Hungarian Method
The Hungarian method is a computational optimization technique that addresses the assignment problem in polynomial time and foreshadows following primal-dual alternatives. In 1955, Harold Kuhn used the term “Hungarian method” to honour two Hungarian mathematicians, Dénes Kőnig and Jenő Egerváry. Let’s go through the steps of the Hungarian method with the help of a solved example.
Hungarian Method to Solve Assignment Problems
The Hungarian method is a simple way to solve assignment problems. Let us first discuss the assignment problems before moving on to learning the Hungarian method.
What is an Assignment Problem?
A transportation problem is a type of assignment problem. The goal is to allocate an equal amount of resources to the same number of activities. As a result, the overall cost of allocation is minimised or the total profit is maximised.
Because available resources such as workers, machines, and other resources have varying degrees of efficiency for executing different activities, and hence the cost, profit, or loss of conducting such activities varies.
Assume we have ‘n’ jobs to do on ‘m’ machines (i.e., one job to one machine). Our goal is to assign jobs to machines for the least amount of money possible (or maximum profit). Based on the notion that each machine can accomplish each task, but at variable levels of efficiency.
Hungarian Method Steps
Check to see if the number of rows and columns are equal; if they are, the assignment problem is considered to be balanced. Then go to step 1. If it is not balanced, it should be balanced before the algorithm is applied.
Step 1 – In the given cost matrix, subtract the least cost element of each row from all the entries in that row. Make sure that each row has at least one zero.
Step 2 – In the resultant cost matrix produced in step 1, subtract the least cost element in each column from all the components in that column, ensuring that each column contains at least one zero.
Step 3 – Assign zeros
- Analyse the rows one by one until you find a row with precisely one unmarked zero. Encircle this lonely unmarked zero and assign it a task. All other zeros in the column of this circular zero should be crossed out because they will not be used in any future assignments. Continue in this manner until you’ve gone through all of the rows.
- Examine the columns one by one until you find one with precisely one unmarked zero. Encircle this single unmarked zero and cross any other zero in its row to make an assignment to it. Continue until you’ve gone through all of the columns.
Step 4 – Perform the Optimal Test
- The present assignment is optimal if each row and column has exactly one encircled zero.
- The present assignment is not optimal if at least one row or column is missing an assignment (i.e., if at least one row or column is missing one encircled zero). Continue to step 5. Subtract the least cost element from all the entries in each column of the final cost matrix created in step 1 and ensure that each column has at least one zero.
Step 5 – Draw the least number of straight lines to cover all of the zeros as follows:
(a) Highlight the rows that aren’t assigned.
(b) Label the columns with zeros in marked rows (if they haven’t already been marked).
(c) Highlight the rows that have assignments in indicated columns (if they haven’t previously been marked).
(d) Continue with (b) and (c) until no further marking is needed.
(f) Simply draw the lines through all rows and columns that are not marked. If the number of these lines equals the order of the matrix, then the solution is optimal; otherwise, it is not.
Step 6 – Find the lowest cost factor that is not covered by the straight lines. Subtract this least-cost component from all the uncovered elements and add it to all the elements that are at the intersection of these straight lines, but leave the rest of the elements alone.
Step 7 – Continue with steps 1 – 6 until you’ve found the highest suitable assignment.
|
---|
Hungarian Method Example
Use the Hungarian method to solve the given assignment problem stated in the table. The entries in the matrix represent each man’s processing time in hours.
\(\begin{array}{l}\begin{bmatrix} & I & II & III & IV & V \\1 & 20 & 15 & 18 & 20 & 25 \\2 & 18 & 20 & 12 & 14 & 15 \\3 & 21 & 23 & 25 & 27 & 25 \\4 & 17 & 18 & 21 & 23 & 20 \\5 & 18 & 18 & 16 & 19 & 20 \\\end{bmatrix}\end{array} \)
With 5 jobs and 5 men, the stated problem is balanced.
\(\begin{array}{l}A = \begin{bmatrix}20 & 15 & 18 & 20 & 25 \\18 & 20 & 12 & 14 & 15 \\21 & 23 & 25 & 27 & 25 \\17 & 18 & 21 & 23 & 20 \\18 & 18 & 16 & 19 & 20 \\\end{bmatrix}\end{array} \)
Subtract the lowest cost element in each row from all of the elements in the given cost matrix’s row. Make sure that each row has at least one zero.
\(\begin{array}{l}A = \begin{bmatrix}5 & 0 & 3 & 5 & 10 \\6 & 8 & 0 & 2 & 3 \\0 & 2 & 4 & 6 & 4 \\0 & 1 & 4 & 6 & 3 \\2 & 2 & 0 & 3 & 4 \\\end{bmatrix}\end{array} \)
Subtract the least cost element in each Column from all of the components in the given cost matrix’s Column. Check to see if each column has at least one zero.
\(\begin{array}{l}A = \begin{bmatrix}5 & 0 & 3 & 3 & 7 \\6 & 8 & 0 & 0 & 0 \\0 & 2 & 4 & 4 & 1 \\0 & 1 & 4 & 4 & 0 \\2 & 2 & 0 & 1 & 1 \\\end{bmatrix}\end{array} \)
When the zeros are assigned, we get the following:
The present assignment is optimal because each row and column contain precisely one encircled zero.
Where 1 to II, 2 to IV, 3 to I, 4 to V, and 5 to III are the best assignments.
Hence, z = 15 + 14 + 21 + 20 + 16 = 86 hours is the optimal time.
Practice Question on Hungarian Method
Use the Hungarian method to solve the following assignment problem shown in table. The matrix entries represent the time it takes for each job to be processed by each machine in hours.
\(\begin{array}{l}\begin{bmatrix}J/M & I & II & III & IV & V \\1 & 9 & 22 & 58 & 11 & 19 \\2 & 43 & 78 & 72 & 50 & 63 \\3 & 41 & 28 & 91 & 37 & 45 \\4 & 74 & 42 & 27 & 49 & 39 \\5 & 36 & 11 & 57 & 22 & 25 \\\end{bmatrix}\end{array} \)
Stay tuned to BYJU’S – The Learning App and download the app to explore all Maths-related topics.
Frequently Asked Questions on Hungarian Method
What is hungarian method.
The Hungarian method is defined as a combinatorial optimization technique that solves the assignment problems in polynomial time and foreshadowed subsequent primal–dual approaches.
What are the steps involved in Hungarian method?
The following is a quick overview of the Hungarian method: Step 1: Subtract the row minima. Step 2: Subtract the column minimums. Step 3: Use a limited number of lines to cover all zeros. Step 4: Add some more zeros to the equation.
What is the purpose of the Hungarian method?
When workers are assigned to certain activities based on cost, the Hungarian method is beneficial for identifying minimum costs.
MATHS Related Links | |
Leave a Comment Cancel reply
Your Mobile number and Email id will not be published. Required fields are marked *
Request OTP on Voice Call
Post My Comment
Register with BYJU'S & Download Free PDFs
Register with byju's & watch live videos.
The Hungarian Method for the Assignment Problem
- First Online: 01 January 2009
Cite this chapter
- Harold W. Kuhn 9
10k Accesses
187 Citations
11 Altmetric
This paper has always been one of my favorite “children,” combining as it does elements of the duality of linear programming and combinatorial tools from graph theory. It may be of some interest to tell the story of its origin.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Subscribe and save.
- Get 10 units per month
- Download Article/Chapter or eBook
- 1 Unit = 1 Article or 1 Chapter
- Cancel anytime
- Available as PDF
- Read on any device
- Instant download
- Own it forever
- Compact, lightweight edition
- Dispatched in 3 to 5 business days
- Free shipping worldwide - see info
Tax calculation will be finalised at checkout
Purchases are for personal use only
Institutional subscriptions
Unable to display preview. Download preview PDF.
Similar content being viewed by others
On weighted means and their inequalities
Constrained Variational Optimization
The Alternating Least-Squares Algorithm for CDPCA
H.W. Kuhn, On the origin of the Hungarian Method , History of mathematical programming; a collection of personal reminiscences (J.K. Lenstra, A.H.G. Rinnooy Kan, and A. Schrijver, eds.), North Holland, Amsterdam, 1991, pp. 77–81.
Google Scholar
A. Schrijver, Combinatorial optimization: polyhedra and efficiency , Vol. A. Paths, Flows, Matchings, Springer, Berlin, 2003.
MATH Google Scholar
Download references
Author information
Authors and affiliations.
Princeton University, Princeton, USA
Harold W. Kuhn
You can also search for this author in PubMed Google Scholar
Corresponding author
Correspondence to Harold W. Kuhn .
Editor information
Editors and affiliations.
Inst. Informatik, Universität Köln, Pohligstr. 1, Köln, 50969, Germany
Michael Jünger
Fac. Sciences de Base (FSB), Ecole Polytechnique Fédérale de Lausanne, Lausanne, 1015, Switzerland
Thomas M. Liebling
Ensimag, Institut Polytechnique de Grenoble, avenue Félix Viallet 46, Grenoble CX 1, 38031, France
Denis Naddef
School of Industrial &, Georgia Institute of Technology, Ferst Drive NW., 765, Atlanta, 30332-0205, USA
George L. Nemhauser
IBM Corporation, Route 100 294, Somers, 10589, USA
William R. Pulleyblank
Inst. Informatik, Universität Heidelberg, Im Neuenheimer Feld 326, Heidelberg, 69120, Germany
Gerhard Reinelt
ed Informatica, CNR - Ist. Analisi dei Sistemi, Viale Manzoni 30, Roma, 00185, Italy
Giovanni Rinaldi
Center for Operations Reserach &, Université Catholique de Louvain, voie du Roman Pays 34, Leuven, 1348, Belgium
Laurence A. Wolsey
Rights and permissions
Reprints and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this chapter
Kuhn, H.W. (2010). The Hungarian Method for the Assignment Problem. In: Jünger, M., et al. 50 Years of Integer Programming 1958-2008. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68279-0_2
Download citation
DOI : https://doi.org/10.1007/978-3-540-68279-0_2
Published : 06 November 2009
Publisher Name : Springer, Berlin, Heidelberg
Print ISBN : 978-3-540-68274-5
Online ISBN : 978-3-540-68279-0
eBook Packages : Mathematics and Statistics Mathematics and Statistics (R0)
Share this chapter
Anyone you share the following link with will be able to read this content:
Sorry, a shareable link is not currently available for this article.
Provided by the Springer Nature SharedIt content-sharing initiative
- Publish with us
Policies and ethics
- Find a journal
- Track your research
- Practice Mathematical Algorithm
- Mathematical Algorithms
- Pythagorean Triplet
- Fibonacci Number
- Euclidean Algorithm
- LCM of Array
- GCD of Array
- Binomial Coefficient
- Catalan Numbers
- Sieve of Eratosthenes
- Euler Totient Function
- Modular Exponentiation
- Modular Multiplicative Inverse
- Stein's Algorithm
- Juggler Sequence
- Chinese Remainder Theorem
- Quiz on Fibonacci Numbers
Hungarian Algorithm for Assignment Problem | Set 2 (Implementation)
Given a 2D array , arr of size N*N where arr[i][j] denotes the cost to complete the j th job by the i th worker. Any worker can be assigned to perform any job. The task is to assign the jobs such that exactly one worker can perform exactly one job in such a way that the total cost of the assignment is minimized.
Input: arr[][] = {{3, 5}, {10, 1}} Output: 4 Explanation: The optimal assignment is to assign job 1 to the 1st worker, job 2 to the 2nd worker. Hence, the optimal cost is 3 + 1 = 4. Input: arr[][] = {{2500, 4000, 3500}, {4000, 6000, 3500}, {2000, 4000, 2500}} Output: 4 Explanation: The optimal assignment is to assign job 2 to the 1st worker, job 3 to the 2nd worker and job 1 to the 3rd worker. Hence, the optimal cost is 4000 + 3500 + 2000 = 9500.
Different approaches to solve this problem are discussed in this article .
Approach: The idea is to use the Hungarian Algorithm to solve this problem. The algorithm is as follows:
- For each row of the matrix, find the smallest element and subtract it from every element in its row.
- Repeat the step 1 for all columns.
- Cover all zeros in the matrix using the minimum number of horizontal and vertical lines.
- Test for Optimality : If the minimum number of covering lines is N , an optimal assignment is possible. Else if lines are lesser than N , an optimal assignment is not found and must proceed to step 5.
- Determine the smallest entry not covered by any line. Subtract this entry from each uncovered row, and then add it to each covered column. Return to step 3.
Consider an example to understand the approach:
Let the 2D array be: 2500 4000 3500 4000 6000 3500 2000 4000 2500 Step 1: Subtract minimum of every row. 2500, 3500 and 2000 are subtracted from rows 1, 2 and 3 respectively. 0 1500 1000 500 2500 0 0 2000 500 Step 2: Subtract minimum of every column. 0, 1500 and 0 are subtracted from columns 1, 2 and 3 respectively. 0 0 1000 500 1000 0 0 500 500 Step 3: Cover all zeroes with minimum number of horizontal and vertical lines. Step 4: Since we need 3 lines to cover all zeroes, the optimal assignment is found. 2500 4000 3500 4000 6000 3500 2000 4000 2500 So the optimal cost is 4000 + 3500 + 2000 = 9500
For implementing the above algorithm, the idea is to use the max_cost_assignment() function defined in the dlib library . This function is an implementation of the Hungarian algorithm (also known as the Kuhn-Munkres algorithm) which runs in O(N 3 ) time. It solves the optimal assignment problem.
Below is the implementation of the above approach:
Time Complexity: O(N 3 ) Auxiliary Space: O(N 2 )
Please Login to comment...
Similar reads.
- Mathematical
- 105 Funny Things to Do to Make Someone Laugh
- Best PS5 SSDs in 2024: Top Picks for Expanding Your Storage
- Best Nintendo Switch Controllers in 2024
- Xbox Game Pass Ultimate: Features, Benefits, and Pricing in 2024
- #geekstreak2024 – 21 Days POTD Challenge Powered By Deutsche Bank
Improve your Coding Skills with Practice
What kind of Experience do you want to share?
Index Assignment problem Hungarian algorithm Solve online
Solve an assignment problem online
Fill in the cost matrix of an assignment problem and click on 'Solve'. The optimal assignment will be determined and a step by step explanation of the hungarian algorithm will be given.
Fill in the cost matrix ( random cost matrix ):
Don't show the steps of the Hungarian algorithm Maximize the total cost
HungarianAlgorithm.com © 2013-2024
Quantitative Techniques: Theory and Problems by P. C. Tulsian, Vishal Pandey
Get full access to Quantitative Techniques: Theory and Problems and 60K+ other titles, with a free 10-day trial of O'Reilly.
There are also live events, courses curated by job role, and more.
HUNGARIAN METHOD
Although an assignment problem can be formulated as a linear programming problem, it is solved by a special method known as Hungarian Method because of its special structure. If the time of completion or the costs corresponding to every assignment is written down in a matrix form, it is referred to as a Cost matrix. The Hungarian Method is based on the principle that if a constant is added to every element of a row and/or a column of cost matrix, the optimum solution of the resulting assignment problem is the same as the original problem and vice versa. The original cost matrix can be reduced to another cost matrix by adding constants to the elements of rows and columns where the total cost or the total completion time of an ...
Get Quantitative Techniques: Theory and Problems now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.
Don’t leave empty-handed
Get Mark Richards’s Software Architecture Patterns ebook to better understand how to design components—and how they should interact.
It’s yours, free.
Check it out now on O’Reilly
Dive in for free with a 10-day trial of the O’Reilly learning platform—then explore all the other resources our members count on to build skills and solve problems every day.
Assignment Problem: Maximization
There are problems where certain facilities have to be assigned to a number of jobs, so as to maximize the overall performance of the assignment.
The Hungarian Method can also solve such assignment problems , as it is easy to obtain an equivalent minimization problem by converting every number in the matrix to an opportunity loss.
The conversion is accomplished by subtracting all the elements of the given matrix from the highest element. It turns out that minimizing opportunity loss produces the same assignment solution as the original maximization problem.
- Unbalanced Assignment Problem
- Multiple Optimal Solutions
Example: Maximization In An Assignment Problem
At the head office of www.universalteacherpublications.com there are five registration counters. Five persons are available for service.
Person | |||||
---|---|---|---|---|---|
Counter | A | B | C | D | E |
1 | 30 | 37 | 40 | 28 | 40 |
2 | 40 | 24 | 27 | 21 | 36 |
3 | 40 | 32 | 33 | 30 | 35 |
4 | 25 | 38 | 40 | 36 | 36 |
5 | 29 | 62 | 41 | 34 | 39 |
How should the counters be assigned to persons so as to maximize the profit ?
Here, the highest value is 62. So we subtract each value from 62. The conversion is shown in the following table.
On small screens, scroll horizontally to view full calculation
Person | |||||
---|---|---|---|---|---|
Counter | A | B | C | D | E |
1 | 32 | 25 | 22 | 34 | 22 |
2 | 22 | 38 | 35 | 41 | 26 |
3 | 22 | 30 | 29 | 32 | 27 |
4 | 37 | 24 | 22 | 26 | 26 |
5 | 33 | 0 | 21 | 28 | 23 |
Now the above problem can be easily solved by Hungarian method . After applying steps 1 to 3 of the Hungarian method, we get the following matrix.
Person | |||||
---|---|---|---|---|---|
Counter | A | B | C | D | E |
1 | 10 | 3 | 8 | ||
2 | 16 | 13 | 15 | 4 | |
3 | 8 | 7 | 6 | 5 | |
4 | 15 | 2 | 4 | ||
5 | 33 | 21 | 24 | 23 |
Draw the minimum number of vertical and horizontal lines necessary to cover all the zeros in the reduced matrix.
Select the smallest element from all the uncovered elements, i.e., 4. Subtract this element from all the uncovered elements and add it to the elements, which lie at the intersection of two lines. Thus, we obtain another reduced matrix for fresh assignment. Repeating step 3, we obtain a solution which is shown in the following table.
Final Table: Maximization Problem
Use Horizontal Scrollbar to View Full Table Calculation
Person | |||||
---|---|---|---|---|---|
Counter | A | B | C | D | E |
1 | 14 | 3 | 8 | ||
2 | 12 | 9 | 11 | ||
3 | 4 | 3 | 2 | 1 | |
4 | 19 | 2 | 4 | ||
5 | 37 | 21 | 24 | 23 |
The total cost of assignment = 1C + 2E + 3A + 4D + 5B
Substituting values from original table: 40 + 36 + 40 + 36 + 62 = 214.
Share This Article
Operations Research Simplified Back Next
Goal programming Linear programming Simplex Method Transportation Problem
IMAGES
VIDEO
COMMENTS
The Hungarian method is a computational optimization technique that addresses the assignment problem in polynomial time and foreshadows following primal-dual alternatives. In 1955, Harold Kuhn used the term "Hungarian method" to honour two Hungarian mathematicians, Dénes Kőnig and Jenő Egerváry. Let's go through the steps of the Hungarian method with the help of a solved example.
The Hungarian algorithm, aka Munkres assignment algorithm, utilizes the following theorem for polynomial runtime complexity (worst case O(n 3)) and guaranteed optimality: If a number is added to or subtracted from all of the entries of any one row or column of a cost matrix, then an optimal assignment for the resulting cost matrix is also an ...
The Hungarian method is a combinatorial optimization algorithm that solves the assignment problem in polynomial time and which anticipated later primal-dual methods.It was developed and published in 1955 by Harold Kuhn, who gave it the name "Hungarian method" because the algorithm was largely based on the earlier works of two Hungarian mathematicians, Dénes Kőnig and Jenő Egerváry.
Hungarian method for assignment problem Step 1. Subtract the entries of each row by the row minimum. Step 2. Subtract the entries of each column by the column minimum. Step 3. Make an assignment to the zero entries in the resulting matrix. A = M 17 10 15 17 18 M 6 10 20 12 5 M 14 19 12 11 15 M 7 16 21 18 6 M −10
Example 1: Hungarian Method. The Funny Toys Company has four men available for work on four separate jobs. Only one man can work on any one job. The cost of assigning each man to each job is given in the following table. The objective is to assign men to jobs in such a way that the total cost of assignment is minimum. Job.
The Hungarian algorithm: An example. We consider an example where four jobs (J1, J2, J3, and J4) need to be executed by four workers (W1, W2, W3, and W4), one job per worker. The matrix below shows the cost of assigning a certain worker to a certain job. The objective is to minimize the total cost of the assignment.
In this lesson we learn what is an assignment problem and how we can solve it using the Hungarian method.
1. INTRODUCTION The Hungarian Method [ 11 is an algorithm for solving assignment problems that is based on the work of D. Konig and J. Egervgry. In one possible interpretation, an assignment problem asks for the best assignment of a set of persons to a set of jobs, where the feasible assignments are ranked by the total scores or ratings of the ...
The Hungarian method is a combinatorial optimization algorithm which solves the assignment problem in polynomial time . Later it was discovered that it was a primal-dual Simplex method.. It was developed and published by Harold Kuhn in 1955, who gave the name "Hungarian method" because the algorithm was largely based on the earlier works of two Hungarian mathematicians: Denes Konig and Jeno ...
The assignment problem deals with assigning machines to tasks, workers to jobs, soccer players to positions, and so on. The goal is to determine the optimum assignment that, for example, minimizes the total cost or maximizes the team effectiveness. The assignment problem is a fundamental problem in the area of combinatorial optimization.
84. THE HUNGARIAN METHOD FOR THE ASSIGNMENT PROBLEM. 1, 2, and 3. 3 and 4. This information can be presented effectively by a qualification matrix. in which horizontal rows stand for individuals and vertical columns for jobs; a qualified individ- ual is marked by a 1 and an unqualified individual by a 0.
The Hungarian Method for the Assignment Problem. Chapter; First Online: 01 January 2009; pp 29-47; Cite this chapter; Download book PDF. 50 Years of Integer Programming 1958-2008. The Hungarian Method for the Assignment Problem Download book PDF.
the general assignment problem to a 0-1 problem. Thus, by putting the two ideas together, the Hungarian Method was born. I tested the algorithm by solving 12 by 12 problems with random 3-digit ratings by hand. I could do any such problem, with pencil and paper, in no more than 2 hours. This seemed to be much better than any other method known ...
For implementing the above algorithm, the idea is to use the max_cost_assignment() function defined in the dlib library. This function is an implementation of the Hungarian algorithm (also known as the Kuhn-Munkres algorithm) which runs in O(N 3) time. It solves the optimal assignment problem. Below is the implementation of the above approach:
The assignment problem is a special case of the transportation problem, which in turn is a special case of the min-cost flow problem, so it can be solved using algorithms that solve the more general cases. Also, our problem is a special case of binary integer linear programming problem (which is NP-hard). But, due to the specifics of the ...
Solve an assignment problem online. Fill in the cost matrix of an assignment problem and click on 'Solve'. The optimal assignment will be determined and a step by step explanation of the hungarian algorithm will be given. Fill in the cost matrix ():
The Hungarian method, also known as the Kuhn-Munkres algorithm, is a computational technique used to solve the assignment problem in polynomial time.It's a precursor to many primal-dual methods used today. The method was named in honor of Hungarian mathematicians Dénes Kőnig and Jenő Egerváry by Harold Kuhn in 1955.
HUNGARIAN METHOD. Although an assignment problem can be formulated as a linear programming problem, it is solved by a special method known as Hungarian Method because of its special structure. If the time of completion or the costs corresponding to every assignment is written down in a matrix form, it is referred to as a Cost matrix. The Hungarian Method is based on the principle that if a ...
📒⏩Comment Below If This Video Helped You 💯Like 👍 & Share With Your Classmates - ALL THE BEST 🔥Do Visit My Second Channel - https://bit.ly/3rMGcSAThis vi...
Step 3. Draw lines through appropriate rows and columns so that all the zero entries of the cost matrix are covered and the minimum number of such lines is used. Step 4. Test for Optimality: (i) If the minimum number of covering lines is n, an optimal assignment of zeros is possible and we are finished.
To use the Hungarian Algorithm, we first arrange the activities and people in a matrix with rows being people, columns being activity, and entries being the costs. Once we've done this, we make ...
The Hungarian Method can also solve such assignment problems, as it is easy to obtain an equivalent minimization problem by converting every number in the matrix to an opportunity loss. The conversion is accomplished by subtracting all the elements of the given matrix from the highest element. It turns out that minimizing opportunity loss ...
📒⏩Comment Below If This Video Helped You 💯Like 👍 & Share With Your Classmates - ALL THE BEST 🔥Do Visit My Second Channel - https://bit.ly/3rMGcSAThis vi...