stream For any edge in the graph, if dist[u] + weight < dist[v], Negative weight cycle is present. Following is the time complexity of the bellman ford algorithm. Time and policy. Like Dijkstra's shortest path algorithm, the Bellman-Ford algorithm is guaranteed to find the shortest path in a graph. After the i-th iteration of the outer loop, the shortest paths with at most i edges are calculated. If there are negative weight cycles, the search for a shortest path will go on forever. You can arrange your time based on your own schedule and time zone. Log in. Bellman-Ford pseudocode: Initialize all distances as infinite, except the distance to the source itself. A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. | Please leave them in the comments section at the bottom of this page if you do. [2] Edward F. Moore also published a variation of the algorithm in 1959, and for this reason it is also sometimes called the BellmanFordMoore algorithm. Cormen et al., 2nd ed., Problem 24-1, pp. The distance to each node is the total distance from the starting node to this specific node. In such a case, the BellmanFord algorithm can detect and report the negative cycle.[1][4]. The algorithm initializes the distance to the source to 0 and all other nodes to INFINITY. 1 Things you need to know. Once the algorithm is over, we can backtrack from the destination vertex to the source vertex to find the path. MIT. The algorithm then iteratively relaxes those estimates by discovering new ways that are shorter than the previously overestimated paths. | A graph having negative weight cycle cannot be solved. Let us consider another graph. // If we get a shorter path, then there is a negative edge cycle. V Negative weight edges can generate negative weight cycles, which reduce the total path distance by returning to the same point. We are sorry that this post was not useful for you! Step 5: To ensure that all possible paths are considered, you must consider alliterations. Bellman Ford Algorithm (Simple Implementation) - GeeksforGeeks algorithm - Bellman-Ford vs Dijkstra: Under what circumstances is A.distance is set to 5, and the predecessor of A is set to S, the source vertex. New Bellman jobs added daily. -CS_CS_Finance_Economic_Statistics__IT__ Positive value, so we don't have a negative cycle. The correctness of the algorithm can be shown by induction: Proof. For example, instead of paying the cost for a path, we may get some advantage if we follow the path. >> V We also want to be able to get the shortest path, not only know the length of the shortest path. Soni Upadhyay is with Simplilearn's Research Analysis Team. A single source vertex, \(s\), must be provided as well, as the Bellman-Ford algorithm is a single-source shortest path algorithm. We have introduced Bellman Ford and discussed on implementation here. {\displaystyle |V|} The standard Bellman-Ford algorithm reports the shortest path only if there are no negative weight cycles. This algorithm is used to find the shortest distance from the single vertex to all the other vertices of a weighted graph. Bellman-Ford Algorithm is an algorithm for single source shortest path where edges can be negative (but if there is a cycle with negative weight, then this problem will be NP). Single-Source Shortest Paths - Bellman-Ford Algorithm Do following for each edge u-v, If dist[v] > dist[u] + weight of edge uv, then update dist[v]to, This step reports if there is a negative weight cycle in the graph. V The algorithm processes all edges 2 more times. Negative weight edges can create negative weight cycles i.e. | The Bellman-Ford algorithm emulates the shortest paths from a single source vertex to all other vertices in a weighted digraph. The first subset, Ef, contains all edges (vi, vj) such that i < j; the second, Eb, contains edges (vi, vj) such that i > j. The credit of Bellman-Ford Algorithm goes to Alfonso Shimbel, Richard Bellman, Lester Ford and Edward F. Moore. << Given a source vertex s from a set of vertices V in a weighted directed graph where its edge weights w(u, v) can be negative, find the shortest path weights d(s, v) from source s for all vertices v present in the graph. edges, the edges must be scanned Dynamic Programming is used in the Bellman-Ford algorithm. It is what increases the accuracy of the distance to any given vertex. Introduction to Algorithms 6.046J/18.401J/SMA5503 Lecture 18 Prof. Erik Demaine. Leverage your professional network, and get hired. Pseudocode of the Bellman-Ford Algorithm Every Vertex's path distance must be maintained. Shortest Paths - TUM If there is a negative weight cycle, then shortest distances are not calculated, negative weight cycle is reported.1) This step initializes distances from source to all vertices as infinite and distance to source itself as 0. Following is the pseudocode for BellmanFord as per Wikipedia. There are several real-world applications for the Bellman-Ford algorithm, including: You will now peek at some applications of the Bellman-Ford algorithm in this tutorial. , at the end of the Bellman Ford Algorithm:The Bellman-Ford algorithm emulates the shortest paths from a single source vertex to all other vertices in a weighted digraph. When the algorithm is used to find shortest paths, the existence of negative cycles is a problem, preventing the algorithm from finding a correct answer. Bellman-Ford, on the other hand, relaxes all of the edges. [3] The BellmanFord algorithm is an algorithm that computes shortest paths from a single source vertex to all of the other vertices in a weighted digraph. Bellman Ford algorithm helps us find the shortest path from a vertex to all other vertices of a weighted graph. Yen (1970) described another improvement to the BellmanFord algorithm. Using negative weights, find the shortest path in a graph. The second iteration guarantees to give all shortest paths which are at most 2 edges long. Put together, the lemmas imply that the Bellman-Ford algorithm computes shortest paths correctly: The first lemma guarantees that v. d is always at least ( s, v). The graph may contain negative weight edges. As stated above, Dijkstra's also achieves the same goal, but if any negative weight cycle is present, it doesn't work as required. times to ensure the shortest path has been found for all nodes. Relaxation is the most important step in Bellman-Ford. This is one of the oldest Internet protocols, and it prevents loops by limiting the number of hops a packet can make on its way to the destination. Usage. Step 2: Let all edges are processed in the following order: (B, E), (D, B), (B, D), (A, B), (A, C), (D, C), (B, C), (E, D). | Today's top 5 Bellman jobs in Phoenix, Arizona, United States. ( Join our newsletter for the latest updates. We get the following distances when all edges are processed the first time. For the base case of induction, consider i=0 and the moment before for loop is executed for the first time. Graphical representation of routes to a baseball game. Step 4:If the new distance is less than the previous one, update the distance for each Edge in each iteration. Imagine a scenario where you need to get to a baseball game from your house. Initialize dist[0] to 0 and rest values to +Inf. {\displaystyle |V|} When attempting to find the shortest path, negative weight cycles may produce an incorrect result. We have introduced Bellman Ford and discussed on implementation here.Input: Graph and a source vertex srcOutput: Shortest distance to all vertices from src. This happened because, in the worst-case scenario, any vertex's path length can be changed N times to an even shorter path length. function bellmanFordAlgorithm(G, s) //G is the graph and s is the source vertex, dist[V] <- infinite // dist is distance, prev[V] <- NULL // prev is previous, temporaryDist <- dist[u] + edgeweight(u, v), If dist[U] + edgeweight(U, V) < dist[V}. Like Dijkstra's algorithm, BellmanFord proceeds by relaxation, in which approximations to the correct distance are replaced by better ones until they eventually reach the solution. V Initially, all vertices except the source vertex, // edge from `u` to `v` having weight `w`, // if the distance to destination `v` can be, // update distance to the new lower value, // run relaxation step once more for n'th time to check for negative-weight cycles, // if the distance to destination `u` can be shortened by taking edge (u, v), // vector of graph edges as per the above diagram, // (x, y, w) > edge from `x` to `y` having weight `w`, // set the maximum number of nodes in the graph, // run the BellmanFord algorithm from every node, // distance[] and parent[] stores the shortest path, // initialize `distance[]` and `parent[]`. Bellman Ford is an algorithm used to compute single source shortest path. If there are no negative-weight cycles, then every shortest path visits each vertex at most once, so at step 3 no further improvements can be made. Detecting negative cycle using Bellman Ford algorithm Do following for each edge u-vIf dist[v] > dist[u] + weight of edge uv, then Graph contains negative weight cycleThe idea of step 3 is, step 2 guarantees shortest distances if graph doesnt contain negative weight cycle. The pseudo-code for the Bellman-Ford algorithm is quite short. //The shortest path of graph that contain Vertex vertices, never contain "Veretx-1" edges. This process is done |V| - 1 times. For instance, if there are different ways to reach from one chemical A to another chemical B, each method will have sub-reactions involving both heat dissipation and absorption. If the new calculated path length is less than the previous path length, go to the source vertex's neighboring Edge and relax the path length of the adjacent Vertex. The fourth row shows when (D, C), (B, C) and (E, D) are processed. The algorithm initializes the distance to the source vertex to 0 and all other vertices to . Moving ahead with this tutorial on the Bellman-Ford algorithm, you will now learn the pseudocode for this algorithm. New user? First, sometimes the road you're using is a toll road, and you have to pay a certain amount of money. You are free to use any sources or references including course slides, books, wikipedia pages, or material you nd online, but again you must cite all of them. Do you have any queries about this tutorial on Bellman-Ford Algorithm? Try Programiz PRO: Bellman-Ford does just this. Each node sends its table to all neighboring nodes. This is high level description of Bellman-Ford written with pseudo-code, not an implementation. A variation of the BellmanFord algorithm known as Shortest Path Faster Algorithm, first described by Moore (1959), reduces the number of relaxation steps that need to be performed within each iteration of the algorithm. Imagining that the edge in question is the edge \((u, v),\) that means that \(u.distance + weight(u, v)\) will actually be less than \(v.distance\), which will trigger a negative cycle report. There will not be any repetition of edges. If we iterate through all edges one more time and get a shorter path for any vertex, then there is a negative weight cycleExampleLet us understand the algorithm with following example graph. Then for all edges, if the distance to the destination can be shortened by taking the edge, the distance is updated to the new lower value. But time complexity of Bellman-Ford is O(V * E), which is more than Dijkstra. Going around the negative cycle an infinite number of times would continue to decrease the cost of the path (even though the path length is increasing). Also in that first for loop, the p value for each vertex is set to nothing. We can store that in an array of size v, where v is the number of vertices. Bellman-Ford algorithm can easily detect any negative cycles in the graph. We also want to be able to get the shortest path, not only know the length of the shortest path. {\displaystyle O(|V|\cdot |E|)} It starts with a starting vertex and calculates the distances of other vertices which can be reached by one edge. In contrast to Dijkstra's algorithm and the A* algorithm, the Bellman-Ford Algorithm also return shortest paths when negative edge weights are present. Since this is of course true, the rest of the function is executed. [5][6], Another improvement, by Bannister & Eppstein (2012), replaces the arbitrary linear order of the vertices used in Yen's second improvement by a random permutation. }OnMk|g?7KY?8 V (E V). And you saw the time complexity for applying the algorithm and the applications and uses that you can put to use in your daily lives. Journal of Physics: Conference Series PAPER OPEN - Institute of Physics A graph without any negative weight cycle will relax in n-1 iterations. // This structure is equal to an edge. Dijkstra doesnt work for Graphs with negative weights, Bellman-Ford works for such graphs. 1. https://en.wikipedia.org/wiki/Bellman%E2%80%93Ford_algorithm, 2. A key difference is that the Bellman-Ford Algorithm is capable of handling negative weights whereas Dijkstra's algorithm can only handle positive weights. For example, consider the following graph: The idea is to use the BellmanFord algorithm to compute the shortest paths from a single source vertex to all the other vertices in a given weighted digraph. 2 The third row shows distances when (A, C) is processed. | This is later changed for the source vertex to equal zero. Learn more about bidirectional Unicode characters . There is another algorithm that does the same thing, which is Dijkstra's algorithm. There are a few short steps to proving Bellman-Ford. algorithm Tutorial => Bellman-Ford Algorithm and Using our Step 2, if we go back through all of the edges, we should see that for all \(v\) in \(V\), \(v.distance = distance(s, v)\). After the Bellman-Ford algorithm shown above has been run, one more short loop is required to check for negative weight cycles. The second lemma guarantees that v. d = ( s, v) after rounds, where is the length of a minimum weight path from s to v. Share Cite Improve this answer Follow Bellman-Ford Algorithm. Subsequent relaxation will only decrease \(v.d\), so this will always remain true. A final scan of all the edges is performed and if any distance is updated, then a path of length Bellman-Ford does not work with an undirected graph with negative edges as it will be declared as a negative cycle. {\displaystyle O(|V|\cdot |E|)} Bellman-Ford algorithm - Wikipedia Unlike Dijkstras where we need to find the minimum value of all vertices, in Bellman-Ford, edges are considered one by one. Can we use Dijkstras algorithm for shortest paths for graphs with negative weights one idea can be, to calculate the minimum weight value, add a positive value (equal to the absolute value of minimum weight value) to all weights and run the Dijkstras algorithm for the modified graph. printf("\nEnter edge %d properties Source, destination, weight respectively\n",i+1); scanf("%d",&graph->edge[i].src); scanf("%d",&graph->edge[i].dest); scanf("%d",&graph->edge[i].wt); //passing created graph and source vertex to BellmanFord Algorithm function. However, I know that the distance to the corner right before the stadium is 10 miles, and I know that from the corner to the stadium, the distance is 1 mile. Because the shortest distance to an edge can be adjusted V - 1 time at most, the number of iterations will increase the same number of vertices. So, I can update my belief to reflect that. [1] It is slower than Dijkstra's algorithm for the same problem, but more versatile, as it is capable of handling graphs in which some of the edge weights are negative numbers. However, the worst-case complexity of SPFA is the same as that of Bellman-Ford, so for . struct Graph* graph = (struct Graph*) malloc( sizeof(struct Graph)); graph->Vertex = Vertex; //assigning values to structure elements that taken form user. Step 1: Make a list of all the graph's edges. x]_1q+Z8r9)9rN"U`0khht]oG_~krkWV2[T/z8t%~^v^H [jvC@$_E/ob_iNnb-vemj{K!9sgmX$o_b)fW]@CfHy}\yI_510]icJ!/(+Fdg3W>pI]`v]uO+&9A8Y]d ;}\~}6wp-4OP /!WE~&\0-FLi |vI_D [`vU0 a|R~zasld9 3]pDYr\qcegW~jW^~Z}7;`~]7NT{qv,KPCWm] Consider this graph, it has a negative weight cycle in it. Bellman Jobs in Phoenix, AZ | Salary.com You will now look at the time and space complexity of the Bellman-Ford algorithm after you have a better understanding of it. Each vertex is visited in the order v1, v2, , v|V|, relaxing each outgoing edge from that vertex in Ef. The final step shows that if that is not the case, then there is indeed a negative weight cycle, which proves the Bellman-Ford negative cycle detection. However, in some scenarios, the number of iterations can be much lower. On each iteration, the number of vertices with correctly calculated distances // grows, from which it follows that eventually all vertices will have their correct distances // Total Runtime: O(VE) i A final scan of all the edges is performed, and if any distance is updated, then a path of length |V| edges have been found, which can only occur if at least one negative cycle exists in the graph. 5. The Shortest Path Faster Algorithm (SPFA) is an improvement of the Bellman-Ford algorithm which computes single-source shortest paths in a weighted directed graph. A Graph Without Negative Cycle For every This method allows the BellmanFord algorithm to be applied to a wider class of inputs than Dijkstra. It is similar to Dijkstra's algorithm but it can work with graphs in which edges can have negative weights. We can store that in an array of size v, where v is the number of vertices. Weights may be negative. A second example is the interior gateway routing protocol. You also learned C programming language code and the output for calculating the distance from the source vertex in a weighted graph. ) The \(i^\text{th}\) iteration will consider all incoming edges to \(v\) for paths with \(\leq i\) edges. You have 48 hours to take this exam (14:00 02/25/2022 - 13:59:59 02/27/2022). 2 Software implementation of the algorithm Second, sometimes someone you know lives on that street (like a family member or a friend). The fourth row shows when (D, C), (B, C) and (E, D) are processed. On the \((i - 1)^\text{th} \) iteration, we've found the shortest path from \(s\) to \(v\) using at most \(i - 1\) edges. no=mBM;u}K6dplsX$eh3f " zN:.2l]. One example is the routing Information protocol. A weighted graph is a graph in which each edge has a numerical value associated with it. BellmanFord runs in Learn to code interactively with step-by-step guidance. // This is the initial step that we know, and we initialize all distances to infinity except the source vertex. /Filter /FlateDecode The Bellman-Ford algorithm follows the bottom-up approach. Then it iteratively relaxes those estimates by finding new paths that are shorter than the previously overestimated paths. Let all edges are processed in following order: (B, E), (D, B), (B, D), (A, B), (A, C), (D, C), (B, C), (E, D). Here n = 7, so 6 times. Floyd-Warshall algorithm - Wikipedia Initialize all distances as infinite, except the distance to source itself. It is slower than Dijkstra's algorithm, but can handle negative- . By inductive assumption, u.distance is the length of some path from source to u. Bellman Ford Algorithm - Java are the number of vertices and edges respectively. | SSSP Algorithm Steps. function BellmanFord(list vertices, list edges, vertex source, distance[], parent[]), This website uses cookies. graph->edge = (struct Edges*) malloc( graph->Edge * sizeof( struct Edges ) ); //Creating "Edge" type structures inside "Graph" structure, the number of edge type structures are equal to number of edges, // This function prints the last solution. / If after n-1 iterations, on the nth iteration any edge is still relaxing, we can say that negative weight cycle is present. In this Bellman-Ford algorithm tutorial, you looked at what the algorithm is and how it works. Phoenix, AZ. The Bellman-Ford algorithm is an example of Dynamic Programming. Imagine that there is an edge coming out of the source vertex, \(S\), to another vertex, \(A\). Pseudocode. If the graph contains a negative-weight cycle, report it. Consider this weighted graph, Given a graph and a source vertex src in the graph, find the shortest paths from src to all vertices in the given graph. You will end up with the shortest distance if you do this. On this Wikipedia the language links are at the top of the page across from the article title. Bellman Ford algorithm works by overestimating the length of the path from the starting vertex to all other vertices. For all cases, the complexity of this algorithm will be determined by the number of edge comparisons. Then, it calculates the shortest paths with at-most 2 edges, and so on. Sign up, Existing user? Learn how and when to remove this template message, "An algorithm for finding shortest routes from all source nodes to a given destination in general networks", "On the history of combinatorial optimization (till 1960)", https://en.wikipedia.org/w/index.php?title=BellmanFord_algorithm&oldid=1141987421, Short description is different from Wikidata, Articles needing additional references from December 2021, All articles needing additional references, Articles needing additional references from March 2019, Creative Commons Attribution-ShareAlike License 3.0. This change makes the worst case for Yen's improvement (in which the edges of a shortest path strictly alternate between the two subsets Ef and Eb) very unlikely to happen. Let u be the last vertex before v on this path. An Example 5.1. Input: Graph and a source vertex src Output: Shortest distance to all vertices from src. Edge contains two endpoints. The idea is, assuming that there is no negative weight cycle if we have calculated shortest paths with at most i edges, then an iteration over all edges guarantees to give the shortest path with at-most (i+1) edges. Assume you're looking for a more in-depth study that goes beyond Mobile and Software Development and covers today's most in-demand programming languages and skills. We notice that edges have stopped changing on the 4th iteration itself. To review, open the file in an editor that reveals hidden Unicode characters. \(O\big(|V| \cdot |E|\big)\)\(\hspace{12mm}\). Consider the shortest path from \(s\) to \(u\), where \(v\) is the predecessor of \(u\). Distance[v] = Distance[u] + wt; //, up to now, the shortest path found. The algorithm processes all edges 2 more times. Our experts will be happy to respond to your questions as earliest as possible! printf("\nVertex\tDistance from Source Vertex\n"); void BellmanFordalgorithm(struct Graph* graph, int src). We will now relax all the edges for n-1 times. Relaxation 4th time The implementation takes a graph, represented as lists of vertices and edges, and fills distance[] and parent[] with the shortest path (least cost/path) information: The following slideshow illustrates the working of the BellmanFord algorithm. Conversely, you want to minimize the number and value of the positively weighted edges you take. Ernest Floyd Bellman Obituary (1944 - 2021) | Phoenix, Arizona - Echovita Do following |V|-1 times where |V| is the number of vertices in given graph. This is done by relaxing all the edges in the graph for n-1 times, where n is the number of vertices in the graph. BellmanFord algorithm can easily detect any negative cycles in the graph. She's a Computer Science and Engineering graduate. Bellman-Ford will only report a negative cycle if \(v.distance \gt u.distance + weight(u, v)\), so there cannot be any false reporting of a negative weight cycle. Shortest path faster algorithm - Wikipedia Find the obituary of Ernest Floyd Bellman (1944 - 2021) from Phoenix, AZ. | 1 {\displaystyle |V|-1} Make a life-giving gesture Johnson's Algorithm for All-Pair Shortest Path - Scaler Topics Then for all edges, if the distance to the destination can be shortened by taking the edge, the distance is updated to the new lower value. The only difference between the two is that Bellman-Ford is also capable of handling negative weights whereas Dijkstra Algorithm can only handle positives. Initially we've set the distance of source as 0, and all other vertices are at +Infinity distance from the source. It first calculates the shortest distances which have at most one edge in the path. It is slower than Dijkstra's algorithm for the same problem but more versatile because it can handle graphs with some edge weights that are negative numbers. As described above, Bellman-Ford makes \(|E|\) relaxations for every iteration, and there are \(|V| - 1\) iterations. Bellman Ford Pseudocode. Relaxation is safe to do because it obeys the "triangle inequality." E Graph 2. Step 3: The first iteration guarantees to give all shortest paths which are at most 1 edge long. However, since it terminates upon finding a negative cycle, the BellmanFord algorithm can be used for applications in which this is the target to be sought for example in cycle-cancelling techniques in network flow analysis.[1]. Relaxation 2nd time | An example of a graph that would only need one round of relaxation is a graph where each vertex only connects to the next one in a linear fashion, like the graphic below: This graph only needs one round of relaxation. algorithm - - Explore this globally recognized Bootcamp program. The algorithm then iteratively relaxes those estimates by discovering new ways that are shorter than the previously overestimated paths.https://www.youtube.com/watch?v=SiI03wnREt4Full Course of Design and Analysis of algorithms (DAA):https://www.youtube.com/playlist?list=PLxCzCOWd7aiHcmS4i14bI0VrMbZTUvlTa Subscribe to our new channel:https://www.youtube.com/c/GateSmashersPlusOther subject playlist Link:--------------------------------------------------------------------------------------------------------------------------------------Computer Architecture:https://www.youtube.com/playlist?list=PLxCzCOWd7aiHMonh3G6QNKq53C6oNXGrXDatabase Management System:https://www.youtube.com/playlist?list=PLxCzCOWd7aiFAN6I8CuViBuCdJgiOkT2Y Theory of Computationhttps://www.youtube.com/playlist?list=PLxCzCOWd7aiFM9Lj5G9G_76adtyb4ef7iArtificial Intelligence:https://www.youtube.com/playlist?list=PLxCzCOWd7aiHGhOHV-nwb0HR5US5GFKFI Computer Networks:https://www.youtube.com/playlist?list=PLxCzCOWd7aiGFBD2-2joCpWOLUrDLvVV_Operating System: https://www.youtube.com/playlist?list=PLxCzCOWd7aiGz9donHRrE9I3Mwn6XdP8pStructured Query Language (SQL):https://www.youtube.com/playlist?list=PLxCzCOWd7aiHqU4HKL7-SITyuSIcD93id Discrete Mathematics:https://www.youtube.com/playlist?list=PLxCzCOWd7aiH2wwES9vPWsEL6ipTaUSl3Compiler Design:https://www.youtube.com/playlist?list=PLxCzCOWd7aiEKtKSIHYusizkESC42diycNumber System:https://www.youtube.com/playlist?list=PLxCzCOWd7aiFOet6KEEqDff1aXEGLdUznCloud Computing \u0026 BIG Data:https://www.youtube.com/playlist?list=PLxCzCOWd7aiHRHVUtR-O52MsrdUSrzuy4Software Engineering:https://www.youtube.com/playlist?list=PLxCzCOWd7aiEed7SKZBnC6ypFDWYLRvB2Data Structure:https://www.youtube.com/playlist?list=PLxCzCOWd7aiEwaANNt3OqJPVIxwp2ebiTGraph Theory:https://www.youtube.com/playlist?list=PLxCzCOWd7aiG0M5FqjyoqB20Edk0tyzVtProgramming in C:https://www.youtube.com/playlist?list=PLxCzCOWd7aiGmiGl_DOuRMJYG8tOVuapBDigital Logic:https://www.youtube.com/playlist?list=PLxCzCOWd7aiGmXg4NoX6R31AsC5LeCPHe---------------------------------------------------------------------------------------------------------------------------------------Our social media Links: Subscribe us on YouTube: https://www.youtube.com/gatesmashers Like our page on Facebook: https://www.facebook.com/gatesmashers Follow us on Instagram: https://www.instagram.com/gate.smashers Follow us on Telegram: https://t.me/gatesmashersofficial-------------------------------------------------------------------------------------------------------------------------------------- For Any Query, Email us at: gatesmashers2018@gmail.comBe a Member \u0026 Give your Support on the below link: https://www.youtube.com/channel/UCJihyK0A38SZ6SdJirEdIOw/join
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