In this homework, you will implement the Horner's method for applying Newton method on polynomials 1. Get the polynomial from the command line in this order, starting from the highest order get the coefficient and then exponent, if the coefficient is 0 do not enter the coefficient and exponent. The last number is the initial point. The coefficients can be float numbers. For example: 24 -3 2 3 1 -4 0-2 Means: 2x^4 -3x^2 + 3x -4 x0 = -2 2. Continue until the relative error is less than 10^-4 or 10 iterations. 3. Use the knowledge that you have from your data structures class to implement an efficient data structure. 4. Print out the results at each step (Like in the example showed in the class and in book) 5. Check for error in the input and do not process in case of error in the input (for example the number of inputs that the users insert should be odd) In this homework, you will implement the Horner's method for applying Newton method on polynomials 1. Get the polynomial from the command line in this order, starting from the highest order get the coefficient and then exponent, if the coefficient is 0 do not enter the coefficient and exponent. The last number is the initial point. The coefficients can be float numbers. For example: 24 -3 2 3 1 -4 0-2 Means: 2x^4 -3x^2 + 3x -4 x0 = -2 2. Continue until the relative error is less than 10^-4 or 10 iterations. 3. Use the knowledge that you have from your data structures class to implement an efficient data structure. 4. Print out the results at each step (Like in the example showed in the class and in book) 5. Check for error in the input and do not process in case of error in the input (for example the number of inputs that the users insert should be odd)