Write a python program using the TensorFlow package to implement backtracking line search with Armijo condition to find an appropriate step-size ?k in the k-th iteration of the steepest descent algorithm. Apply your implementation to minimize the Rosenbrock function and benchmark the required number of iterations to converge to the minimum (within 10^(?6) toler- ance) against the built-in method GradientDescentOptimizer() with constant learning rate 0.001.