Write a program to find the nth Fibonacci number using dynamic programming.

Here is a program in Python that finds the n th F ib on acci number using dynamic programming : \n ``` \n def fib on acci ( n ): \n # base case : if n is 0 or 1 , return 0 and 1 \n if n == 0 : \n return 0 \n if n == 1 : \n return 1 \n \n # initialize two variables to store the previous two numbers \n # and their indices in the sequence \n prev 1 , prev 2 = 0 , 1 \n \n # loop through the remaining numbers in the sequence \n for i in range ( 2 , n ): \n # calculate the current number \n curr = prev 1 + prev 2 \n \n # update the previous two numbers and their indices \n prev 1 , prev 2 = curr , i \n \n # return the n th number in the sequence \n return prev 2 \n \n # test the function with some values \n print ( f ib on acci ( 0 )) # should print 0 \n print ( f ib on acci ( 1 )) # should print 1 \n print ( f ib on acci ( 5 )) # should print 8 \n ``` \n This program uses a loop to calculate the n th F ib on acci number by keeping track of the previous two numbers in the sequence and their indices . At each step , it calcul ates the current number as the sum of the previous two numbers and updates the previous two numbers and their indices . The loop continues until it reaches the desired index ` n `. Finally , the program returns the n th number in the sequence . </s>