Please help with the program below. Need to write a program called dfs-stack.py in python that uses the algorithm below without an agency list but instead uses an adjacency matrix. The program should prompt the user for the number of vertices V, in the graph.Please read the directions below I will post a picture of the instructions and the algorithm. Algorithm 2.3: Graph depth-first search with a stack.StackDFS (G, node) → visitedInput: G=(V, E), a graph1234node, the starting vertex in GOutput: visited, an array of size |V| such that visited[i] is TRUE if wehave visited node i, FALSE otherwiseS-CreateStack()25 Push (S, node)68visited CreateArray (VI)for i-0 to V| do91011visited[i] FALSEwhile not IsStackEmpty(S) do1-c-Pop (s)visited[c] TRUEforeach in AdjacencyList (G, c) doif not visited[v] thenPush (S.)return visitedadded only if it is not already in the stack. To do this we use an additionalarray. An element of that array will be true if that element is currently in thestack and false otherwise. Algorithm 2.4 is the result. The algorithm is prettymuch the same as algorithm 2.4 but uses the additional array instack, where8+199+fg14410▶11▶▶ins 1. Using Python, you will write a program called dfs-stack.py that implements Algorithm 2.3 (p. 49): Graph depth-first search (DFS) with a stack.2. You will not use an adjacency list, as indicated in Algorithm 2.3. Instead, you will use an adjacency matrix (i.e., a two-dimensional array, or, in Python, a list of lists).3. You may use ANY list method you wish (e.g., append, pop, etc.).IMPLEMENTATION DETAILS:41. Based upon the REQUIREMENTS above, along with the IMPLEMENTATION DETAILS (i.e., this section), you MUST develop a FINAL algorithmic solution using pseudocode.This includes both your logic (in pseudocode) and the logic presented in the pseudocode indicated in Algorithm 2.3.2. Be sure to include your name, along with the Certificate of Authenticity, as comments at the very beginning of your Python code. Also, if you collaborated with others,be sure to state their names as well.3. Your program should begin by prompting the user for the number of vertices, V, in the graph, G.4. Your program will represent the graph G using an adjacency matrix, which is a square matrix with a row and a column for each vertex. Thus, your program will need tocreate a matrix M that consists of a Vx Vtwo-dimensional array -- in Python, a list of lists. (I recommend that your program initialize each element of the matrix equalto zero.)5. Next, your program should prompt the user to indicate which elements in the matrix should be assigned the value of 1 (i.e., information about vertices). Recall thateach element in the matrix is the intersection of a row and a column.6. The result of step 4 should be an adjacency matrix representation of a graph, G.7. At this point, your program should print the newly-created adjacency matrix on the screen.8. Next, your program should prompt the user to specify node -- i.e., the starting vertex in G.9. From here, you then proceed with the implementation of Algorithm 2.3, with the following enhancements:o Be sure to use the newly-created adjacency matrix, instead of an adjacency list.o Immediately following line 5 (but before line 6) of Algorithm 2.3, your program should print the values currently on the stack.o At the end of the while block, your program should print the values currently on the stack.In effect, the result of step 8 above should be a display of the stack evolution for your implementation of the DFS algorithm on graph G.Back to Top

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#It uses a Python dict for easinessgraphDFS = { '1': ['4', '6'], '5': ['1', '9'], '9':…