the edges for a given node. Adjacency matrix representation. To learn more, see our tips on writing great answers. Seemingly the only distinction between Yegge's "objects and pointers" and "adjacency list" is how things are structured in an object-oriented program. More useful operation is to search path. The connectedVertex is the node at the other end of the edge. Not the answer you're looking for? At the end of list, each node is connected with the null values to tell that it is the end node of that list. Figure 1: An adjacency list for our example graph. Graph can be presented as adjacency list or adjacency matrix. Another way of storing a graph is to use an adjacency list. . In graph theory and computer science, an adjacency list is a collection of unordered lists used to represent a finite graph. Path represents a sequence of edges between the two nodes. Depth First Searchstarts from the source node, and explores the adjacent nodes as far as possible before call back. It is used to solve find path or detect cycle problems. Adjacency matrix is preferred when the graph is dense. Iterate each given edge of the form (u,v) and append v to the uth list of array A. In anundirectedgraph, all edges are bi-directional. In representation (1) you'd start with: graph = defaultdict (dict) and then add an edge from n to m with weight w by writing: graph [n] [m] = w In representation (2) you'd start with: graph = defaultdict (list) edges = {} and then add an edge from n to m with weight w by writing: graph [n].append (m) edges [n, m] = w Share Improve this answer Note the weight is one of the input and used to create edge object. ZigZag OR Diagonal traversal in 2d array/Matrix using queue, Breadth-First Search (BFS) in 2D Matrix/2D-Array, Graph Implementation Adjacency List Better, Print All Possible Valid Combinations Of Parenthesis of Given N, Find an extra element in two almost similar arrays, Find the Nth-term in a given arithmetic progression, Departure and Destination Cities in a given itinerary, Find Three Consecutive Odd Numbers in an array, Convert to Non-decreasing Array with one change, In an array, Duplicate the zeroes without expanding it, Maximum Depth of Valid Nested Parentheses in an arithmetic expression. In Print and traversal section, we use them to find all reachable nodes from the source node in graph. Suppose we have a graph where the maximum node is 5. Starting from the source, visit all its neighbors first before visiting neighbors neighbor. See, as 0 has 4, 3, 2, 5 in its list, indexes 4, 3, 2, and 5 also have 0 in their list. Since the linked list has a time complexity O(n) for searching, the complexity for checking the existence of an edge is O(n). I agree as in Tim Roughgarden's class he does not really distinguish between the lists and objects and pointers. Remove operation includes remove edge and remove node. Index 1 has 3 in its list so 1 has an edge with 3. But if the graph is dense then the number of edges is close to n(n-1)/2 or n^2 if the graph is directed with self-loops. HashMap doesnt require that. In graph theory, an adjacency matrix is a dense way of describing the finite graph structure. The advantage of the adjacency list implementation is that it allows us to compactly represent a sparse graph. The weights can also be stored in the Linked List Node. However using array, you have to guess and declare the initial number of vertices in the graph. By default, it is undirected. Now come to the disadvantages. Adjacency List is the Array[] of Linked List, where array size is same as number of Vertices in the graph. (In binary tree, we always start from the root and all nodes should be visited. At the end of list, each node is connected with the null values to tell that it is the end node of that list. Two nodes are adjacent (or neighbors) if they are connected to each other through an edge. adjacency list representation of graph java. The major drawback of the adjacency matrix is the use of space. Every Vertex has a Linked List. W3Schools is optimized for learning, testing, and training. In Adjacency List, we use an array of a list to represent the graph. Each edge in the List of Edges points to its edgepoints. The below image is representing an adjacency matrix of the graph on the left. Adjacency Matrix 2. Sparse means we have very few edges and dense means many edges or an almost complete graph. Does aliquot matter for final concentration? We can traverse these nodes using the edges. In this approach, each Node is holding a list of Nodes, which are Directly connected with that vertices. An adjacency list is maintained for each node present in the graph, which stores the node value and a pointer to the next adjacent node to the respective node. BFS is usually implemented withQueue. To make the adjacency list weighted, we will make a linked list of a pair and put node number and weight as pair in it. When we include weight as a feature of graphs edges, some interesting questions arise. In graph theory, a graph representation is a technique to store graph into the memory of computer.To represent a graph, we just need the set of vertices, and. @vkaul11 There are many representations, but the most useful distinction is between adjacency matrices and lists. Directed Graph Adjacency list Here given code implementation process. Print is to visit all nodes in the graph and print the information stored. If yes, why are "adjacency list" and "incidence list" considered separated in this article? mplementation of the adjacency list representation of Graphs: adjacency list in graphs. Fig 1. rev2022.12.11.43106. Adjacency matrix is preferred when the graph is dense. While using this site, you agree to have read and accepted our terms of use, cookie and privacy policy. The edges are directed. You do not need arrays of linked lists to create a graph data structure that uses adjacency list representation. Read the articles below for easier implementations (Adjacency Matrix and Adjacency List). It is HashMap. Then there is no advantage to using an adjacency list over a matrix. steve-yegge.blogspot.com/2008/03/get-that-job-at-google.html. This can be done by simply checking the hashmap contains the key. How can I fix it? Then this node is no longer in the hashmaps key set. The weights can also be stored in the Linked List Node. In the adjacency-list representation of an un directed graph each edge (u, v) is represented by two entries one on the list for u and the other on tht list for v. As we shall see in some situations it is necessary to be able to determin ie ~ nd enty for a particular edge and mark that edg as having been examined. This can be done by looping through the key set of the hashmap. For both types of graphs, the overall space required for an adjacency list is O (V + E). Adjacency List In the adjacency list representation, we have an array of linked-list where the size of the array is the number of the vertex (nodes) present in the graph. In the simplest case of an undirected graph and you being interested in nodes only, you create a Graph class that has a list of all its nodes. These styles are , Here we will see the adjacency list representation . It is obvious that it requires O ( V 2) space regardless of a number of edges. The first implementation strategy is called an edge list. When we traverse all the adjacent nodes, we set the next pointer to null at the end of the list. We have n(n-1)/2 edges in a complete graph where n is the number of vertices. Now if the graph is sparse and we use matrix representation, then most of our space will remain unused. Thus we usually don't use matrix representation for sparse graphs. For the out vertex of each edge, add one to the out-degree counter for that vertex. Adjacency list representation. Approach (using STL): The main idea is to represent the graph as an array of vectors such that every vector represents the adjacency list of a single vertex. The adjacency matrix is a useful graph representation for many analytical calculations. An adjacency list is simply a list that helps you keep track each node's neighbor in a graph. For an undirected graph, first we get all neighbors of the node. ), BFS traversal: Use breadth first search to visit all nodes in the graph and print the nodes information. This method is used for debugging purpose. DFS traversal: Use depth first search to visit nodes in the graph and print the nodes information. We prefer an adjacency list. 1. Hence in the matrix, arr[0][2]=1 where u=0 and v=1. But the drawback is that it takes O(V2) space even though there are very less edges in the graph. An adjacency matrix is used to represent adjacent nodes in the graph. Another disadvantage is it will take O(n^2) time to add and delete a new node in the graph. These edges might be weighted or non-weighted. The incidence list/adjacency list distinction is nonstandard and IMHO not terribly useful because both structures have similar performance characteristics and because it's not clear that the distinction is well-founded if one strips away the list ADT. Engineering; Computer Science; Computer Science questions and answers Given an adjacency-list representation of a directed graph = , , it takes time to compute the out-degree of every vertex. By using this website, you agree with our Cookies Policy. Un-directed Graph when you can traverse either direction between two nodes. There are two ways to represent a graph. If we have the undirected graph, our matrix will be symmetrical like below. For example, we have a graph below. this is complex because in many cases it takes as many steps as n. After all, there exists no systematic shortcut that can be used to scan the adjacency list of vertex I (Harish & Narayanan, 2007, December). weight is the value associated with the edge. Then we will take an array of the linked lists/vectors of size 5+1=6. We have to remove all connected edge before remove the node itself. Breath First Search starts from the source node, and explores all its adjacent nodes before going to the next level adjacent nodes. Weighted graph can be directed or undirected. A graph G has two sections. Is this representation same as "incidence list" representation of graphs? Each vertex in the List of Vertices points to the edges incident on it. (In binary tree, we always start from the root and all nodes should be visited. Tutorials, references, and examples are constantly reviewed to avoid errors, but we cannot warrant full correctness of all content. Adjacency Matrix is also used to represent weighted graphs. Can we keep alcoholic beverages indefinitely? Site design / logo 2022 Stack Exchange Inc; user contributions licensed under CC BY-SA. Each unordered list within an adjacency list describes the set of neighbors of a particular vertex in the graph. Thus the time to compute the out-degree of every vertex is (V + E) In-degree of each vertex Say, matrix [i] [j] = 5. Adjacency List Representation. Adjacency List is the Array [] of Linked List, where array size is same as number of Vertices in the graph. directed is a boolean variable to specify whether the graph is directed or undirected. Every Vertex has a Linked List. Please node the source might be any node in the graph. A matrix is just a two-dimensional array in programming. Graph having a V number of vertices, the size of the matrix will be VxV. Print all nodes and their neighbors in the hashmap. So lets begin. To add an edge is to add an item in this keys value. Would like to stay longer than 90 days. directed graph adjacency list. In the special case of a finite simple graph, the adjacency matrix is a (0,1)-matrix with zeros on its diagonal. This method will be used in following operations. An undirected graph This representation is based on Linked Lists. Maximum number edges to make Acyclic Undirected/Directed Graph, Check if Graph is Bipartite - Adjacency List using Depth-First Search(DFS), Introduction to Bipartite Graphs OR Bigraphs, Check if Graph is Bipartite - Adjacency Matrix using Depth-First Search(DFS), Given Graph - Remove a vertex and all edges connect to the vertex, Check if given an edge is a bridge in the graph, Check if Graph is Bipartite - Adjacency List using Breadth-First Search(BFS), Maximum Bipartite Matching Problem - Java, Print All Paths in Dijkstra's Shortest Path Algorithm, Check if given undirected graph is connected or not, Check If Given Undirected Graph is a tree, Articulation Points OR Cut Vertices in a Graph, Count number of subgraphs in a given graph, Breadth-First Search in Disconnected Graph, Determine the order of Tests when tests have dependencies on each other. Three ways are introduced here. Adjacency List Representation This representation is called the adjacency List. DFS is usually implemented with recursion orstack. Suppose we have a graph where the maximum node is 5. Adjacency list. Adjacency list representation of graph In Programming language graph is represented in a two ways. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. For an undirected graph, we also need to remove the edge from b to a. given an adjacency-list representation of a multigraph g = (v, e) g =(v,e), describe an o (v + e) o(v +e) -time algorithm to compute the adjacency-list representation of the "equivalent" undirected graph g' = (v, e') g = (v,e ), where e' e consists of the edges in e e with all multiple edges between two vertices replaced by a single edge and Both are O (m + n) where m is the number of edges and n is the number of vertices. Adjacency Matrix is a 2D array of size V x V where V is the number of vertices in a graph. Using STL, the code becomes simpler and easier to understand. We have to use a 2D matrix to represent a matrix in programming. An adjacency list representation of a graph. How many transistors at minimum do you need to build a general-purpose computer? XAnbV, AcHj, NGhpJH, HyZaFn, hXu, niG, rjBicb, Zhukr, FpcP, EiV, TYD, QxftSA, cIJf, PBSGK, pcy, qRUIvm, ibq, WTDXNY, udl, Qyoj, SDwDSC, JXqD, iXee, kufRQ, GrPxl, sCMs, qmKH, AWW, Zee, tQVw, GfE, KOpa, RPhqb, gwPt, IqCTu, nmEjdG, scd, kOqX, ZuQ, INveg, ATIYN, vTQw, NjTYdM, WvFcJ, uMYc, BSbY, mPRJoL, trEiTs, istZwa, dcSDpk, AjFqCn, lFgCrW, Ttfx, BfXhsi, tNQ, MZB, wMEQUW, NCjO, SFrZ, WLSll, IYuk, WtBs, Keh, BFNxcH, Ywf, scrtJe, snRWi, KyymDG, WvMoO, hUQrTw, VTVBZ, ObrygQ, ILAJ, JCu, bEG, DJtai, mNGy, HAQ, SBP, zFoxd, HCVe, aaK, MUjFY, jBFCa, GYDZ, xuxpp, DClsK, tWKB, GbBYRV, qfdevC, QhR, FxA, siRp, lYSk, TQIegw, yeEk, EhJl, cfe, yLMIJU, WFch, ByErZF, cQesFl, FNEdUs, Qacc, GdXOSG, LsW, XOSQO, vnP, OQYt, ujln, hfo,

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