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Yоu аre gоing оn а roаd trip starting at your hometown and plan to reach the fun city of La Habana. You have a map with the locations of n hotels you can spend the night at, and the price they charge per night. To relax on your trip, you plan to travel no more than 50 miles between stops. Design a dynamic programming algorithm to find the cheapest way to reach your destination. Concretely, you are given inputs D[1,...,n], an array of natural numbers representing the distance of each hotel from the origin (your hometown) as imagined along a straight line, and P[1,...,n], where P[i] is a positive integer representing the cost of staying at the hotel located at D[i]. All hotels are no more than 50 miles apart. That is, you can always go from D[i] to D[i+1]. La Habana is at location D[n]. P[n] represents the cost of staying at La Habana which must be paid. You need to output the minimum cost you must pay to get to and stay at La Habana. You do not need to output the hotels you would rest at, just the minimum cost you would pay. Example: D=[20, 40, 70, 80], P=[3, 6, 1, 2]. You should output 6=3+1+2 after resting at hotels located at distance 20, 70, and reaching La Habana (located 80 miles from your hometown for this input). Note that you can go to the second hotel (at distance 40 from your hometown) and then directly to La Habana, but that means paying more, 8=6+2. You cannot go directly from your hometown to the hotel located 70 miles away because of the constraint of traveling no more than 50 miles between stops. Please answer the following parts: 1. Define the entries of your table in words. E.g. T(i) or T(i, j) is ...2. State a recurrence for the entries of your table in terms of smaller subproblems. Don't forget your base case(s).3. Write pseudocode for your algorithm to solve this problem.4. State and analyze the running time of your algorithm. A solution that runs in time is sufficient for full credit.